sphinx.addnodesdocument)}( rawsourcechildren](docutils.nodestarget)}(h.. _MAVRIC:h]
attributes}(ids]classes]names]dupnames]backrefs]refidmavricutagnameh
lineKparenthhhsource0/Users/john/Documents/SCALE-test/docs/MAVRIC.rstubh section)}(hhh](h title)}(hNMAVRIC: Monaco with Automated Variance Reduction using Importance Calculationsh]h TextNMAVRIC: Monaco with Automated Variance Reduction using Importance Calculations}(hh,h h*hhh!NhNubah}(h]h]h]h]h]uhh(h h%hhh!h"hKubh paragraph)}(h*D. E. Peplow and C. Celik*h]h emphasis)}(hh>h]h/D. E. Peplow and C. Celik}(hhh hBubah}(h]h]h]h]h]uhh@h hubh;)}(hXVCADIS is well described in the literature, so only a
brief overview is given here. Consider a class source-detector problem
described by a unit source with emission probability distribution
function :math:`q\left(\overrightarrow{r},E \right)` and a detector
response function :math:`\sigma_{d}\left(\overrightarrow{r},E \right)`.
To determine the total detector response, *R*, the forward scalar flux
:math:`\phi\left(\overrightarrow{r},E \right)` must be known. The
response is found by integrating the product of the detector response
function and the flux over the detector volume :math:`V_{d}`:h](h/CADIS is well described in the literature, so only a
brief overview is given here. Consider a class source-detector problem
described by a unit source with emission probability distribution
function }(hCADIS is well described in the literature, so only a
brief overview is given here. Consider a class source-detector problem
described by a unit source with emission probability distribution
function h jhhh!NhNubh math)}(h+:math:`q\left(\overrightarrow{r},E \right)`h]h/#q\left(\overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/" and a detector
response function }(h" and a detector
response function h jhhh!NhNubj
)}(h4:math:`\sigma_{d}\left(\overrightarrow{r},E \right)`h]h/,\sigma_{d}\left(\overrightarrow{r},E \right)}(hhh j!ubah}(h]h]h]h]h]uhjh jubh/,.
To determine the total detector response, }(h,.
To determine the total detector response, h jhhh!NhNubhA)}(h*R*h]h/R}(hhh j4ubah}(h]h]h]h]h]uhh@h jubh/, the forward scalar flux
}(h, the forward scalar flux
h jhhh!NhNubj
)}(h.:math:`\phi\left(\overrightarrow{r},E \right)`h]h/&\phi\left(\overrightarrow{r},E \right)}(hhh jGubah}(h]h]h]h]h]uhjh jubh/ must be known. The
response is found by integrating the product of the detector response
function and the flux over the detector volume }(h must be known. The
response is found by integrating the product of the detector response
function and the flux over the detector volume h jhhh!NhNubj
)}(h
:math:`V_{d}`h]h/V_{d}}(hhh jZubah}(h]h]h]h]h]uhjh jubh/:}(h:h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hK@h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-1uhh
h jhhh!h"hNubh
math_block)}(hR = \int_{V_{d}}^{}{\int_{E}^{}{\sigma_{d}\left( \overrightarrow{r},E \right)}}\phi\left(\overrightarrow{r},E \right)\textit{dE dV.}h]h/R = \int_{V_{d}}^{}{\int_{E}^{}{\sigma_{d}\left( \overrightarrow{r},E \right)}}\phi\left(\overrightarrow{r},E \right)\textit{dE dV.}}(hhh jubah}(h]j|ah]h]h]h]docnamejnumberKlabelmavric-1nowrap xml:spacepreserveuhj}h!h"hKKh jhhexpect_referenced_by_name}expect_referenced_by_id}j|jssubh;)}(hXAlternatively, if the adjoint scalar flux,
:math:`\phi^{+}\left(\overrightarrow{r},E \right)`, is known from the
corresponding adjoint problem with adjoint source
:math:`q^{+}\left(\overrightarrow{r},E \right) = \sigma_{d}\left(\overrightarrow{r},E \right)`,
then the total detector response could be found by integrating the
product of the forward source and the adjoint flux over the source
volume, :math:`V_{s}`:h](h/+Alternatively, if the adjoint scalar flux,
}(h+Alternatively, if the adjoint scalar flux,
h jhhh!NhNubj
)}(h2:math:`\phi^{+}\left(\overrightarrow{r},E \right)`h]h/*\phi^{+}\left(\overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/F, is known from the
corresponding adjoint problem with adjoint source
}(hF, is known from the
corresponding adjoint problem with adjoint source
h jhhh!NhNubj
)}(h^:math:`q^{+}\left(\overrightarrow{r},E \right) = \sigma_{d}\left(\overrightarrow{r},E \right)`h]h/Vq^{+}\left(\overrightarrow{r},E \right) = \sigma_{d}\left(\overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/,
then the total detector response could be found by integrating the
product of the forward source and the adjoint flux over the source
volume, }(h,
then the total detector response could be found by integrating the
product of the forward source and the adjoint flux over the source
volume, h jhhh!NhNubj
)}(h
:math:`V_{s}`h]h/V_{s}}(hhh jubah}(h]h]h]h]h]uhjh jubh/:}(hjlh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKQh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-2uhh
h jhhh!h"hNubj~)}(hR = \int_{V_{s}}^{}{\int_{E}^{}{q\left(\overrightarrow{r},E \right)}}\phi^{+}\left( \overrightarrow{r},E \right)\textit{dE dV.}h]h/R = \int_{V_{s}}^{}{\int_{E}^{}{q\left(\overrightarrow{r},E \right)}}\phi^{+}\left( \overrightarrow{r},E \right)\textit{dE dV.}}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabelmavric-2nowrapjjuhj}h!h"hKZh jhhj}j}jjsubh;)}(hXUnfortunately, the exact adjoint flux may be just as difficult to
determine as the forward flux, but an approximation of the adjoint flux
can still be used to form an importance map and a biased source
distribution for use in the forward Monte Carlo calculation.h]h/XUnfortunately, the exact adjoint flux may be just as difficult to
determine as the forward flux, but an approximation of the adjoint flux
can still be used to form an importance map and a biased source
distribution for use in the forward Monte Carlo calculation.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hK_h jhhubh;)}(hXkWagner :cite:`wagner_acceleration_1997` showed that if an estimate of the adjoint scalar flux
for the corresponding adjoint problem can be found, then an estimate
of the response *R* can be made using :eq:`mavric-2`. The adjoint source for the
adjoint problem is typically separable and corresponds to the detector
response and spatial area of the tally to be optimized:
:math:`q^{+}\left(\overrightarrow{r},E \right) = \sigma_{d}\left(E \right)g\left( \overrightarrow{r} \right)`,
where :math:`\sigma_{d}\left( E \right)` is a flux-to-dose conversion
factor and :math:`g\left( \overrightarrow{r} \right)` is 1 in the tally
volume and is 0 otherwise. Then, from the adjoint flux
:math:`\phi^{+}\left( \overrightarrow{r},E \right)` and response
estimate *R*, a biased source distribution,
:math:`\widehat{q}\left( \overrightarrow{r},E \right)`, for source
sampling of the formh](h/Wagner }(hWagner h jhhh!NhNubhp)}(hwagner_acceleration_1997h]hv)}(hjh]h/[wagner_acceleration_1997]}(hhh jubah}(h]h]h]h]h]uhhuh jubah}(h]id8ah]hah]h]h] refdomainhreftypeh reftargetjrefwarnsupport_smartquotesuhhoh!h"hKdh jhhubh/ showed that if an estimate of the adjoint scalar flux
for the corresponding adjoint problem can be found, then an estimate
of the response }(h showed that if an estimate of the adjoint scalar flux
for the corresponding adjoint problem can be found, then an estimate
of the response h jhhh!NhNubhA)}(h*R*h]h/R}(hhh j7ubah}(h]h]h]h]h]uhh@h jubh/ can be made using }(h can be made using h jhhh!NhNubhp)}(h:eq:`mavric-2`h]h literal)}(hjLh]h/mavric-2}(hhh jPubah}(h]h](jeqeh]h]h]uhjNh jJubah}(h]h]h]h]h]refdocj refdomainjreftypejZrefexplicitrefwarnjmavric-2uhhoh!h"hKdh jubh/. The adjoint source for the
adjoint problem is typically separable and corresponds to the detector
response and spatial area of the tally to be optimized:
}(h. The adjoint source for the
adjoint problem is typically separable and corresponds to the detector
response and spatial area of the tally to be optimized:
h jhhh!NhNubj
)}(hm:math:`q^{+}\left(\overrightarrow{r},E \right) = \sigma_{d}\left(E \right)g\left( \overrightarrow{r} \right)`h]h/eq^{+}\left(\overrightarrow{r},E \right) = \sigma_{d}\left(E \right)g\left( \overrightarrow{r} \right)}(hhh joubah}(h]h]h]h]h]uhjh jubh/,
where }(h,
where h jhhh!NhNubj
)}(h":math:`\sigma_{d}\left( E \right)`h]h/\sigma_{d}\left( E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/) is a flux-to-dose conversion
factor and }(h) is a flux-to-dose conversion
factor and h jhhh!NhNubj
)}(h*:math:`g\left( \overrightarrow{r} \right)`h]h/"g\left( \overrightarrow{r} \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/J is 1 in the tally
volume and is 0 otherwise. Then, from the adjoint flux
}(hJ is 1 in the tally
volume and is 0 otherwise. Then, from the adjoint flux
h jhhh!NhNubj
)}(h3:math:`\phi^{+}\left( \overrightarrow{r},E \right)`h]h/+\phi^{+}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/ and response
estimate }(h and response
estimate h jhhh!NhNubhA)}(h*R*h]h/R}(hhh jubah}(h]h]h]h]h]uhh@h jubh/ , a biased source distribution,
}(h , a biased source distribution,
h jhhh!NhNubj
)}(h6:math:`\widehat{q}\left( \overrightarrow{r},E \right)`h]h/.\widehat{q}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/!, for source
sampling of the form}(h!, for source
sampling of the formh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKdh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-3uhh
h jhhh!h"hNubj~)}(h\widehat{q}\left(\overrightarrow{r},E \right) = \frac{1}{R}q\left(\overrightarrow{r},E\right)\phi^{+}\left( \overrightarrow{r},E \right)h]h/\widehat{q}\left(\overrightarrow{r},E \right) = \frac{1}{R}q\left(\overrightarrow{r},E\right)\phi^{+}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabelmavric-3nowrapjjuhj}h!h"hKsh jhhj}j}jjsubh;)}(h|and weight window target values,
:math:`\overline{w}\left( \overrightarrow{r},E \right)`, for particle
transport of the formh](h/!and weight window target values,
}(h!and weight window target values,
h jhhh!NhNubj
)}(h7:math:`\overline{w}\left( \overrightarrow{r},E \right)`h]h//\overline{w}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/$, for particle
transport of the form}(h$, for particle
transport of the formh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKyh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-4uhh
h jhhh!h"hNubj~)}(hg\overline{w}\left( \overrightarrow{r},E \right) = \frac{R}{\phi^{+}\left( \overrightarrow{r},E \right)}h]h/g\overline{w}\left( \overrightarrow{r},E \right) = \frac{R}{\phi^{+}\left( \overrightarrow{r},E \right)}}(hhh j2ubah}(h]j1ah]h]h]h]docnamejnumberKlabelmavric-4nowrapjjuhj}h!h"hK~h jhhj}j}j1j(subh;)}(h_can be constructed, which minimizes the variance in the forward Monte
Carlo calculation of *R*.h](h/[can be constructed, which minimizes the variance in the forward Monte
Carlo calculation of }(h[can be constructed, which minimizes the variance in the forward Monte
Carlo calculation of h jGhhh!NhNubhA)}(h*R*h]h/R}(hhh jPubah}(h]h]h]h]h]uhh@h jGubh/.}(hjh jGhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh;)}(hWhen a particle is sampled from the biased source distribution
:math:`\widehat{q}\left( \overrightarrow{r},E \right)`, to preserve a
fair game, its initial weight is set toh](h/?When a particle is sampled from the biased source distribution
}(h?When a particle is sampled from the biased source distribution
h jhhhh!NhNubj
)}(h6:math:`\widehat{q}\left( \overrightarrow{r},E \right)`h]h/.\widehat{q}\left( \overrightarrow{r},E \right)}(hhh jqubah}(h]h]h]h]h]uhjh jhubh/7, to preserve a
fair game, its initial weight is set to}(h7, to preserve a
fair game, its initial weight is set toh jhhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-5uhh
h jhhh!h"hNubj~)}(hw_{0}\left(\overrightarrow{r},E \right) = \frac{q\left(\overrightarrow{r},E \right)}{\widehat{q}\left( \overrightarrow{r},E \right)} = \frac{R}{\phi^{+}\left( \overrightarrow{r},E \right)}\,h]h/w_{0}\left(\overrightarrow{r},E \right) = \frac{q\left(\overrightarrow{r},E \right)}{\widehat{q}\left( \overrightarrow{r},E \right)} = \frac{R}{\phi^{+}\left( \overrightarrow{r},E \right)}\,}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabelmavric-5nowrapjjuhj}h!h"hKh jhhj}j}jjsubh;)}(hX*which exactly matches the target weight for that particle’s position and
energy. This is the “consistent” part of CADIS—source particles are born
with a weight matching the weight window of the region/energy into which they are
born. The source biasing and the weight windows work together.h]h/X*which exactly matches the target weight for that particle’s position and
energy. This is the “consistent” part of CADIS—source particles are born
with a weight matching the weight window of the region/energy into which they are
born. The source biasing and the weight windows work together.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hKh jhhubh;)}(hXCADIS has been applied to many problems—including reactor ex-core
detectors, well-logging instruments, cask shielding studies, and
independent spent fuel storage facility models—and has demonstrated very
significant speed-ups in calculation time compared to analog
simulations.h]h/XCADIS has been applied to many problems—including reactor ex-core
detectors, well-logging instruments, cask shielding studies, and
independent spent fuel storage facility models—and has demonstrated very
significant speed-ups in calculation time compared to analog
simulations.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hKh jhhubeh}(h]overview-of-cadisah]h]overview of cadisah]h]uhh#h jhhh!h"hK>ubh$)}(hhh](h))}(hMultiple sources with CADISh]h/Multiple sources with CADIS}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hKubh;)}(hXFor a typical Monte Carlo calculation with multiple sources---each with a
probability distribution function
:math:`q_{i}\left( \overrightarrow{r},E \right)` and a strength
:math:`S_{i}`, giving a total source strength of
:math:`S = \sum_{}^{}S_{i}`---the source is sampled in two steps. First,
the specific source *i* is sampled with probability
:math:`p\left( i \right) = \ S_{i}/S`, and then the particle is sampled
from the specific source distribution
:math:`q_{i}\left( \overrightarrow{r},E \right)`.h](h/lFor a typical Monte Carlo calculation with multiple sources—each with a
probability distribution function
}(hlFor a typical Monte Carlo calculation with multiple sources---each with a
probability distribution function
h jhhh!NhNubj
)}(h0:math:`q_{i}\left( \overrightarrow{r},E \right)`h]h/(q_{i}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/ and a strength
}(h and a strength
h jhhh!NhNubj
)}(h
:math:`S_{i}`h]h/S_{i}}(hhh jubah}(h]h]h]h]h]uhjh jubh/$, giving a total source strength of
}(h$, giving a total source strength of
h jhhh!NhNubj
)}(h:math:`S = \sum_{}^{}S_{i}`h]h/S = \sum_{}^{}S_{i}}(hhh j
ubah}(h]h]h]h]h]uhjh jubh/B—the source is sampled in two steps. First,
the specific source }(hB---the source is sampled in two steps. First,
the specific source h jhhh!NhNubhA)}(h*i*h]h/i}(hhh j ubah}(h]h]h]h]h]uhh@h jubh/ is sampled with probability
}(h is sampled with probability
h jhhh!NhNubj
)}(h%:math:`p\left( i \right) = \ S_{i}/S`h]h/p\left( i \right) = \ S_{i}/S}(hhh j3ubah}(h]h]h]h]h]uhjh jubh/I, and then the particle is sampled
from the specific source distribution
}(hI, and then the particle is sampled
from the specific source distribution
h jhhh!NhNubj
)}(h0:math:`q_{i}\left( \overrightarrow{r},E \right)`h]h/(q_{i}\left( \overrightarrow{r},E \right)}(hhh jFubah}(h]h]h]h]h]uhjh jubh/.}(hjh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh;)}(hXThe source sampling can be biased at both levels: from which source to sample
and how to sample each source. For example, the specific source can
be sampled using some arbitrary distribution,
:math:`\widehat{p}\left( i \right)`, and then the individual sources can
be sampled using distributions
:math:`{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)`. Particles
would then have a birth weight ofh](h/The source sampling can be biased at both levels: from which source to sample
and how to sample each source. For example, the specific source can
be sampled using some arbitrary distribution,
}(hThe source sampling can be biased at both levels: from which source to sample
and how to sample each source. For example, the specific source can
be sampled using some arbitrary distribution,
h j^hhh!NhNubj
)}(h#:math:`\widehat{p}\left( i \right)`h]h/\widehat{p}\left( i \right)}(hhh jgubah}(h]h]h]h]h]uhjh j^ubh/E, and then the individual sources can
be sampled using distributions
}(hE, and then the individual sources can
be sampled using distributions
h j^hhh!NhNubj
)}(h<:math:`{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)`h]h/4{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)}(hhh jzubah}(h]h]h]h]h]uhjh j^ubh/-. Particles
would then have a birth weight of}(h-. Particles
would then have a birth weight ofh j^hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-6uhh
h jhhh!h"hNubj~)}(hw_{0} \equiv \ \left(\frac{p\left( i \right)}{\widehat{p}\left( i \right)} \right)\left(\frac{q_{i}\left( \overrightarrow{r},E \right)}{{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)} \right)\text{.}h]h/w_{0} \equiv \ \left(\frac{p\left( i \right)}{\widehat{p}\left( i \right)} \right)\left(\frac{q_{i}\left( \overrightarrow{r},E \right)}{{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)} \right)\text{.}}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabelmavric-6nowrapjjuhj}h!h"hKh jhhj}j}jjsubh;)}(hXFor CADIS, a biased multiple source needs to be developed so that the
birth weights of sampled particles still match the target weights of the
importance map. For a problem with multiple sources---each with a
distribution :math:`q_{i}\left( \overrightarrow{r},E \right)` and a
strength :math:`S_{i}`---the goal of the Monte Carlo calculation is to
compute some response :math:`R` for a response function
:math:`\sigma_{d}\left( \overrightarrow{r},E \right)` at a given
detector,h](h/For CADIS, a biased multiple source needs to be developed so that the
birth weights of sampled particles still match the target weights of the
importance map. For a problem with multiple sources—each with a
distribution }(hFor CADIS, a biased multiple source needs to be developed so that the
birth weights of sampled particles still match the target weights of the
importance map. For a problem with multiple sources---each with a
distribution h jhhh!NhNubj
)}(h0:math:`q_{i}\left( \overrightarrow{r},E \right)`h]h/(q_{i}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/ and a
strength }(h and a
strength h jhhh!NhNubj
)}(h
:math:`S_{i}`h]h/S_{i}}(hhh jubah}(h]h]h]h]h]uhjh jubh/G—the goal of the Monte Carlo calculation is to
compute some response }(hG---the goal of the Monte Carlo calculation is to
compute some response h jhhh!NhNubj
)}(h :math:`R`h]h/R}(hhh jubah}(h]h]h]h]h]uhjh jubh/ for a response function
}(h for a response function
h jhhh!NhNubj
)}(h5:math:`\sigma_{d}\left( \overrightarrow{r},E \right)`h]h/-\sigma_{d}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/ at a given
detector,}(h at a given
detector,h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-7uhh
h jhhh!h"hNubj~)}(hR = \ \int_{V}^{}{\int_{E}^{}{\sigma_{d}\left( \overrightarrow{r},E \right)\phi \left( \overrightarrow{r},E \right)\textit{dE dV.}}}h]h/R = \ \int_{V}^{}{\int_{E}^{}{\sigma_{d}\left( \overrightarrow{r},E \right)\phi \left( \overrightarrow{r},E \right)\textit{dE dV.}}}}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabelmavric-7nowrapjjuhj}h!h"hKh jhhj}j}jj
subh;)}(hXRNote that the flux :math:`\phi\left( \overrightarrow{r},E \right)` has
contributions from each source. The response, :math:`R_{i}`, from each
specific source (:math:`S_{i}` with
:math:`q_{i}\left( \overrightarrow{r},E \right)`) can be expressed using
just the flux from that source,
:math:`\phi_{i}\left( \overrightarrow{r},E \right)`, ash](h/Note that the flux }(hNote that the flux h j,hhh!NhNubj
)}(h/:math:`\phi\left( \overrightarrow{r},E \right)`h]h/'\phi\left( \overrightarrow{r},E \right)}(hhh j5ubah}(h]h]h]h]h]uhjh j,ubh/3 has
contributions from each source. The response, }(h3 has
contributions from each source. The response, h j,hhh!NhNubj
)}(h
:math:`R_{i}`h]h/R_{i}}(hhh jHubah}(h]h]h]h]h]uhjh j,ubh/, from each
specific source (}(h, from each
specific source (h j,hhh!NhNubj
)}(h
:math:`S_{i}`h]h/S_{i}}(hhh j[ubah}(h]h]h]h]h]uhjh j,ubh/ with
}(h with
h j,hhh!NhNubj
)}(h0:math:`q_{i}\left( \overrightarrow{r},E \right)`h]h/(q_{i}\left( \overrightarrow{r},E \right)}(hhh jnubah}(h]h]h]h]h]uhjh j,ubh/9) can be expressed using
just the flux from that source,
}(h9) can be expressed using
just the flux from that source,
h j,hhh!NhNubj
)}(h3:math:`\phi_{i}\left( \overrightarrow{r},E \right)`h]h/+\phi_{i}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh j,ubh/, as}(h, ash j,hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-8uhh
h jhhh!h"hNubj~)}(hR_{i} = \ \int_{V}^{}{\int_{E}^{}{\sigma_{d}\left(\overrightarrow{r},E \right)\ \phi_{i}\left(\overrightarrow{r},E \right)\textit{dE dV .}}}h]h/R_{i} = \ \int_{V}^{}{\int_{E}^{}{\sigma_{d}\left(\overrightarrow{r},E \right)\ \phi_{i}\left(\overrightarrow{r},E \right)\textit{dE dV .}}}}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabelmavric-8nowrapjjuhj}h!h"hKh jhhj}j}jjsubh;)}(hAThe total response is then found as :math:`R = \sum_{i}^{}R_{i}`.h](h/$The total response is then found as }(h$The total response is then found as h jhhh!NhNubj
)}(h:math:`R = \sum_{i}^{}R_{i}`h]h/R = \sum_{i}^{}R_{i}}(hhh jubah}(h]h]h]h]h]uhjh jubh/.}(hjh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh;)}(hFor the adjoint problem, using the adjoint source of
:math:`q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( \overrightarrow{r},E \right)`,
the response :math:`R` can also be calculated ash](h/5For the adjoint problem, using the adjoint source of
}(h5For the adjoint problem, using the adjoint source of
h jhhh!NhNubj
)}(h`:math:`q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( \overrightarrow{r},E \right)`h]h/Xq^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/,
the response }(h,
the response h jhhh!NhNubj
)}(h :math:`R`h]h/R}(hhh jubah}(h]h]h]h]h]uhjh jubh/ can also be calculated as}(h can also be calculated ash jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-9uhh
h jhhh!h"hNubj~)}(hR = \ \int_{V}^{}{\int_{E}^{}{\left\lbrack \sum_{i}^{}{S_{i}q_{i}\left( \overrightarrow{r},E \right)} \right\rbrack\ \phi^{+}\left( \overrightarrow{r},E \right)\textit{dE dV}}},h]h/R = \ \int_{V}^{}{\int_{E}^{}{\left\lbrack \sum_{i}^{}{S_{i}q_{i}\left( \overrightarrow{r},E \right)} \right\rbrack\ \phi^{+}\left( \overrightarrow{r},E \right)\textit{dE dV}}},}(hhh jubah}(h]jah]h]h]h]docnamejnumberK labelmavric-9nowrapjjuhj}h!h"hKh jhhj}j}jjsubh;)}(h>with the response contribution from each specific source beingh]h/>with the response contribution from each specific source being}(hj0h j.hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-10uhh
h jhhh!h"hNubj~)}(hR_{i} = \ \int_{V}^{}{\int_{E}^{}{\ {S_{i}q_{i}\left( \overrightarrow{r},E \right)\phi^{+}}\left( \overrightarrow{r}, E \right)\textit{dE dV.}}}h]h/R_{i} = \ \int_{V}^{}{\int_{E}^{}{\ {S_{i}q_{i}\left( \overrightarrow{r},E \right)\phi^{+}}\left( \overrightarrow{r}, E \right)\textit{dE dV.}}}}(hhh jFubah}(h]jEah]h]h]h]docnamejnumberK
label mavric-10nowrapjjuhj}h!h"hKh jhhj}j}jEj<subh;)}(hpThe target weights
:math:`\overline{w}\left( \overrightarrow{r},E \right)` of the
importance map are found usingh](h/The target weights
}(hThe target weights
h j[hhh!NhNubj
)}(h7:math:`\overline{w}\left( \overrightarrow{r},E \right)`h]h//\overline{w}\left( \overrightarrow{r},E \right)}(hhh jdubah}(h]h]h]h]h]uhjh j[ubh/& of the
importance map are found using}(h& of the
importance map are found usingh j[hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-11uhh
h jhhh!h"hNubj~)}(hl\overline{w}\left( \overrightarrow{r},E \right) = \frac{R/S}{\phi^{+}\left( \overrightarrow{r},E \right)\ }.h]h/l\overline{w}\left( \overrightarrow{r},E \right) = \frac{R/S}{\phi^{+}\left( \overrightarrow{r},E \right)\ }.}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabel mavric-11nowrapjjuhj}h!h"hKh jhhj}j}jj}subh;)}(hbEach biased source
:math:`{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)` pdf is
found usingh](h/Each biased source
}(hEach biased source
h jhhh!NhNubj
)}(h<:math:`{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)`h]h/4{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/ pdf is
found using}(h pdf is
found usingh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hKh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-12uhh
h jhhh!h"hNubj~)}(h{\widehat{q}}_{i}\left(\overrightarrow{r},E \right) = \frac{S_{i}}{R_{i}}{q_{i}\left( \overrightarrow{r},E \right)\phi}^{+}\left( \overrightarrow{r},E \right)\ ,h]h/{\widehat{q}}_{i}\left(\overrightarrow{r},E \right) = \frac{S_{i}}{R_{i}}{q_{i}\left( \overrightarrow{r},E \right)\phi}^{+}\left( \overrightarrow{r},E \right)\ ,}(hhh jubah}(h]jah]h]h]h]docnamejnumberKlabel mavric-12nowrapjjuhj}h!h"hKh jhhj}j}jjsubh;)}(hand the biased distribution used to select an individual source is
:math:`\widehat{p}\left( i \right) = \ R_{i}/\sum_{}^{}{R_{i} = R_{i}/R}`.h](h/Cand the biased distribution used to select an individual source is
}(hCand the biased distribution used to select an individual source is
h jhhh!NhNubj
)}(hI:math:`\widehat{p}\left( i \right) = \ R_{i}/\sum_{}^{}{R_{i} = R_{i}/R}`h]h/A\widehat{p}\left( i \right) = \ R_{i}/\sum_{}^{}{R_{i} = R_{i}/R}}(hhh jubah}(h]h]h]h]h]uhjh jubh/.}(hjh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hWhen using the biased distribution used to select an individual source,
:math:`\widehat{p}\left( i \right)`, and the biased source distribution,
:math:`{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)`, the birth
weight of the sampled particle will beh](h/HWhen using the biased distribution used to select an individual source,
}(hHWhen using the biased distribution used to select an individual source,
h jhhh!NhNubj
)}(h#:math:`\widehat{p}\left( i \right)`h]h/\widehat{p}\left( i \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/&, and the biased source distribution,
}(h&, and the biased source distribution,
h jhhh!NhNubj
)}(h<:math:`{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)`h]h/4{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubh/2, the birth
weight of the sampled particle will be}(h2, the birth
weight of the sampled particle will beh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-13uhh
h jhhh!h"hNubj~)}(hX" \begin{matrix}
w_{0} & \equiv & \left( \frac{p\left( i \right)}{\widehat{p}\left( i \right)} \right)\left( \frac{q_{i}\left( \overrightarrow{r}, E \right)}{{\widehat{q}}_{i}\left(\overrightarrow{r},E \right)} \right) \\ & = & \ \left( \frac{\frac{S_{i}}{S}}{\frac{R_{i}}{R}} \right) \left( \frac{q_{i}\left( \overrightarrow{r},E \right)}{\frac{S_{i}}{R_{i}}{q_{i}\left( \overrightarrow{r},E \right)\phi^{+}}\left( \overrightarrow{r},E \right)} \right) \\
& = & \frac{R/S}{{\phi}^{+}\left( \overrightarrow{r},E \right)\ }, \\
\end{matrix}h]h/X" \begin{matrix}
w_{0} & \equiv & \left( \frac{p\left( i \right)}{\widehat{p}\left( i \right)} \right)\left( \frac{q_{i}\left( \overrightarrow{r}, E \right)}{{\widehat{q}}_{i}\left(\overrightarrow{r},E \right)} \right) \\ & = & \ \left( \frac{\frac{S_{i}}{S}}{\frac{R_{i}}{R}} \right) \left( \frac{q_{i}\left( \overrightarrow{r},E \right)}{\frac{S_{i}}{R_{i}}{q_{i}\left( \overrightarrow{r},E \right)\phi^{+}}\left( \overrightarrow{r},E \right)} \right) \\
& = & \frac{R/S}{{\phi}^{+}\left( \overrightarrow{r},E \right)\ }, \\
\end{matrix}}(hhh j=ubah}(h]j<ah]h]h]h]docnamejnumberK
label mavric-13nowrapjjuhj}h!h"hMh jhhj}j}j<j3subh;)}(hYwhich matches the target weight,
:math:`\overline{w}\left( \overrightarrow{r},E \right)`.h](h/!which matches the target weight,
}(h!which matches the target weight,
h jRhhh!NhNubj
)}(h7:math:`\overline{w}\left( \overrightarrow{r},E \right)`h]h//\overline{w}\left( \overrightarrow{r},E \right)}(hhh j[ubah}(h]h]h]h]h]uhjh jRubh/.}(hjh jRhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubeh}(h]multiple-sources-with-cadisah]h]multiple sources with cadisah]h]uhh#h jhhh!h"hKubh$)}(hhh](h))}(hMultiple tallies with CADISh]h/Multiple tallies with CADIS}(hjh j~hhh!NhNubah}(h]h]h]h]h]uhh(h j{hhh!h"hMubh;)}(hXWThe CADIS methodology works quite well for classic source/detector problems.
The statistical uncertainty of the tally that serves as the adjoint source is greatly reduced since the
Monte Carlo transport is optimized to spend more simulation time on those particles that contribute to the
tally, at the expense of tracking particles in other parts of phase space. However, more recently,
Monte Carlo has been applied to problems in which multiple tallies need to all be found with low statistical
uncertainties. The extension of this idea is the mesh tally—where each voxel is a tally for which the user desires
low statistical uncertainties. For these problems, the user must accept a total simulation time that is controlled
by the tally with the slowest convergence and simulation results where the tallies have a wide range of relative
uncertainties.h]h/XWThe CADIS methodology works quite well for classic source/detector problems.
The statistical uncertainty of the tally that serves as the adjoint source is greatly reduced since the
Monte Carlo transport is optimized to spend more simulation time on those particles that contribute to the
tally, at the expense of tracking particles in other parts of phase space. However, more recently,
Monte Carlo has been applied to problems in which multiple tallies need to all be found with low statistical
uncertainties. The extension of this idea is the mesh tally—where each voxel is a tally for which the user desires
low statistical uncertainties. For these problems, the user must accept a total simulation time that is controlled
by the tally with the slowest convergence and simulation results where the tallies have a wide range of relative
uncertainties.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j{hhubh;)}(hXhThe obvious way around this problem is to create a separate problem for each tally and use CADIS to optimize each.
Each simulation can then be run until the tally reaches the level of acceptable uncertainty.
For more than a few tallies, this approach becomes complicated and time-consuming for the user.
For large mesh tallies, this approach is not reasonable.h]h/XhThe obvious way around this problem is to create a separate problem for each tally and use CADIS to optimize each.
Each simulation can then be run until the tally reaches the level of acceptable uncertainty.
For more than a few tallies, this approach becomes complicated and time-consuming for the user.
For large mesh tallies, this approach is not reasonable.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM%h j{hhubh;)}(hXAnother approach to treat several tallies, if they are in close proximity to each other,
or a mesh tally covering a small portion of the physical problem, is to use the CADIS methodology
with the adjoint source near the middle of the tallies to be optimized. Since particles in the
forward Monte Carlo simulation are optimized to reach the location of the adjoint source, all the
tallies surrounding that adjoint source should converge quickly. This approach requires the
difficult question of “how close.” If the tallies are too far apart, then certain energies or regions that are
needed for one tally may be of low importance for getting particles to the central adjoint source. This may
under-predict the flux or dose at the tally sites far from the adjoint source.h]h/XAnother approach to treat several tallies, if they are in close proximity to each other,
or a mesh tally covering a small portion of the physical problem, is to use the CADIS methodology
with the adjoint source near the middle of the tallies to be optimized. Since particles in the
forward Monte Carlo simulation are optimized to reach the location of the adjoint source, all the
tallies surrounding that adjoint source should converge quickly. This approach requires the
difficult question of “how close.” If the tallies are too far apart, then certain energies or regions that are
needed for one tally may be of low importance for getting particles to the central adjoint source. This may
under-predict the flux or dose at the tally sites far from the adjoint source.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM*h j{hhubh;)}(hXMAVRIC has the capability to have multiple adjoint sources with this problem in mind.
For several tallies that are far from each other, multiple adjoint sources could be used.
In the forward Monte Carlo, particles would be drawn to one of those adjoint sources.
The difficulty with this approach is that typically the tally that is closest to the true
physical source converges faster than the other tallies—--showing that the closest adjoint source
seems to attract more particles than the others. Assigning more strength to the adjoint
source further from the true physical source helps to address this issue, but finding the correct strengths so
that all of the tallies converge to the same relative uncertainty in one simulation is an iterative process for the user.h]h/XMAVRIC has the capability to have multiple adjoint sources with this problem in mind.
For several tallies that are far from each other, multiple adjoint sources could be used.
In the forward Monte Carlo, particles would be drawn to one of those adjoint sources.
The difficulty with this approach is that typically the tally that is closest to the true
physical source converges faster than the other tallies—–showing that the closest adjoint source
seems to attract more particles than the others. Assigning more strength to the adjoint
source further from the true physical source helps to address this issue, but finding the correct strengths so
that all of the tallies converge to the same relative uncertainty in one simulation is an iterative process for the user.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM3h j{hhubeh}(h]multiple-tallies-with-cadisah]h]multiple tallies with cadisah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(hForward-weighted CADISh]h/Forward-weighted CADIS}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hM=ubh;)}(hXeTo converge several tallies to the same relative uncertainty in
one simulation, the adjoint source corresponding to each of those
tallies must be weighted inversely by the expected tally value. To calculate the
dose rate at two points—--say one near a reactor
and one far from a reactor—--in one simulation, then the total adjoint
source used to develop the weight windows and biased source must
have two parts. The adjoint source far from the reactor must have
more strength than the adjoint source near the reactor by a factor equal
to the ratio of the expected near dose rate to the expected far dose
rate.h]h/XgTo converge several tallies to the same relative uncertainty in
one simulation, the adjoint source corresponding to each of those
tallies must be weighted inversely by the expected tally value. To calculate the
dose rate at two points—–say one near a reactor
and one far from a reactor—–in one simulation, then the total adjoint
source used to develop the weight windows and biased source must
have two parts. The adjoint source far from the reactor must have
more strength than the adjoint source near the reactor by a factor equal
to the ratio of the expected near dose rate to the expected far dose
rate.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM?h jhhubh;)}(hXtThis concept can be extended to mesh tallies, as well. Instead of using a
uniform adjoint source strength over the entire mesh tally volume, each
voxel of the adjoint source should be weighted inversely by the expected
forward tally value for that voxel. Areas of low flux or low dose rate
would have more adjoint source strength than areas of high flux or high
dose rate.h]h/XtThis concept can be extended to mesh tallies, as well. Instead of using a
uniform adjoint source strength over the entire mesh tally volume, each
voxel of the adjoint source should be weighted inversely by the expected
forward tally value for that voxel. Areas of low flux or low dose rate
would have more adjoint source strength than areas of high flux or high
dose rate.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMJh jhhubh;)}(hXiAn estimate of the expected tally results can be found by using a quick
discrete-ordinates calculation. This leads to an extension of the CADIS
method: forward-weighted CADIS (FW-CADIS). First, a forward S\ :sub:`N` calculation is performed to
estimate the expected tally results. A total adjoint source is
constructed so that the adjoint source corresponding to each tally is
weighted inversely by those forward tally estimates. Then the standard
CADIS approach is used—an importance map (target weight windows) and a
biased source are made using the adjoint flux computed from the adjoint
S\ :sub:`N` calculation.h](h/An estimate of the expected tally results can be found by using a quick
discrete-ordinates calculation. This leads to an extension of the CADIS
method: forward-weighted CADIS (FW-CADIS). First, a forward S }(hAn estimate of the expected tally results can be found by using a quick
discrete-ordinates calculation. This leads to an extension of the CADIS
method: forward-weighted CADIS (FW-CADIS). First, a forward S\ h jhhh!NhNubh subscript)}(h:sub:`N`h]h/N}(hhh j ubah}(h]h]h]h]h]uhj h jubh/X} calculation is performed to
estimate the expected tally results. A total adjoint source is
constructed so that the adjoint source corresponding to each tally is
weighted inversely by those forward tally estimates. Then the standard
CADIS approach is used—an importance map (target weight windows) and a
biased source are made using the adjoint flux computed from the adjoint
S }(hX} calculation is performed to
estimate the expected tally results. A total adjoint source is
constructed so that the adjoint source corresponding to each tally is
weighted inversely by those forward tally estimates. Then the standard
CADIS approach is used—an importance map (target weight windows) and a
biased source are made using the adjoint flux computed from the adjoint
S\ h jhhh!NhNubj )}(h:sub:`N`h]h/N}(hhh j ubah}(h]h]h]h]h]uhj h jubh/
calculation.}(h
calculation.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMQh jhhubh;)}(hXFor example, if the goal is to calculate a detector response function
:math:`\sigma_{d}\left( E \right)` (such as dose rate using
flux-to-dose-rate conversion factors) over a volume (defined by
:math:`g\left( \overrightarrow{r} \right)`) corresponding to mesh tally,
then instead of simply using
:math:`q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\ g(\overrightarrow{r})`,
the adjoint source would beh](h/FFor example, if the goal is to calculate a detector response function
}(hFFor example, if the goal is to calculate a detector response function
h j0 hhh!NhNubj
)}(h":math:`\sigma_{d}\left( E \right)`h]h/\sigma_{d}\left( E \right)}(hhh j9 ubah}(h]h]h]h]h]uhjh j0 ubh/Z (such as dose rate using
flux-to-dose-rate conversion factors) over a volume (defined by
}(hZ (such as dose rate using
flux-to-dose-rate conversion factors) over a volume (defined by
h j0 hhh!NhNubj
)}(h*:math:`g\left( \overrightarrow{r} \right)`h]h/"g\left( \overrightarrow{r} \right)}(hhh jL ubah}(h]h]h]h]h]uhjh j0 ubh/<) corresponding to mesh tally,
then instead of simply using
}(h<) corresponding to mesh tally,
then instead of simply using
h j0 hhh!NhNubj
)}(hd:math:`q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\ g(\overrightarrow{r})`h]h/\q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\ g(\overrightarrow{r})}(hhh j_ ubah}(h]h]h]h]h]uhjh j0 ubh/,
the adjoint source would be}(h,
the adjoint source would beh j0 hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM[h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-14uhh
h jhhh!h"hNubj~)}(h q^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}{\int_{}^{}{\sigma_{d}\left( E \right)\phi\left( \overrightarrow{r},E \right)}\textit{dE}}\ ,h]h/ q^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}{\int_{}^{}{\sigma_{d}\left( E \right)\phi\left( \overrightarrow{r},E \right)}\textit{dE}}\ ,}(hhh j ubah}(h]j ah]h]h]h]docnamejnumberKlabel mavric-14nowrapjjuhj}h!h"hMdh jhhj}j}j jx subh;)}(hXdwhere :math:`\phi\left( \overrightarrow{r},E \right)` is an estimate of
the forward flux, and the energy integral is over the voxel at :math:`\overrightarrow{r}`.
The adjoint source is nonzero only where the mesh tally is defined
(:math:`g\left( \overrightarrow{r} \right)`), and its strength is
inversely proportional to the forward estimate of dose rate.h](h/where }(hwhere h j hhh!NhNubj
)}(h/:math:`\phi\left( \overrightarrow{r},E \right)`h]h/'\phi\left( \overrightarrow{r},E \right)}(hhh j ubah}(h]h]h]h]h]uhjh j ubh/R is an estimate of
the forward flux, and the energy integral is over the voxel at }(hR is an estimate of
the forward flux, and the energy integral is over the voxel at h j hhh!NhNubj
)}(h:math:`\overrightarrow{r}`h]h/\overrightarrow{r}}(hhh j ubah}(h]h]h]h]h]uhjh j ubh/F.
The adjoint source is nonzero only where the mesh tally is defined
(}(hF.
The adjoint source is nonzero only where the mesh tally is defined
(h j hhh!NhNubj
)}(h*:math:`g\left( \overrightarrow{r} \right)`h]h/"g\left( \overrightarrow{r} \right)}(hhh j ubah}(h]h]h]h]h]uhjh j ubh/S), and its strength is
inversely proportional to the forward estimate of dose rate.}(hS), and its strength is
inversely proportional to the forward estimate of dose rate.h j hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMih jhhubh;)}(hXThe relative uncertainty of a tally is controlled by two components:
(1) the number of tracks contributing to the tally and (2) the
shape of the distribution of scores contributing to that tally. In the
Monte Carlo game, the number of simulated particles,
:math:`m\left( \overrightarrow{r},E \right)`, can be related to the true
physical particle density, :math:`n\left( \overrightarrow{r},E \right),`
by the average Monte Carlo weight of scoring particles,
:math:`\overline{w}\left( \overrightarrow{r},E \right)`, byh](h/XThe relative uncertainty of a tally is controlled by two components:
(1) the number of tracks contributing to the tally and (2) the
shape of the distribution of scores contributing to that tally. In the
Monte Carlo game, the number of simulated particles,
}(hXThe relative uncertainty of a tally is controlled by two components:
(1) the number of tracks contributing to the tally and (2) the
shape of the distribution of scores contributing to that tally. In the
Monte Carlo game, the number of simulated particles,
h j hhh!NhNubj
)}(h,:math:`m\left( \overrightarrow{r},E \right)`h]h/$m\left( \overrightarrow{r},E \right)}(hhh j ubah}(h]h]h]h]h]uhjh j ubh/8, can be related to the true
physical particle density, }(h8, can be related to the true
physical particle density, h j hhh!NhNubj
)}(h-:math:`n\left( \overrightarrow{r},E \right),`h]h/%n\left( \overrightarrow{r},E \right),}(hhh j ubah}(h]h]h]h]h]uhjh j ubh/9
by the average Monte Carlo weight of scoring particles,
}(h9
by the average Monte Carlo weight of scoring particles,
h j hhh!NhNubj
)}(h7:math:`\overline{w}\left( \overrightarrow{r},E \right)`h]h//\overline{w}\left( \overrightarrow{r},E \right)}(hhh j
ubah}(h]h]h]h]h]uhjh j ubh/, by}(h, byh j hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMoh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-15uhh
h jhhh!h"hNubj~)}(hn\left( \overrightarrow{r},E \right) = \ \overline{w}\left( \overrightarrow{r},E \right)\text{m}\left( \overrightarrow{r},E \right).h]h/n\left( \overrightarrow{r},E \right) = \ \overline{w}\left( \overrightarrow{r},E \right)\text{m}\left( \overrightarrow{r},E \right).}(hhh j1
ubah}(h]j0
ah]h]h]h]docnamejnumberKlabel mavric-15nowrapjjuhj}h!h"hMyh jhhj}j}j0
j'
subh;)}(hXIn a typical Monte Carlo calculation, tallies are made by adding some
score, multiplied by the current particle weight, to an accumulator. To
calculate a similar quantity related to the Monte Carlo particle density
would be very close to calculating any other quantity but without
including the particle weight. The goal of FW-CADIS is to make the Monte
Carlo particle density, :math:`m\left( \overrightarrow{r},E \right)`,
uniform over the tally areas, so an importance map must be developed
that represents the importance of achieving uniform Monte Carlo particle
density. By attempting to keep the Monte Carlo particle density more
uniform, more uniform relative errors for the tallies should be
realized.h](h/XzIn a typical Monte Carlo calculation, tallies are made by adding some
score, multiplied by the current particle weight, to an accumulator. To
calculate a similar quantity related to the Monte Carlo particle density
would be very close to calculating any other quantity but without
including the particle weight. The goal of FW-CADIS is to make the Monte
Carlo particle density, }(hXzIn a typical Monte Carlo calculation, tallies are made by adding some
score, multiplied by the current particle weight, to an accumulator. To
calculate a similar quantity related to the Monte Carlo particle density
would be very close to calculating any other quantity but without
including the particle weight. The goal of FW-CADIS is to make the Monte
Carlo particle density, h jF
hhh!NhNubj
)}(h,:math:`m\left( \overrightarrow{r},E \right)`h]h/$m\left( \overrightarrow{r},E \right)}(hhh jO
ubah}(h]h]h]h]h]uhjh jF
ubh/X,
uniform over the tally areas, so an importance map must be developed
that represents the importance of achieving uniform Monte Carlo particle
density. By attempting to keep the Monte Carlo particle density more
uniform, more uniform relative errors for the tallies should be
realized.}(hX,
uniform over the tally areas, so an importance map must be developed
that represents the importance of achieving uniform Monte Carlo particle
density. By attempting to keep the Monte Carlo particle density more
uniform, more uniform relative errors for the tallies should be
realized.h jF
hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hXTwo options for forward weighting are possible. For tallies over some
area where the entire group-wise flux is needed with low relative
uncertainties, the adjoint source should be weighted inversely by the
forward flux, :math:`\phi\left( \overrightarrow{r},E \right)`. The other
option, for a tally in which only an energy-integrated quantity is desired,
is to weight the adjoint inversely by that energy-integrated
quantity,\ :math:`\int_{}^{}{\sigma_{d}\left( E \right)\phi\left( \overrightarrow{r},E \right)}\text{\ dE}`.
For a tally in which the total flux is desired, then the response in the
adjoint source is simply :math:`\sigma_{d}\left( E \right) = 1`.h](h/Two options for forward weighting are possible. For tallies over some
area where the entire group-wise flux is needed with low relative
uncertainties, the adjoint source should be weighted inversely by the
forward flux, }(hTwo options for forward weighting are possible. For tallies over some
area where the entire group-wise flux is needed with low relative
uncertainties, the adjoint source should be weighted inversely by the
forward flux, h jh
hhh!NhNubj
)}(h/:math:`\phi\left( \overrightarrow{r},E \right)`h]h/'\phi\left( \overrightarrow{r},E \right)}(hhh jq
ubah}(h]h]h]h]h]uhjh jh
ubh/. The other
option, for a tally in which only an energy-integrated quantity is desired,
is to weight the adjoint inversely by that energy-integrated
quantity, }(h. The other
option, for a tally in which only an energy-integrated quantity is desired,
is to weight the adjoint inversely by that energy-integrated
quantity,\ h jh
hhh!NhNubj
)}(h`:math:`\int_{}^{}{\sigma_{d}\left( E \right)\phi\left( \overrightarrow{r},E \right)}\text{\ dE}`h]h/X\int_{}^{}{\sigma_{d}\left( E \right)\phi\left( \overrightarrow{r},E \right)}\text{\ dE}}(hhh j
ubah}(h]h]h]h]h]uhjh jh
ubh/d.
For a tally in which the total flux is desired, then the response in the
adjoint source is simply }(hd.
For a tally in which the total flux is desired, then the response in the
adjoint source is simply h jh
hhh!NhNubj
)}(h&:math:`\sigma_{d}\left( E \right) = 1`h]h/\sigma_{d}\left( E \right) = 1}(hhh j
ubah}(h]h]h]h]h]uhjh jh
ubh/.}(hjh jh
hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hXTo optimize the forward Monte Carlo simulation for the calculation of
some quantity at multiple tally locations or across a mesh tally, the
adjoint source must be weighted by the estimate of that quantity.
For a tally defined by its spatial location
:math:`g\left( \overrightarrow{r} \right)` and its optional response
:math:`\sigma_{d}\left( E \right)`, the standard adjoint source would be
:math:`q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)`.
The forward-weighted adjoint source,
:math:`q^{+}\left( \overrightarrow{r},E \right)`, depending on what
quantity is to be optimized, is listed below.h](h/To optimize the forward Monte Carlo simulation for the calculation of
some quantity at multiple tally locations or across a mesh tally, the
adjoint source must be weighted by the estimate of that quantity.
For a tally defined by its spatial location
}(hTo optimize the forward Monte Carlo simulation for the calculation of
some quantity at multiple tally locations or across a mesh tally, the
adjoint source must be weighted by the estimate of that quantity.
For a tally defined by its spatial location
h j
hhh!NhNubj
)}(h*:math:`g\left( \overrightarrow{r} \right)`h]h/"g\left( \overrightarrow{r} \right)}(hhh j
ubah}(h]h]h]h]h]uhjh j
ubh/ and its optional response
}(h and its optional response
h j
hhh!NhNubj
)}(h":math:`\sigma_{d}\left( E \right)`h]h/\sigma_{d}\left( E \right)}(hhh j
ubah}(h]h]h]h]h]uhjh j
ubh/', the standard adjoint source would be
}(h', the standard adjoint source would be
h j
hhh!NhNubj
)}(hv:math:`q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)`h]h/nq^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}(hhh j
ubah}(h]h]h]h]h]uhjh j
ubh/'.
The forward-weighted adjoint source,
}(h'.
The forward-weighted adjoint source,
h j
hhh!NhNubj
)}(h0:math:`q^{+}\left( \overrightarrow{r},E \right)`h]h/(q^{+}\left( \overrightarrow{r},E \right)}(hhh j
ubah}(h]h]h]h]h]uhjh j
ubh/A, depending on what
quantity is to be optimized, is listed below.}(hA, depending on what
quantity is to be optimized, is listed below.h j
hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh table)}(hhh]h tgroup)}(hhh](h colspec)}(hhh]h}(h]h]h]h]h]colwidthK2uhjh jubj)}(hhh]h}(h]h]h]h]h]jKduhjh jubj)}(hhh]h}(h]h]h]h]h]jKuhjh jubh thead)}(hhh]h row)}(hhh](h entry)}(hhh]h;)}(hFor the calculation ofh]h/For the calculation of}(hjCh jAubah}(h]h]h]h]h]uhh:h!h"hMh j>ubah}(h]h]h]h]h]uhj<h j9ubj=)}(hhh]h}(h]h]h]h]h]uhj<h j9ubj=)}(hhh]h;)}(hAdjoint sourceh]h/Adjoint source}(hjch jaubah}(h]h]h]h]h]uhh:h!h"hMh j^ubah}(h]h]h]h]h]uhj<h j9ubeh}(h]h]h]h]h]uhj7h j4ubah}(h]h]h]h]h]uhj2h jubh tbody)}(hhh](j8)}(hhh](j=)}(hhh]h;)}(h#Energy and spatially dependent fluxh]h/#Energy and spatially dependent flux}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(h.:math:`\phi\left(\overrightarrow{r},E \right)`h]j
)}(h.:math:`\phi\left(\overrightarrow{r},E \right)`h]h/&\phi\left(\overrightarrow{r},E \right)}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]j~)}(hR\frac{g\left( \overrightarrow{r}\right)}{\phi\left(\overrightarrow{r},E \right)}
h]h/R\frac{g\left( \overrightarrow{r}\right)}{\phi\left(\overrightarrow{r},E \right)}
}(hhh jubah}(h]h]h]h]h]docnamejnumberNlabelNnowrapjjuhj}h!h"hMh jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(hSpatially dependent total fluxh]h/Spatially dependent total flux}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hF:math:`\int_{}^{}{\phi\left( \overrightarrow{r},E \right)}\textit{dE}`h]j
)}(hF:math:`\int_{}^{}{\phi\left( \overrightarrow{r},E \right)}\textit{dE}`h]h/>\int_{}^{}{\phi\left( \overrightarrow{r},E \right)}\textit{dE}}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]j~)}(hj\frac{g\left( \overrightarrow{r}\right)}{\int_{}^{}{\phi\left( \overrightarrow{r},E \right)}\textit{dE}}
h]h/j\frac{g\left( \overrightarrow{r}\right)}{\int_{}^{}{\phi\left( \overrightarrow{r},E \right)}\textit{dE}}
}(hhh j ubah}(h]h]h]h]h]docnamejnumberNlabelNnowrapjjuhj}h!h"hMh jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(h"Spatially dependent total responseh]h/"Spatially dependent total response}(hjFh jDubah}(h]h]h]h]h]uhh:h!h"hMh jAubah}(h]h]h]h]h]uhj<h j>ubj=)}(hhh]h;)}(hb:math:`\int_{}^{}{\sigma_{d}\left( E \right)\phi \left(\overrightarrow{r},E\right)}\textit{dE}`h]j
)}(hb:math:`\int_{}^{}{\sigma_{d}\left( E \right)\phi \left(\overrightarrow{r},E\right)}\textit{dE}`h]h/Z\int_{}^{}{\sigma_{d}\left( E \right)\phi \left(\overrightarrow{r},E\right)}\textit{dE}}(hhh j_ubah}(h]h]h]h]h]uhjh j[ubah}(h]h]h]h]h]uhh:h!h"hMh jXubah}(h]h]h]h]h]uhj<h j>ubj=)}(hhh]j~)}(h\frac{\sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}{\int_{}^{}{\sigma_{d}\left( E \right)\phi \left( \overrightarrow{r},E \right)}\textit{dE}}
h]h/\frac{\sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}{\int_{}^{}{\sigma_{d}\left( E \right)\phi \left( \overrightarrow{r},E \right)}\textit{dE}}
}(hhh j|ubah}(h]h]h]h]h]docnamejnumberNlabelNnowrapjjuhj}h!h"hMh jyubah}(h]h]h]h]h]uhj<h j>ubeh}(h]h]h]h]h]uhj7h jubeh}(h]h]h]h]h]uhjh jubeh}(h]h]h]h]h]colsKuhjh jubah}(h]h]colwidths-givenah]h]h]aligndefaultuhj
h jhhh!NhNubh;)}(hXThe bottom line of FW-CADIS is that in order to calculate a quantity at
multiple tally locations (or across a mesh tally) with more uniform
relative uncertainties, an adjoint source must be developed for an
objective function that keeps some non-physical quantity—related to the
Monte Carlo particle density and similar in form to the desired
quantity—constant. FW-CADIS uses the solution of a forward
discrete-ordinates calculation to properly weight the adjoint source.
After that, the standard CADIS approach is used.h]h/XThe bottom line of FW-CADIS is that in order to calculate a quantity at
multiple tally locations (or across a mesh tally) with more uniform
relative uncertainties, an adjoint source must be developed for an
objective function that keeps some non-physical quantity—related to the
Monte Carlo particle density and similar in form to the desired
quantity—constant. FW-CADIS uses the solution of a forward
discrete-ordinates calculation to properly weight the adjoint source.
After that, the standard CADIS approach is used.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubeh}(h]forward-weighted-cadisah]h]forward-weighted cadisah]h]uhh#h jhhh!h"hM=ubh$)}(hhh](h))}(hMAVRIC Implementation of CADISh]h/MAVRIC Implementation of CADIS}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubh;)}(hXFWith MAVRIC, as with other shielding codes, the user defines the problem as a set of
physical models—the material compositions, the geometry, the source, and the detectors
(locations and response functions)—as well as some mathematical parameters on how to solve
the problem (number of histories, etc.). For the variance reduction portion of MAVRIC, the
only additional inputs required are (1) the mesh planes to use in the discrete-ordinates
calculation(s) and (2) the adjoint source description—--basically the location and the response
of each tally to optimize in the forward Monte Carlo calculation. MAVRIC uses this information
to construct a Denovo adjoint problem. (The adjoint source is weighted by a Denovo forward flux
or response estimate for FW-CADIS applications.) MAVRIC then uses the CADIS methodology: it combines
the adjoint flux from the Denovo calculation with the source description and creates the importance map
(weight window targets) and the mesh-based biased source. Monaco is then run using the CADIS biased source
distribution and the weight window targets.h]h/XGWith MAVRIC, as with other shielding codes, the user defines the problem as a set of
physical models—the material compositions, the geometry, the source, and the detectors
(locations and response functions)—as well as some mathematical parameters on how to solve
the problem (number of histories, etc.). For the variance reduction portion of MAVRIC, the
only additional inputs required are (1) the mesh planes to use in the discrete-ordinates
calculation(s) and (2) the adjoint source description—–basically the location and the response
of each tally to optimize in the forward Monte Carlo calculation. MAVRIC uses this information
to construct a Denovo adjoint problem. (The adjoint source is weighted by a Denovo forward flux
or response estimate for FW-CADIS applications.) MAVRIC then uses the CADIS methodology: it combines
the adjoint flux from the Denovo calculation with the source description and creates the importance map
(weight window targets) and the mesh-based biased source. Monaco is then run using the CADIS biased source
distribution and the weight window targets.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubh$)}(hhh](h))}(hDenovoh]h/Denovo}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubh;)}(hXDenovo is a parallel three-dimensional SN code that is used to generate adjoint (and, for FW-CADIS, forward)
scalar fluxes for the CADIS methods in MAVRIC. For use in MAVRIC/CADIS, it is highly desirable that the SN code be fast,
positive, and robust. The phase-space shape of the forward and adjoint fluxes, as opposed to a highly accurate solution,
is the most important quality for Monte Carlo weight-window generation. Accordingly,
Denovo provides a step-characteristics spatial differencing option that produces positive scalar fluxes as
long as the source (volume plus in-scatter) is positive. Denovo uses an orthogonal, nonuniform mesh that is
ideal for CADIS applications because of the speed and robustness of calculations on this mesh type.h]h/XDenovo is a parallel three-dimensional SN code that is used to generate adjoint (and, for FW-CADIS, forward)
scalar fluxes for the CADIS methods in MAVRIC. For use in MAVRIC/CADIS, it is highly desirable that the SN code be fast,
positive, and robust. The phase-space shape of the forward and adjoint fluxes, as opposed to a highly accurate solution,
is the most important quality for Monte Carlo weight-window generation. Accordingly,
Denovo provides a step-characteristics spatial differencing option that produces positive scalar fluxes as
long as the source (volume plus in-scatter) is positive. Denovo uses an orthogonal, nonuniform mesh that is
ideal for CADIS applications because of the speed and robustness of calculations on this mesh type.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hXDenovo uses the highly robust GMRES (Generalized Minimum Residual) Krylov method to solve the SN equations in each group. GMRES has been shown to be more robust and efficient than traditional source (fixed-point) iteration. The in-group discrete SN equations are defined ash]h/XDenovo uses the highly robust GMRES (Generalized Minimum Residual) Krylov method to solve the SN equations in each group. GMRES has been shown to be more robust and efficient than traditional source (fixed-point) iteration. The in-group discrete SN equations are defined as}(hj
h j
hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-16uhh
h jhhh!h"hNubj~)}(h+\mathbf{L}\psi = \mathbf{\text{MS}}\phi + qh]h/+\mathbf{L}\psi = \mathbf{\text{MS}}\phi + q}(hhh j
ubah}(h]j
ah]h]h]h]docnamejnumberKlabel mavric-16nowrapjjuhj}h!h"hMh jhhj}j}j
j
subh;)}(hXwhere **L** is the differential transport operator, **M** is the
moment-to-discrete operator, **S** is the matrix of scattering
cross section moments, *q* is the external and in-scatter source,
:math:`\phi` is the vector of angular flux moments, and :math:`\psi` is
the vector of angular fluxes at discrete angles. Applying the operator
**D**, where :math:`\phi = \mathbf{D}\psi`, and rearranging terms, casts
the in-group equations in the form of a traditional linear system,
:math:`\mathbf{A}x = b`,h](h/where }(hwhere h j1
hhh!NhNubh strong)}(h**L**h]h/L}(hhh j<
ubah}(h]h]h]h]h]uhj:
h j1
ubh/) is the differential transport operator, }(h) is the differential transport operator, h j1
hhh!NhNubj;
)}(h**M**h]h/M}(hhh jO
ubah}(h]h]h]h]h]uhj:
h j1
ubh/% is the
moment-to-discrete operator, }(h% is the
moment-to-discrete operator, h j1
hhh!NhNubj;
)}(h**S**h]h/S}(hhh jb
ubah}(h]h]h]h]h]uhj:
h j1
ubh/4 is the matrix of scattering
cross section moments, }(h4 is the matrix of scattering
cross section moments, h j1
hhh!NhNubhA)}(h*q*h]h/q}(hhh ju
ubah}(h]h]h]h]h]uhh@h j1
ubh/( is the external and in-scatter source,
}(h( is the external and in-scatter source,
h j1
hhh!NhNubj
)}(h:math:`\phi`h]h/\phi}(hhh j
ubah}(h]h]h]h]h]uhjh j1
ubh/, is the vector of angular flux moments, and }(h, is the vector of angular flux moments, and h j1
hhh!NhNubj
)}(h:math:`\psi`h]h/\psi}(hhh j
ubah}(h]h]h]h]h]uhjh j1
ubh/K is
the vector of angular fluxes at discrete angles. Applying the operator
}(hK is
the vector of angular fluxes at discrete angles. Applying the operator
h j1
hhh!NhNubj;
)}(h**D**h]h/D}(hhh j
ubah}(h]h]h]h]h]uhj:
h j1
ubh/, where }(h, where h j1
hhh!NhNubj
)}(h:math:`\phi = \mathbf{D}\psi`h]h/\phi = \mathbf{D}\psi}(hhh j
ubah}(h]h]h]h]h]uhjh j1
ubh/b, and rearranging terms, casts
the in-group equations in the form of a traditional linear system,
}(hb, and rearranging terms, casts
the in-group equations in the form of a traditional linear system,
h j1
hhh!NhNubj
)}(h:math:`\mathbf{A}x = b`h]h/\mathbf{A}x = b}(hhh j
ubah}(h]h]h]h]h]uhjh j1
ubh/,}(h,h j1
hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh block_quote)}(hhh](h)}(hhh]h}(h]h]h]h]h]hequation-mavric-17uhh
h j
ubj~)}(hh\left( \mathbf{I} - \mathbf{D}\mathbf{L}^{- 1}\mathbf{\text{MS}} \right) = \mathbf{D}\mathbf{L}^{- 1}q .h]h/h\left( \mathbf{I} - \mathbf{D}\mathbf{L}^{- 1}\mathbf{\text{MS}} \right) = \mathbf{D}\mathbf{L}^{- 1}q .}(hhh j
ubah}(h]j
ah]h]h]h]docnamejnumberKlabel mavric-17nowrapjjuhj}h!h"hMh j
j}j}j
j
subeh}(h]h]h]h]h]uhj
h jhhh!NhNubh;)}(hXThe operation :math:`\mathbf{L}^{- 1}\nu`, where :math:`\nu` is an
iteration vector, is performed using a traditional wave-front solve
(transport sweep). The parallel implementation of the Denovo wave-front
solver uses the well-known Koch-Baker-Alcouffe (KBA) algorithm, which is
a two-dimensional block‑spatial decomposition of a three-dimensional
orthogonal mesh :cite:`baker_sn_1998`. The Trilinos package is used for the GMRES
implementation :cite:`willenbring_trilinos_2003` Denovo stores the mesh-based scalar fluxes in a
double precision binary file (\*.dff) called a *Denovo flux file*. Past
versions of SCALE/Denovo used the TORT :cite:`rhoades_tort_1997` \*.varscl file format
(DOORS package :cite:`rhoades_doors_1998`), but this was limited to single precision. Since
the rest of the MAVRIC sequence has not yet been parallelized, Denovo is
currently used only in serial mode within MAVRIC.h](h/The operation }(hThe operation h jhhh!NhNubj
)}(h:math:`\mathbf{L}^{- 1}\nu`h]h/\mathbf{L}^{- 1}\nu}(hhh j ubah}(h]h]h]h]h]uhjh jubh/, where }(h, where h jhhh!NhNubj
)}(h:math:`\nu`h]h/\nu}(hhh j3ubah}(h]h]h]h]h]uhjh jubh/X3 is an
iteration vector, is performed using a traditional wave-front solve
(transport sweep). The parallel implementation of the Denovo wave-front
solver uses the well-known Koch-Baker-Alcouffe (KBA) algorithm, which is
a two-dimensional block‑spatial decomposition of a three-dimensional
orthogonal mesh }(hX3 is an
iteration vector, is performed using a traditional wave-front solve
(transport sweep). The parallel implementation of the Denovo wave-front
solver uses the well-known Koch-Baker-Alcouffe (KBA) algorithm, which is
a two-dimensional block‑spatial decomposition of a three-dimensional
orthogonal mesh h jhhh!NhNubhp)}(h
baker_sn_1998h]hv)}(hjHh]h/[baker_sn_1998]}(hhh jJubah}(h]h]h]h]h]uhhuh jFubah}(h]id9ah]hah]h]h] refdomainhreftypeh reftargetjHrefwarnsupport_smartquotesuhhoh!h"hMh jhhubh/<. The Trilinos package is used for the GMRES
implementation }(h<. The Trilinos package is used for the GMRES
implementation h jhhh!NhNubhp)}(hwillenbring_trilinos_2003h]hv)}(hjjh]h/[willenbring_trilinos_2003]}(hhh jlubah}(h]h]h]h]h]uhhuh jhubah}(h]id10ah]hah]h]h] refdomainhreftypeh reftargetjjrefwarnsupport_smartquotesuhhoh!h"hMh jhhubh/` Denovo stores the mesh-based scalar fluxes in a
double precision binary file (*.dff) called a }(h` Denovo stores the mesh-based scalar fluxes in a
double precision binary file (\*.dff) called a h jhhh!NhNubhA)}(h*Denovo flux file*h]h/Denovo flux file}(hhh jubah}(h]h]h]h]h]uhh@h jubh/.. Past
versions of SCALE/Denovo used the TORT }(h.. Past
versions of SCALE/Denovo used the TORT h jhhh!NhNubhp)}(hrhoades_tort_1997h]hv)}(hjh]h/[rhoades_tort_1997]}(hhh jubah}(h]h]h]h]h]uhhuh jubah}(h]id11ah]hah]h]h] refdomainhreftypeh reftargetjrefwarnsupport_smartquotesuhhoh!h"hMh jhhubh/& *.varscl file format
(DOORS package }(h& \*.varscl file format
(DOORS package h jhhh!NhNubhp)}(hrhoades_doors_1998h]hv)}(hjh]h/[rhoades_doors_1998]}(hhh jubah}(h]h]h]h]h]uhhuh jubah}(h]id12ah]hah]h]h] refdomainhreftypeh reftargetjrefwarnsupport_smartquotesuhhoh!h"hMh jhhubh/), but this was limited to single precision. Since
the rest of the MAVRIC sequence has not yet been parallelized, Denovo is
currently used only in serial mode within MAVRIC.}(h), but this was limited to single precision. Since
the rest of the MAVRIC sequence has not yet been parallelized, Denovo is
currently used only in serial mode within MAVRIC.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubeh}(h]denovoah]h]denovoah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(hMonacoh]h/Monaco}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubh;)}(hXThe forward Monte Carlo transport is performed using Monaco, a
fixed-source shielding code that uses the SCALE General Geometry
Package (SGGP, the same as used by the criticality code KENO-VI) and the
standard SCALE material information processor. Monaco can use either MG
or CE cross section libraries. Monaco was originally based on the MORSE
Monte Carlo code but has been extensively modified to modernize the
coding, incorporate more flexibility in terms of sources/tallies, and
read a user-friendly block/keyword style input.h]h/XThe forward Monte Carlo transport is performed using Monaco, a
fixed-source shielding code that uses the SCALE General Geometry
Package (SGGP, the same as used by the criticality code KENO-VI) and the
standard SCALE material information processor. Monaco can use either MG
or CE cross section libraries. Monaco was originally based on the MORSE
Monte Carlo code but has been extensively modified to modernize the
coding, incorporate more flexibility in terms of sources/tallies, and
read a user-friendly block/keyword style input.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hMuch of the input to MAVRIC is the same as Monaco. More details can be
found in the Monaco chapter of the SCALE manual (SECTIONREFERENCE).h]h/Much of the input to MAVRIC is the same as Monaco. More details can be
found in the Monaco chapter of the SCALE manual (SECTIONREFERENCE).}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubeh}(h]monacoah]h]monacoah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(hRunning MAVRICh]h/Running MAVRIC}(hj)h j'hhh!NhNubah}(h]h]h]h]h]uhh(h j$hhh!h"hM ubh;)}(hXUThe objective of a SCALE sequence is to execute several codes, passing
the output from one to the input of the next, in order to perform some
analysis—--tasks that users typically had to do in the past. MAVRIC does
this for difficult shielding problems by running approximate
discrete-ordinates calculations, constructing an importance map and
biased source for one or more tallies that the user wants to optimize in
the Monte Carlo calculation, and then using those in a forward Monaco
Monte Carlo calculation. MAVRIC also prepares the forward and adjoint
cross sections when needed. The steps of a MAVRIC sequence are listed in
:numref:`Mavric-sequence`. The user can instruct MAVRIC to run this whole sequence of
steps or just some subset of the steps to verify the
intermediate steps or to reuse previously calculated quantities in a new
analyses.h](h/XyThe objective of a SCALE sequence is to execute several codes, passing
the output from one to the input of the next, in order to perform some
analysis—–tasks that users typically had to do in the past. MAVRIC does
this for difficult shielding problems by running approximate
discrete-ordinates calculations, constructing an importance map and
biased source for one or more tallies that the user wants to optimize in
the Monte Carlo calculation, and then using those in a forward Monaco
Monte Carlo calculation. MAVRIC also prepares the forward and adjoint
cross sections when needed. The steps of a MAVRIC sequence are listed in
}(hXxThe objective of a SCALE sequence is to execute several codes, passing
the output from one to the input of the next, in order to perform some
analysis—--tasks that users typically had to do in the past. MAVRIC does
this for difficult shielding problems by running approximate
discrete-ordinates calculations, constructing an importance map and
biased source for one or more tallies that the user wants to optimize in
the Monte Carlo calculation, and then using those in a forward Monaco
Monte Carlo calculation. MAVRIC also prepares the forward and adjoint
cross sections when needed. The steps of a MAVRIC sequence are listed in
h j5hhh!NhNubhp)}(h:numref:`Mavric-sequence`h]jO)}(hj@h]h/Mavric-sequence}(hhh jBubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j>ubah}(h]h]h]h]h]refdocj refdomainjLreftypenumrefrefexplicitrefwarnjmavric-sequenceuhhoh!h"hMh j5ubh/. The user can instruct MAVRIC to run this whole sequence of
steps or just some subset of the steps to verify the
intermediate steps or to reuse previously calculated quantities in a new
analyses.}(h. The user can instruct MAVRIC to run this whole sequence of
steps or just some subset of the steps to verify the
intermediate steps or to reuse previously calculated quantities in a new
analyses.h j5hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j$hhubh;)}(hXThe MAVRIC sequence can be stopped after key points by using the
“parm= *parameter* ” operator on the “=mavric” command line, which is
the first line of the input file. The various parameters are listed in
Table :numref:`mavric-param`. These parameters allow the user to perform checks and make
changes to the importance map calculation before the actual Monte Carlo
calculation in Monaco.h](h/JThe MAVRIC sequence can be stopped after key points by using the
“parm= }(hJThe MAVRIC sequence can be stopped after key points by using the
“parm= h jihhh!NhNubhA)}(h*parameter*h]h/ parameter}(hhh jrubah}(h]h]h]h]h]uhh@h jiubh/ ” operator on the “=mavric” command line, which is
the first line of the input file. The various parameters are listed in
Table }(h ” operator on the “=mavric” command line, which is
the first line of the input file. The various parameters are listed in
Table h jihhh!NhNubhp)}(h:numref:`mavric-param`h]jO)}(hjh]h/mavric-param}(hhh jubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jubah}(h]h]h]h]h]refdocj refdomainjreftypenumrefrefexplicitrefwarnjmavric-paramuhhoh!h"hMh jiubh/. These parameters allow the user to perform checks and make
changes to the importance map calculation before the actual Monte Carlo
calculation in Monaco.}(h. These parameters allow the user to perform checks and make
changes to the importance map calculation before the actual Monte Carlo
calculation in Monaco.h jihhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j$hhubh;)}(hXMAVRIC also allows the sequence to start at several different points. If
an importance map and biased source have already been computed, they can then
be used directly. If the adjoint scalar fluxes are known, they can
quickly be used to create the importance map and biased source and then
begin the forward Monte Carlo calculation. All of the different combinations of
starting MAVRIC with some previously calculated quantities are listed in
the following section detailing the input options.h]h/XMAVRIC also allows the sequence to start at several different points. If
an importance map and biased source have already been computed, they can then
be used directly. If the adjoint scalar fluxes are known, they can
quickly be used to create the importance map and biased source and then
begin the forward Monte Carlo calculation. All of the different combinations of
starting MAVRIC with some previously calculated quantities are listed in
the following section detailing the input options.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM h j$hhubh;)}(hWhen using MG cross section libraries that do not have flux-to-dose-rate
conversion factors, use “parm=nodose” to prevent the cross section
processing codes from trying to move these values into the working
library.h]h/When using MG cross section libraries that do not have flux-to-dose-rate
conversion factors, use “parm=nodose” to prevent the cross section
processing codes from trying to move these values into the working
library.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM(h j$hhubh;)}(hXMAVRIC creates many files that use the base problem name from the output
file. For an output file called “c:\path1\path2\\\ *outputName*.out” or
“/home/path1/path2/ *outputName*.inp”, spaces in the output name will
cause trouble and should not be used.h](h/~MAVRIC creates many files that use the base problem name from the output
file. For an output file called “c:path1path2\ }(h~MAVRIC creates many files that use the base problem name from the output
file. For an output file called “c:\path1\path2\\\ h jhhh!NhNubhA)}(h*outputName*h]h/
outputName}(hhh jubah}(h]h]h]h]h]uhh@h jubh/!.out” or
“/home/path1/path2/ }(h!.out” or
“/home/path1/path2/ h jhhh!NhNubhA)}(h*outputName*h]h/
outputName}(hhh jubah}(h]h]h]h]h]uhh@h jubh/M.inp”, spaces in the output name will
cause trouble and should not be used.}(hM.inp”, spaces in the output name will
cause trouble and should not be used.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM-h j$hhubj)}(hhh](h))}(hSteps in the MAVRIC sequenceh]h/Steps in the MAVRIC sequence}(hjh jubah}(h]h]h]h]h]uhh(h!h"hM2h jubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jubj)}(hhh]h}(h]h]h]h]h]jKduhjh jubj)}(hhh](j8)}(hhh](j=)}(hhh]h;)}(h**Cross section calculation**h]j;
)}(hj2h]h/Cross section calculation}(hhh j4ubah}(h]h]h]h]h]uhj:
h j0ubah}(h]h]h]h]h]uhh:h!h"hM8h j-ubah}(h]h]h]h]h]uhj<h j*ubj=)}(hhh]h;)}(hBXSProc is used to calculate the forward cross sections for Monacoh]h/BXSProc is used to calculate the forward cross sections for Monaco}(hjRh jPubah}(h]h]h]h]h]uhh:h!h"hM9h jMubah}(h]h]h]h]h]uhj<h j*ubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(h**Forward Denovo (optional)**h]j;
)}(hjrh]h/Forward Denovo (optional)}(hhh jtubah}(h]h]h]h]h]uhj:
h jpubah}(h]h]h]h]h]uhh:h!h"hM:h jmubah}(h]h]h]h]h]uhj<h jjubj=)}(hhh]h}(h]h]h]h]h]uhj<h jjubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(hCross section calculationh]h/Cross section calculation}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM<h jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hBXSProc is used to calculate the forward cross sections for Denovoh]h/BXSProc is used to calculate the forward cross sections for Denovo}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM=h jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(hForward flux calculationh]h/Forward flux calculation}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM>h jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(h2Denovo calculates the estimate of the forward fluxh]h/2Denovo calculates the estimate of the forward flux}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM?h jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(h**Adjoint Denovo (optional)**h]j;
)}(hjh]h/Adjoint Denovo (optional)}(hhh jubah}(h]h]h]h]h]uhj:
h jubah}(h]h]h]h]h]uhh:h!h"hM@h j
ubah}(h]h]h]h]h]uhj<h j
ubj=)}(hhh]h}(h]h]h]h]h]uhj<h j
ubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(hCross section calculationh]h/Cross section calculation}(hjDh jBubah}(h]h]h]h]h]uhh:h!h"hMBh j?ubah}(h]h]h]h]h]uhj<h j<ubj=)}(hhh]h;)}(hBXSProc is used to calculate the adjoint cross sections for Denovoh]h/BXSProc is used to calculate the adjoint cross sections for Denovo}(hj[h jYubah}(h]h]h]h]h]uhh:h!h"hMCh jVubah}(h]h]h]h]h]uhj<h j<ubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(hAdjoint flux calculationh]h/Adjoint flux calculation}(hj{h jyubah}(h]h]h]h]h]uhh:h!h"hMDh jvubah}(h]h]h]h]h]uhj<h jsubj=)}(hhh]h;)}(h2Denovo calculates the estimate of the adjoint fluxh]h/2Denovo calculates the estimate of the adjoint flux}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMEh jubah}(h]h]h]h]h]uhj<h jsubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(h**CADIS (optional)**h]j;
)}(hjh]h/CADIS (optional)}(hhh jubah}(h]h]h]h]h]uhj:
h jubah}(h]h]h]h]h]uhh:h!h"hMFh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hsThe scalar flux file from Denovo is then used to create the biased source distribution and transport weight windowsh]h/sThe scalar flux file from Denovo is then used to create the biased source distribution and transport weight windows}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMGh jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h j'ubj8)}(hhh](j=)}(hhh]h;)}(h**Monte Carlo calculation**h]j;
)}(hjh]h/Monte Carlo calculation}(hhh jubah}(h]h]h]h]h]uhj:
h jubah}(h]h]h]h]h]uhh:h!h"hMHh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hhMonaco uses the biased source distribution and transport weight windows to calculate the various talliesh]h/hMonaco uses the biased source distribution and transport weight windows to calculate the various tallies}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMIh j
ubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h j'ubeh}(h]h]h]h]h]uhjh jubeh}(h]h]h]h]h]colsKuhjh jubeh}(h]mavric-sequenceah]jah]mavric-sequenceah]h]jcenteruhj
h j$hhh!NhNubj)}(hhh](h))}(h7Parameters for the MAVRIC command line (“parm=…”)h]h/7Parameters for the MAVRIC command line (“parm=…”)}(hjEh jCubah}(h]h]h]h]h]uhh(h!h"hMKh j@ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jK2uhjh jQubj)}(hhh]h}(h]h]h]h]h]jK2uhjh jQubj3)}(hhh]j8)}(hhh](j=)}(hhh]h;)}(h Parameterh]h/ Parameter}(hjqh joubah}(h]h]h]h]h]uhh:h!h"hMQh jlubah}(h]h]h]h]h]uhj<h jiubj=)}(hhh]h;)}(hMAVRIC will stop afterh]h/MAVRIC will stop after}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMRh jubah}(h]h]h]h]h]uhj<h jiubeh}(h]h]h]h]h]uhj7h jfubah}(h]h]h]h]h]uhj2h jQubj)}(hhh](j8)}(hhh](j=)}(hhh]h;)}(hcheckh]h/check}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMSh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hinput checkingh]h/input checking}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMTh jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(hforinph]h/forinp}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMUh jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hHForward Denovo input construction (makes ``xkba_b.inp`` in the tmp area)h](h/)Forward Denovo input construction (makes }(h)Forward Denovo input construction (makes h jubjO)}(h``xkba_b.inp``h]h/
xkba_b.inp}(hhh jubah}(h]h]h]h]h]uhjNh jubh/ in the tmp area)}(h in the tmp area)h jubeh}(h]h]h]h]h]uhh:h!h"hMVh jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(hforwardh]h/forward}(hj3h j1ubah}(h]h]h]h]h]uhh:h!h"hMWh j.ubah}(h]h]h]h]h]uhj<h j+ubj=)}(hhh]h;)}(hThe forward Denovo calculationh]h/The forward Denovo calculation}(hjJh jHubah}(h]h]h]h]h]uhh:h!h"hMXh jEubah}(h]h]h]h]h]uhj<h j+ubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(hadjinph]h/adjinp}(hjjh jhubah}(h]h]h]h]h]uhh:h!h"hMYh jeubah}(h]h]h]h]h]uhj<h jbubj=)}(hhh]h;)}(hHAdjoint Denovo input construction (makes ``xkba_b.inp`` in the tmp area)h](h/)Adjoint Denovo input construction (makes }(h)Adjoint Denovo input construction (makes h jubjO)}(h``xkba_b.inp``h]h/
xkba_b.inp}(hhh jubah}(h]h]h]h]h]uhjNh jubh/ in the tmp area)}(h in the tmp area)h jubeh}(h]h]h]h]h]uhh:h!h"hMZh j|ubah}(h]h]h]h]h]uhj<h jbubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(hadjointh]h/adjoint}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM[h jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(hThe adjoint Denovo calculationh]h/The adjoint Denovo calculation}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM\h jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h jubj8)}(hhh](j=)}(hhh]h;)}(himpmaph]h/impmap}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM]h jubah}(h]h]h]h]h]uhj<h jubj=)}(hhh]h;)}(h/Calculation of importance map and biased sourceh]h//Calculation of importance map and biased source}(hjh jubah}(h]h]h]h]h]uhh:h!h"hM^h jubah}(h]h]h]h]h]uhj<h jubeh}(h]h]h]h]h]uhj7h jubeh}(h]h]h]h]h]uhjh jQubeh}(h]h]h]h]h]colsKuhjh j@ubeh}(h]mavric-paramah]jah]mavric-paramah]h]jcenteruhj
h j$hhh!NhNubeh}(h]running-mavricah]h]running mavricah]h]uhh#h jhhh!h"hM ubeh}(h]mavric-implementation-of-cadisah]h]mavric implementation of cadisah]h]uhh#h jhhh!h"hMubeh}(h]cadis-methodologyah]h]cadis methodologyah]h]uhh#h h%hhh!h"hK4ubh$)}(hhh](h))}(hMAVRIC inputh]h/MAVRIC input}(hjNh jLhhh!NhNubah}(h]h]h]h]h]uhh(h jIhhh!h"hMaubh;)}(hXThe input file for MAVRIC consists of three lines of text (“=mavric”
command line with optional parameters, the problem title, and SCALE
cross section library name) and then several blocks, with each block
starting with “read xxxx” and ending with “end xxxx”. There are three
required blocks and nine optional blocks. Material and geometry blocks
must be listed first and in the specified order. Other blocks may be
listed in any order.h]h/XThe input file for MAVRIC consists of three lines of text (“=mavric”
command line with optional parameters, the problem title, and SCALE
cross section library name) and then several blocks, with each block
starting with “read xxxx” and ending with “end xxxx”. There are three
required blocks and nine optional blocks. Material and geometry blocks
must be listed first and in the specified order. Other blocks may be
listed in any order.}(hj\h jZhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMch jIhhubh;)}(hBlocks (must be in this order):h]h/Blocks (must be in this order):}(hjjh jhhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMkh jIhhubh bullet_list)}(hhh](h list_item)}(h]Composition – (required) SCALE standard composition, list of materials used in the problem
h]h;)}(h\Composition – (required) SCALE standard composition, list of materials used in the problemh]h/\Composition – (required) SCALE standard composition, list of materials used in the problem}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMmh j}ubah}(h]h]h]h]h]uhj{h jxhhh!h"hNubj|)}(h,Celldata – SCALE resonance self-shielding
h]h;)}(h+Celldata – SCALE resonance self-shieldingh]h/+Celldata – SCALE resonance self-shielding}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMoh jubah}(h]h]h]h]h]uhj{h jxhhh!h"hNubj|)}(h;Geometry – (required) SCALE general geometry description
h]h;)}(h:Geometry – (required) SCALE general geometry descriptionh]h/:Geometry – (required) SCALE general geometry description}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMqh jubah}(h]h]h]h]h]uhj{h jxhhh!h"hNubj|)}(h>Array – optional addition to the above geometry description
h]h;)}(h=Array – optional addition to the above geometry descriptionh]h/=Array – optional addition to the above geometry description}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMsh jubah}(h]h]h]h]h]uhj{h jxhhh!h"hNubj|)}(h=Volume – optional calculation or listing of region volumes
h]h;)}(hubah}(h]h]h]h]h]uhj{h j#hhh!h"hNubj|)}(hfTallies – description of what to calculate: point detector tallies, region tallies, or mesh tallies
h]h;)}(heTallies – description of what to calculate: point detector tallies, region tallies, or mesh talliesh]h/eTallies – description of what to calculate: point detector tallies, region tallies, or mesh tallies}(hj\h jZubah}(h]h]h]h]h]uhh:h!h"hMh jVubah}(h]h]h]h]h]uhj{h j#hhh!h"hNubj|)}(h\Parameters – how to perform the simulation (random number seed, how many histories, etc.)
h]h;)}(h[Parameters – how to perform the simulation (random number seed, how many histories, etc.)h]h/[Parameters – how to perform the simulation (random number seed, how many histories, etc.)}(hjth jrubah}(h]h]h]h]h]uhh:h!h"hMh jnubah}(h]h]h]h]h]uhj{h j#hhh!h"hNubj|)}(h=Biasing – data for reducing the variance of the simulation
h]h;)}(hubah}(h]h]h]h]h]uhh@h j5ubeh}(h]h]h]h]h]uhh:h!h"hM6h j2ubh;)}(hSources – *Sources Block*h](h/Sources – }(hSources – h jRubhA)}(h*Sources Block*h]h/
Sources Block}(hhh j[ubah}(h]h]h]h]h]uhh@h jRubeh}(h]h]h]h]h]uhh:h!h"hM8h j2ubh;)}(hTallies – *Tallies Block*h](h/Tallies – }(hTallies – h joubhA)}(h*Tallies Block*h]h/
Tallies Block}(hhh jxubah}(h]h]h]h]h]uhh@h joubeh}(h]h]h]h]h]uhh:h!h"hM:h j2ubh;)}(hBiasing – *Biasing Block*h](h/Biasing – }(hBiasing – h jubhA)}(h*Biasing Block*h]h/
Biasing Block}(hhh jubah}(h]h]h]h]h]uhh@h jubeh}(h]h]h]h]h]uhh:h!h"hM<h j2ubeh}(h]h]h]h]h]uhj
h jhhh!h"hNubh;)}(hXRThe parameters block includes several keywords that are not included in
Monaco (see the *Parameter Block* section of the Monaco chapter (SECTIONREFERENCE)) which
are used when the cross section library used in the importance
calculations differs from the library used in the final forward
Monaco Monte Carlo calculation. The library listed at the beginning of
the MAVRIC input file will be used for the importance calculations
(forward and adjoint Denovo calculation, formation of the importance
map, and biased sources). To use a different MG library in the final
Monaco simulation, use the keyword “library=” with the cross section
library name in quotes. A cross section library for Monaco will be made
using csas-mg. If there are any extra parameters to use (“parm=” in the
“=csas-mg” line of the csas-mg input), they can be passed along using
the keyword “parmString=” with the extra information in quotes. For
example, the following input file would use a coarse-group library for
the importance calculations and a fine-group library for the final
Monaco, each with CENTRM processing.h](h/XThe parameters block includes several keywords that are not included in
Monaco (see the }(hXThe parameters block includes several keywords that are not included in
Monaco (see the h jhhh!NhNubhA)}(h*Parameter Block*h]h/Parameter Block}(hhh jubah}(h]h]h]h]h]uhh@h jubh/X section of the Monaco chapter (SECTIONREFERENCE)) which
are used when the cross section library used in the importance
calculations differs from the library used in the final forward
Monaco Monte Carlo calculation. The library listed at the beginning of
the MAVRIC input file will be used for the importance calculations
(forward and adjoint Denovo calculation, formation of the importance
map, and biased sources). To use a different MG library in the final
Monaco simulation, use the keyword “library=” with the cross section
library name in quotes. A cross section library for Monaco will be made
using csas-mg. If there are any extra parameters to use (“parm=” in the
“=csas-mg” line of the csas-mg input), they can be passed along using
the keyword “parmString=” with the extra information in quotes. For
example, the following input file would use a coarse-group library for
the importance calculations and a fine-group library for the final
Monaco, each with CENTRM processing.}(hX section of the Monaco chapter (SECTIONREFERENCE)) which
are used when the cross section library used in the importance
calculations differs from the library used in the final forward
Monaco Monte Carlo calculation. The library listed at the beginning of
the MAVRIC input file will be used for the importance calculations
(forward and adjoint Denovo calculation, formation of the importance
map, and biased sources). To use a different MG library in the final
Monaco simulation, use the keyword “library=” with the cross section
library name in quotes. A cross section library for Monaco will be made
using csas-mg. If there are any extra parameters to use (“parm=” in the
“=csas-mg” line of the csas-mg input), they can be passed along using
the keyword “parmString=” with the extra information in quotes. For
example, the following input file would use a coarse-group library for
the importance calculations and a fine-group library for the final
Monaco, each with CENTRM processing.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM>h jhhubjy)}(h=mavric parm=centrm
v7-27n19g
…
read parameters
library=”v7-200n47g” parmString=”centrm”
…
end parameters
…
end data
endh]h/=mavric parm=centrm
v7-27n19g
…
read parameters
library=”v7-200n47g” parmString=”centrm”
…
end parameters
…
end data
end}(hhh jubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMOh jhhubh;)}(hX|To use a CE cross section in the final Monaco step, use the keyword “ceLibrary=” with the cross section
library name in quotes. When the “library=” or “ceLibrary=” keywords are used, they should precede the “neutron”, “photon”,
“noNeutron”, and “noPhoton” keywords. :numref:`extra-keywords` summarizes all of the keywords in the MAVRIC parameter block.h](h/X&To use a CE cross section in the final Monaco step, use the keyword “ceLibrary=” with the cross section
library name in quotes. When the “library=” or “ceLibrary=” keywords are used, they should precede the “neutron”, “photon”,
“noNeutron”, and “noPhoton” keywords. }(hX&To use a CE cross section in the final Monaco step, use the keyword “ceLibrary=” with the cross section
library name in quotes. When the “library=” or “ceLibrary=” keywords are used, they should precede the “neutron”, “photon”,
“noNeutron”, and “noPhoton” keywords. h jhhh!NhNubhp)}(h:numref:`extra-keywords`h]jO)}(hjh]h/extra-keywords}(hhh jubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jubah}(h]h]h]h]h]refdocj refdomainjreftypenumrefrefexplicitrefwarnjextra-keywordsuhhoh!h"hMdh jubh/> summarizes all of the keywords in the MAVRIC parameter block.}(h> summarizes all of the keywords in the MAVRIC parameter block.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMdh jhhubh;)}(hXWhen using two different cross section libraries, be sure that the responses and distributions are
defined in ways that do not depend on the cross section library. For example, any response that is
just a list of n values (corresponding to a cross section library of n groups) needs to have the
group energies specifically listed so that it can be evaluated properly on the other group structure.h]h/XWhen using two different cross section libraries, be sure that the responses and distributions are
defined in ways that do not depend on the cross section library. For example, any response that is
just a list of n values (corresponding to a cross section library of n groups) needs to have the
group energies specifically listed so that it can be evaluated properly on the other group structure.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMhh jhhubj)}(hhh](h))}(h'Extra keywords for the parameters blockh]h/'Extra keywords for the parameters block}(hj*h j(ubah}(h]h]h]h]h]uhh(h!h"hMmh j%ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh j6ubj)}(hhh]j8)}(hhh]j=)}(hhh]h image)}(h#.. image:: figs/MAVRIC/table4.4.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/table4.4.png
candidates}*jXsuhjKh jHh!h"hKubah}(h]h]h]h]h]uhj<h jEubah}(h]h]h]h]h]uhj7h jBubah}(h]h]h]h]h]uhjh j6ubeh}(h]h]h]h]h]colsKuhjh j%ubeh}(h]extra-keywordsah]h]extra-keywordsah]h]jcenteruhj
h jhhh!NhNubeh}(h]other-blocks-shared-with-monacoah]h]other blocks shared with monacoah]h]uhh#h jIhhh!h"hM0ubh$)}(hhh](h))}(hImportance map blockh]h/Importance map block}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMtubh;)}(hXThe importance map block is the “heart and soul” of MAVRIC. This block lists the parameters for creating an
importance map and biased source from one (adjoint) or two (forward, followed by adjoint) Denovo
discrete-ordinates calculations. Without an importance map block, MAVRIC can be used to run Monaco
and use its conventional types of variance reduction. If both the importance map and biasing blocks
are specified, then only the importance map block will be used. The various ways to use the importance map block
are explained in the subsections below. Keywords for this block are summarized at the end of this section, in
:numref:`keywords-importance`.h](h/XwThe importance map block is the “heart and soul” of MAVRIC. This block lists the parameters for creating an
importance map and biased source from one (adjoint) or two (forward, followed by adjoint) Denovo
discrete-ordinates calculations. Without an importance map block, MAVRIC can be used to run Monaco
and use its conventional types of variance reduction. If both the importance map and biasing blocks
are specified, then only the importance map block will be used. The various ways to use the importance map block
are explained in the subsections below. Keywords for this block are summarized at the end of this section, in
}(hXwThe importance map block is the “heart and soul” of MAVRIC. This block lists the parameters for creating an
importance map and biased source from one (adjoint) or two (forward, followed by adjoint) Denovo
discrete-ordinates calculations. Without an importance map block, MAVRIC can be used to run Monaco
and use its conventional types of variance reduction. If both the importance map and biasing blocks
are specified, then only the importance map block will be used. The various ways to use the importance map block
are explained in the subsections below. Keywords for this block are summarized at the end of this section, in
h jhhh!NhNubhp)}(h:numref:`keywords-importance`h]jO)}(hjh]h/keywords-importance}(hhh jubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jubah}(h]h]h]h]h]refdocj refdomainjreftypenumrefrefexplicitrefwarnjkeywords-importanceuhhoh!h"hMvh jubh/.}(hjh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMvh jhhubh$)}(hhh](h))}(h3Constructing a mesh for the S\ :sub:`N` calculationh](h/Constructing a mesh for the S }(hConstructing a mesh for the S\ h jhhh!NhNubj )}(h:sub:`N`h]h/N}(hhh jubah}(h]h]h]h]h]uhj h jubh/ calculation}(h calculationh jhhh!NhNubeh}(h]h]h]h]h]uhh(h jhhh!h"hMubh;)}(hX?All uses of the importance map block that run the
discrete-ordinates code require the use of a grid geometry that overlays
the physical geometry. Grid geometries are defined in the definitions
block of the MAVRIC input. The extent and level of detail needed in a
grid geometry are discussed in the following paragraphs.h]h/X?All uses of the importance map block that run the
discrete-ordinates code require the use of a grid geometry that overlays
the physical geometry. Grid geometries are defined in the definitions
block of the MAVRIC input. The extent and level of detail needed in a
grid geometry are discussed in the following paragraphs.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hXWhen using S\ :sub:`N` methods alone for solving radiation transport in
shielding problems, a good rule of thumb is to use mesh cell sizes on
the order of a meanfree path of the particle. In complex shielding
problems, this could lead to an extremely large number of mesh cells,
especially when considering the size of the meanfree path of the lowest
energy neutrons and photons in common shielding materials.h](h/When using S }(hWhen using S\ h jhhh!NhNubj )}(h:sub:`N`h]h/N}(hhh jubah}(h]h]h]h]h]uhj h jubh/X methods alone for solving radiation transport in
shielding problems, a good rule of thumb is to use mesh cell sizes on
the order of a meanfree path of the particle. In complex shielding
problems, this could lead to an extremely large number of mesh cells,
especially when considering the size of the meanfree path of the lowest
energy neutrons and photons in common shielding materials.}(hX methods alone for solving radiation transport in
shielding problems, a good rule of thumb is to use mesh cell sizes on
the order of a meanfree path of the particle. In complex shielding
problems, this could lead to an extremely large number of mesh cells,
especially when considering the size of the meanfree path of the lowest
energy neutrons and photons in common shielding materials.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hXIn MAVRIC, the goal is to use the S\ :sub:`N` calculation for a quick
approximate solution. Accuracy is not paramount—just getting an idea of
the overall shape of the true importance map will help accelerate the
convergence of the forward Monte Carlo calculation. The more accurate
the importance map, the better the forward Monte Carlo acceleration will
be. At some point there is a time trade-off when the computational time
for calculating the importance map followed by the time to perform the Monte Carlo
calculation exceeds that of a standard analog Monte Carlo calculation.
Large numbers of mesh cells that result from using very small mesh sizes
for S\ :sub:`N` calculations also use a great deal of computer memory.h](h/%In MAVRIC, the goal is to use the S }(h%In MAVRIC, the goal is to use the S\ h jhhh!NhNubj )}(h:sub:`N`h]h/N}(hhh j(ubah}(h]h]h]h]h]uhj h jubh/Xj calculation for a quick
approximate solution. Accuracy is not paramount—just getting an idea of
the overall shape of the true importance map will help accelerate the
convergence of the forward Monte Carlo calculation. The more accurate
the importance map, the better the forward Monte Carlo acceleration will
be. At some point there is a time trade-off when the computational time
for calculating the importance map followed by the time to perform the Monte Carlo
calculation exceeds that of a standard analog Monte Carlo calculation.
Large numbers of mesh cells that result from using very small mesh sizes
for S }(hXj calculation for a quick
approximate solution. Accuracy is not paramount—just getting an idea of
the overall shape of the true importance map will help accelerate the
convergence of the forward Monte Carlo calculation. The more accurate
the importance map, the better the forward Monte Carlo acceleration will
be. At some point there is a time trade-off when the computational time
for calculating the importance map followed by the time to perform the Monte Carlo
calculation exceeds that of a standard analog Monte Carlo calculation.
Large numbers of mesh cells that result from using very small mesh sizes
for S\ h jhhh!NhNubj )}(h:sub:`N`h]h/N}(hhh j;ubah}(h]h]h]h]h]uhj h jubh/7 calculations also use a great deal of computer memory.}(h7 calculations also use a great deal of computer memory.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubh;)}(hXBecause the deterministic solution(s) for CADIS and FW-CADIS can have
moderate fidelity and still provide variance reduction parameters that
substantially accelerate the Monte Carlo solution, mesh cell sizes in
MAVRIC applications can be larger than what most S\ :sub:`N` practioners
would typically use. The use of relatively coarse mesh reduces memory
requirements and the run time of the deterministic solution(s). Some
general guidelines to keep in mind when creating a mesh for the
importance map/biased source are as follows:h](h/XBecause the deterministic solution(s) for CADIS and FW-CADIS can have
moderate fidelity and still provide variance reduction parameters that
substantially accelerate the Monte Carlo solution, mesh cell sizes in
MAVRIC applications can be larger than what most S }(hXBecause the deterministic solution(s) for CADIS and FW-CADIS can have
moderate fidelity and still provide variance reduction parameters that
substantially accelerate the Monte Carlo solution, mesh cell sizes in
MAVRIC applications can be larger than what most S\ h jThhh!NhNubj )}(h:sub:`N`h]h/N}(hhh j]ubah}(h]h]h]h]h]uhj h jTubh/X practioners
would typically use. The use of relatively coarse mesh reduces memory
requirements and the run time of the deterministic solution(s). Some
general guidelines to keep in mind when creating a mesh for the
importance map/biased source are as follows:}(hX practioners
would typically use. The use of relatively coarse mesh reduces memory
requirements and the run time of the deterministic solution(s). Some
general guidelines to keep in mind when creating a mesh for the
importance map/biased source are as follows:h jThhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jhhubjw)}(hhh](j|)}(h]The true source regions should be included in the mesh with mesh
planes at their boundaries.
h]h;)}(h\The true source regions should be included in the mesh with mesh
planes at their boundaries.h]h/\The true source regions should be included in the mesh with mesh
planes at their boundaries.}(hjh j}ubah}(h]h]h]h]h]uhh:h!h"hMh jyubah}(h]h]h]h]h]uhj{h jvhhh!h"hNubj|)}(hXPlace point or very small sources in the center of a mesh cell, not on the mesh planes.
h]h;)}(hWPlace point or very small sources in the center of a mesh cell, not on the mesh planes.h]h/WPlace point or very small sources in the center of a mesh cell, not on the mesh planes.}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj{h jvhhh!h"hNubj|)}(hAny region of the geometry where particles could eventually
contribute to the tallies (the “important” areas) should be included
in the mesh.
h]h;)}(hAny region of the geometry where particles could eventually
contribute to the tallies (the “important” areas) should be included
in the mesh.h]h/Any region of the geometry where particles could eventually
contribute to the tallies (the “important” areas) should be included
in the mesh.}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj{h jvhhh!h"hNubj|)}(hXPoint adjoint sources (corresponding to point detector locations) in
standard CADIS calculations do not have to be included inside the
mesh. For FW-CADIS, they must be in the mesh and should be located at
a mesh cell center, not on any of the mesh planes.
h]h;)}(hPoint adjoint sources (corresponding to point detector locations) in
standard CADIS calculations do not have to be included inside the
mesh. For FW-CADIS, they must be in the mesh and should be located at
a mesh cell center, not on any of the mesh planes.h]h/Point adjoint sources (corresponding to point detector locations) in
standard CADIS calculations do not have to be included inside the
mesh. For FW-CADIS, they must be in the mesh and should be located at
a mesh cell center, not on any of the mesh planes.}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj{h jvhhh!h"hNubj|)}(h`Volumetric adjoint sources should be included in the mesh with mesh
planes at their boundaries.
h]h;)}(h_Volumetric adjoint sources should be included in the mesh with mesh
planes at their boundaries.h]h/_Volumetric adjoint sources should be included in the mesh with mesh
planes at their boundaries.}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj{h jvhhh!h"hNubj|)}(hAMesh planes should be placed at significant material boundaries.
h]h;)}(h@Mesh planes should be placed at significant material boundaries.h]h/@Mesh planes should be placed at significant material boundaries.}(hjh jubah}(h]h]h]h]h]uhh:h!h"hMh jubah}(h]h]h]h]h]uhj{h jvhhh!h"hNubj|)}(hubah}(h]h]h]h]h]uhh@h j5ubh/ = sampled fraction of material }(h = sampled fraction of material h j5hhh!NhNubhA)}(h*m*h]h/m}(hhh jQubah}(h]h]h]h]h]uhh@h j5ubh/ in the voxel,}(h in the voxel,h j5hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM@h j]hhubh;)}(h(*d* = direction of the rays (*x, y, z*),h](hA)}(h*d*h]h/d}(hhh jnubah}(h]h]h]h]h]uhh@h jjubh/ = direction of the rays (}(h = direction of the rays (h jjhhh!NhNubhA)}(h *x, y, z*h]h/x, y, z}(hhh jubah}(h]h]h]h]h]uhh@h jjubh/),}(h),h jjhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMBh j]hhubh;)}(h*r* = ray number,h](hA)}(h*r*h]h/r}(hhh jubah}(h]h]h]h]h]uhh@h jubh/ = ray number,}(h = ray number,h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMDh j]hhubh;)}(hE:math:`N_r` = total number of rays in the voxel for direction of *d*,h](j
)}(h:math:`N_r`h]h/N_r}(hhh jubah}(h]h]h]h]h]uhjh jubh/6 = total number of rays in the voxel for direction of }(h6 = total number of rays in the voxel for direction of h jhhh!NhNubhA)}(h*d*h]h/d}(hhh jubah}(h]h]h]h]h]uhh@h jubh/,}(hj
h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMFh j]hhubh;)}(h*s* = step number,h](hA)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhh@h jubh/ = step number,}(h = step number,h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMHh j]hhubh;)}(hP:math:`N_s` = total number of steps for ray r in the voxel for direction of
*d*,h](j
)}(h:math:`N_s`h]h/N_s}(hhh jubah}(h]h]h]h]h]uhjh jubh/A = total number of steps for ray r in the voxel for direction of
}(hA = total number of steps for ray r in the voxel for direction of
h jhhh!NhNubhA)}(h*d*h]h/d}(hhh jubah}(h]h]h]h]h]uhh@h jubh/,}(hj
h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMJh j]hhubh;)}(hV:math:`L_{d,r,s}` = length of the steps s for ray r in the voxel for direction
of *d*,h](j
)}(h:math:`L_{d,r,s}`h]h/ L_{d,r,s}}(hhh j6ubah}(h]h]h]h]h]uhjh j2ubh/A = length of the steps s for ray r in the voxel for direction
of }(hA = length of the steps s for ray r in the voxel for direction
of h j2hhh!NhNubhA)}(h*d*h]h/d}(hhh jIubah}(h]h]h]h]h]uhh@h j2ubh/,}(hj
h j2hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMMh j]hhubh;)}(h9:math:`L_d` = length of the voxel along direction of *d*,h](j
)}(h:math:`L_d`h]h/L_d}(hhh jeubah}(h]h]h]h]h]uhjh jaubh/* = length of the voxel along direction of }(h* = length of the voxel along direction of h jahhh!NhNubhA)}(h*d*h]h/d}(hhh jxubah}(h]h]h]h]h]uhh@h jaubh/,}(hj
h jahhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMPh j]hhubh;)}(h#:math:`m_s` = material of step *s*,h](j
)}(h:math:`m_s`h]h/m_s}(hhh jubah}(h]h]h]h]h]uhjh jubh/ = material of step }(h = material of step h jhhh!NhNubhA)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhh@h jubh/,}(hj
h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMRh j]hhubh;)}(h*m* = material number,h](hA)}(h*m*h]h/m}(hhh jubah}(h]h]h]h]h]uhh@h jubh/ = material number,}(h = material number,h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMTh j]hhubh;)}(h9:math:`N_m` = total number of materials in the voxel, andh](j
)}(h:math:`N_m`h]h/N_m}(hhh jubah}(h]h]h]h]h]uhjh jubh/. = total number of materials in the voxel, and}(h. = total number of materials in the voxel, andh jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMVh j]hhubh;)}(h9:math:`V_m` = volume fraction of material m in the voxel.h](j
)}(h:math:`V_m`h]h/V_m}(hhh jubah}(h]h]h]h]h]uhjh jubh/. = volume fraction of material m in the voxel.}(h. = volume fraction of material m in the voxel.h jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMXh j]hhubeh}(h]ray-tracingah]h]ray tracingah]h]uhh#h jnhhh!h"hMubh$)}(hhh](h))}(h
Point Testingh]h/
Point Testing}(hj# h j! hhh!NhNubah}(h]h]h]h]h]uhh(h j hhh!h"hM[ubh;)}(hXThe recursive bisection method is utilized in point testing and uses a
series of point tests to determine the macromaterial fractions. For a
given voxel, the material at the center is compared to the material at
the eight corners. If they are all the same, then the entire volume is
considered to be made of that material. If they are different, then the volume is
divided into two in each dimension. Each subvolume is tested, and the
method is then applied to the subvolumes that are not of a single
material. When the ratio of the volume of the tested region to the
original voxel becomes less than a user-specified tolerance (in the
range of 10-1 to 10-4), then further subdivision and testing are
stopped. This is illustrated in :numref:`rec-macro`.h](h/XThe recursive bisection method is utilized in point testing and uses a
series of point tests to determine the macromaterial fractions. For a
given voxel, the material at the center is compared to the material at
the eight corners. If they are all the same, then the entire volume is
considered to be made of that material. If they are different, then the volume is
divided into two in each dimension. Each subvolume is tested, and the
method is then applied to the subvolumes that are not of a single
material. When the ratio of the volume of the tested region to the
original voxel becomes less than a user-specified tolerance (in the
range of 10-1 to 10-4), then further subdivision and testing are
stopped. This is illustrated in }(hXThe recursive bisection method is utilized in point testing and uses a
series of point tests to determine the macromaterial fractions. For a
given voxel, the material at the center is compared to the material at
the eight corners. If they are all the same, then the entire volume is
considered to be made of that material. If they are different, then the volume is
divided into two in each dimension. Each subvolume is tested, and the
method is then applied to the subvolumes that are not of a single
material. When the ratio of the volume of the tested region to the
original voxel becomes less than a user-specified tolerance (in the
range of 10-1 to 10-4), then further subdivision and testing are
stopped. This is illustrated in h j/ hhh!NhNubhp)}(h:numref:`rec-macro`h]jO)}(hj: h]h/ rec-macro}(hhh j< ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j8 ubah}(h]h]h]h]h]refdocj refdomainjF reftypenumrefrefexplicitrefwarnj rec-macrouhhoh!h"hM]h j/ ubh/.}(hjh j/ hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM]h j hhubh)}(h.. _rec-macro:h]h}(h]h]h]h]h]h rec-macrouhh
hMkh j hhh!h"ubj)}(hhh]jL)}(h9.. figure:: figs/MAVRIC/rec-macro.png
:width: 99 %
h]h}(h]h]h]h]h]width99%urifigs/MAVRIC/rec-macro.pngjY}j[j} suhjKh jm h!h"hNubah}(h]jl ah]h] rec-macroah]h]jjuhjh j hhh!h"hNj}j jb sj}jl jb subhcentered)}(h=Fig. 4 Successive steps in the recursive macromaterial methodh]hA)}(h?*Fig. 4 Successive steps in the recursive macromaterial method*h]h/=Fig. 4 Successive steps in the recursive macromaterial method}(hhh j ubah}(h]h]h]h]h]uhh@h j ubah}(h]h]h]h]h]uhj h j hhh!h"hMtubh;)}(hXlIn point testing, the keyword “mmTolerance=f” is interpreted to be where *f* is the smallest
fraction of the voxel volume that can be achieved by bisection method and hence the limiting
factor for dividing the voxel. This same tolerance *f* is also used to limit the number of macromaterials.
Before a new macromaterial is created, if one already exists where the fraction of each actual
material matches to within the given tolerance, then the existing material will be used. If
using only a single point at the center of each voxel, then use “mmTolerance=1”.
The mmSubCell keyword is not used in point testing.h](h/MIn point testing, the keyword “mmTolerance=f” is interpreted to be where }(hMIn point testing, the keyword “mmTolerance=f” is interpreted to be where h j hhh!NhNubhA)}(h*f*h]h/f}(hhh j ubah}(h]h]h]h]h]uhh@h j ubh/ is the smallest
fraction of the voxel volume that can be achieved by bisection method and hence the limiting
factor for dividing the voxel. This same tolerance }(h is the smallest
fraction of the voxel volume that can be achieved by bisection method and hence the limiting
factor for dividing the voxel. This same tolerance h j hhh!NhNubhA)}(h*f*h]h/f}(hhh j ubah}(h]h]h]h]h]uhh@h j ubh/Xx is also used to limit the number of macromaterials.
Before a new macromaterial is created, if one already exists where the fraction of each actual
material matches to within the given tolerance, then the existing material will be used. If
using only a single point at the center of each voxel, then use “mmTolerance=1”.
The mmSubCell keyword is not used in point testing.}(hXx is also used to limit the number of macromaterials.
Before a new macromaterial is created, if one already exists where the fraction of each actual
material matches to within the given tolerance, then the existing material will be used. If
using only a single point at the center of each voxel, then use “mmTolerance=1”.
The mmSubCell keyword is not used in point testing.h j hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMuh j hhubeh}(h]
point-testingah]h]
point testingah]h]uhh#h jnhhh!h"hM[ubh$)}(hhh](h))}(hExampleh]h/Example}(hj h j hhh!NhNubah}(h]h]h]h]h]uhh(h j hhh!h"hM~ubh;)}(hX:numref:`cask-geom` shows an example of a cask geometry with two types of spent fuel (yellows),
steel (blue), resin (green), and other metals (gray). When the Denovo geometry is set up by
testing only the center of each mesh cell, the curved surfaces are not well represented (upper right).
By applying the ray-tracing method and defining a new material made of partial fractions of the original materials,
an improved Denovo model can be made. In the lower left of the figure, the Denovo
model was constructed using one ray (in each dimension) per voxel and a tolerance of 0.1.
This gives 20 new materials that are a mixture of the original 13 actual materials and void.
With mmSubCells=3 and an mmTolerance=0.01, 139 macromaterials are created.h](hp)}(h:numref:`cask-geom`h]jO)}(hj h]h/ cask-geom}(hhh j ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j ubah}(h]h]h]h]h]refdocj refdomainj!reftypenumrefrefexplicitrefwarnj cask-geomuhhoh!h"hMh j ubh/X shows an example of a cask geometry with two types of spent fuel (yellows),
steel (blue), resin (green), and other metals (gray). When the Denovo geometry is set up by
testing only the center of each mesh cell, the curved surfaces are not well represented (upper right).
By applying the ray-tracing method and defining a new material made of partial fractions of the original materials,
an improved Denovo model can be made. In the lower left of the figure, the Denovo
model was constructed using one ray (in each dimension) per voxel and a tolerance of 0.1.
This gives 20 new materials that are a mixture of the original 13 actual materials and void.
With mmSubCells=3 and an mmTolerance=0.01, 139 macromaterials are created.}(hX shows an example of a cask geometry with two types of spent fuel (yellows),
steel (blue), resin (green), and other metals (gray). When the Denovo geometry is set up by
testing only the center of each mesh cell, the curved surfaces are not well represented (upper right).
By applying the ray-tracing method and defining a new material made of partial fractions of the original materials,
an improved Denovo model can be made. In the lower left of the figure, the Denovo
model was constructed using one ray (in each dimension) per voxel and a tolerance of 0.1.
This gives 20 new materials that are a mixture of the original 13 actual materials and void.
With mmSubCells=3 and an mmTolerance=0.01, 139 macromaterials are created.h j hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j hhubh;)}(hXA macromaterial table listing the fractions of each macromaterial is saved to a file called “outputName.mmt”,
where outputName is the name the user chose for his or her output file. This file can be used by the Mesh File
Viewer to display the macromaterials as mixtures of the actual materials, as seen in the lower row of :numref:`cask-geom`.
See the Mesh File Viewer help pages for more information on how to use colormap files and macromaterial tables.h](h/XGA macromaterial table listing the fractions of each macromaterial is saved to a file called “outputName.mmt”,
where outputName is the name the user chose for his or her output file. This file can be used by the Mesh File
Viewer to display the macromaterials as mixtures of the actual materials, as seen in the lower row of }(hXGA macromaterial table listing the fractions of each macromaterial is saved to a file called “outputName.mmt”,
where outputName is the name the user chose for his or her output file. This file can be used by the Mesh File
Viewer to display the macromaterials as mixtures of the actual materials, as seen in the lower row of h j!hhh!NhNubhp)}(h:numref:`cask-geom`h]jO)}(hj*!h]h/ cask-geom}(hhh j,!ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j(!ubah}(h]h]h]h]h]refdocj refdomainj6!reftypenumrefrefexplicitrefwarnj cask-geomuhhoh!h"hMh j!ubh/q.
See the Mesh File Viewer help pages for more information on how to use colormap files and macromaterial tables.}(hq.
See the Mesh File Viewer help pages for more information on how to use colormap files and macromaterial tables.h j!hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j hhubh)}(h.. _cask-geom:h]h}(h]h]h]h]h]h cask-geomuhh
hMh j hhh!h"ubj)}(hhh](jL)}(hX8.. figure:: figs/MAVRIC/cask-geom.png
Cask geometry model (upper left) and the Denovo representation using cell center testing (upper right). Representations using macromaterials determined by ray tracing are shown for mmSubCell=1/mmTolerance=0.1 (lower left) and mmSubCell=3/mmTolerance=0.01 (lower right).*
h]h}(h]h]h]h]h]urifigs/MAVRIC/cask-geom.pngjY}j[jl!suhjKh j^!h!h"hMubj)}(hXCask geometry model (upper left) and the Denovo representation using cell center testing (upper right). Representations using macromaterials determined by ray tracing are shown for mmSubCell=1/mmTolerance=0.1 (lower left) and mmSubCell=3/mmTolerance=0.01 (lower right).*h]h/XCask geometry model (upper left) and the Denovo representation using cell center testing (upper right). Representations using macromaterials determined by ray tracing are shown for mmSubCell=1/mmTolerance=0.1 (lower left) and mmSubCell=3/mmTolerance=0.01 (lower right).*}(hjp!h jn!ubah}(h]h]h]h]h]uhjh!h"hMh j^!ubeh}(h](id30j]!eh]h] cask-geomah]h]jjuhjhMh j hhh!h"j}j!jS!sj}j]!jS!subeh}(h]exampleah]h]exampleah]h]uhh#h jnhhh!h"hM~ubeh}(h]( macromaterials-for-sn-geometriesjeeh]h]( macromaterials for sn geometriesmacromaterialseh]h]uhh#h jhhh!h"hMj}j!j[sj}jej[subh$)}(hhh](h))}(h#Optimizing source/detector problemsh]h/#Optimizing source/detector problems}(hj!h j!hhh!NhNubah}(h]h]h]h]h]uhh(h j!hhh!h"hMubh;)}(hXFor standard source/detector problems in which one tally is to be optimized
in the forward Monte Carlo calculation, an adjoint source based on that
tally must be constructed. An adjoint source requires a unique and
positive identification number, a physical location, and an energy
spectrum. The adjoint source location can be specified either by (1) a
point location (“locationID=” keyword) or (2) a volume described by a
box (“boundingBox” array). A bounding box is specified by maximum and
minimum extent in each dimension—\ :math:`x_{max}` :math:`x_{min}` :math:`y_{max}` :math:`y_{min}` :math:`z_{max}`
:math:`z_{min}`—in global coordinates. The boundingBox should not be degenerate
(should have volume>0) but can be optionally limited to areas matching a
given unit number (“unit=”), a given region number (“region=”), or a
given material mixture number (“mixture=”). A mixture and a region
cannot both be specified, since that would either be redundant or
mutually exclusive. The energy spectrum of an adjoint source is a
response function (“responseID=”) listing one of the ID numbers of the
responses defined in the definitions block. An optional weight can be
assigned to each adjoint source using the “weight=” keyword. If not
given, the default weight is 1.0.h](h/XFor standard source/detector problems in which one tally is to be optimized
in the forward Monte Carlo calculation, an adjoint source based on that
tally must be constructed. An adjoint source requires a unique and
positive identification number, a physical location, and an energy
spectrum. The adjoint source location can be specified either by (1) a
point location (“locationID=” keyword) or (2) a volume described by a
box (“boundingBox” array). A bounding box is specified by maximum and
minimum extent in each dimension— }(hXFor standard source/detector problems in which one tally is to be optimized
in the forward Monte Carlo calculation, an adjoint source based on that
tally must be constructed. An adjoint source requires a unique and
positive identification number, a physical location, and an energy
spectrum. The adjoint source location can be specified either by (1) a
point location (“locationID=” keyword) or (2) a volume described by a
box (“boundingBox” array). A bounding box is specified by maximum and
minimum extent in each dimension—\ h j!hhh!NhNubj
)}(h:math:`x_{max}`h]h/x_{max}}(hhh j!ubah}(h]h]h]h]h]uhjh j!ubh/ }(hhh j!hhh!NhNubj
)}(h:math:`x_{min}`h]h/x_{min}}(hhh j!ubah}(h]h]h]h]h]uhjh j!ubh/ }(hhh j!ubj
)}(h:math:`y_{max}`h]h/y_{max}}(hhh j!ubah}(h]h]h]h]h]uhjh j!ubh/ }(hhh j!ubj
)}(h:math:`y_{min}`h]h/y_{min}}(hhh j!ubah}(h]h]h]h]h]uhjh j!ubh/ }(hhh j!ubj
)}(h:math:`z_{max}`h]h/z_{max}}(hhh j!ubah}(h]h]h]h]h]uhjh j!ubh/
}(hjh j!hhh!NhNubj
)}(h:math:`z_{min}`h]h/z_{min}}(hhh j
"ubah}(h]h]h]h]h]uhjh j!ubh/X—in global coordinates. The boundingBox should not be degenerate
(should have volume>0) but can be optionally limited to areas matching a
given unit number (“unit=”), a given region number (“region=”), or a
given material mixture number (“mixture=”). A mixture and a region
cannot both be specified, since that would either be redundant or
mutually exclusive. The energy spectrum of an adjoint source is a
response function (“responseID=”) listing one of the ID numbers of the
responses defined in the definitions block. An optional weight can be
assigned to each adjoint source using the “weight=” keyword. If not
given, the default weight is 1.0.}(hX—in global coordinates. The boundingBox should not be degenerate
(should have volume>0) but can be optionally limited to areas matching a
given unit number (“unit=”), a given region number (“region=”), or a
given material mixture number (“mixture=”). A mixture and a region
cannot both be specified, since that would either be redundant or
mutually exclusive. The energy spectrum of an adjoint source is a
response function (“responseID=”) listing one of the ID numbers of the
responses defined in the definitions block. An optional weight can be
assigned to each adjoint source using the “weight=” keyword. If not
given, the default weight is 1.0.h j!hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j!hhubh;)}(hX?For example, to optimize a region tally, the user would construct an
adjoint source located in the same place as the tally, with an adjoint
source spectrum equal to the response function that the tally is
computing. Note that the grid geometry 1 and response function 3 must
already be defined in the definitions block.h]h/X?For example, to optimize a region tally, the user would construct an
adjoint source located in the same place as the tally, with an adjoint
source spectrum equal to the response function that the tally is
computing. Note that the grid geometry 1 and response function 3 must
already be defined in the definitions block.}(hj("h j&"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j!hhubjy)}(hread importanceMap
gridGeometryID=1
adjointSource 24
boundingBox 12.0 10.0 5.0 -5.0 10.0 -10.0
unit=1 region=5
responseID=3
end adjointSource
end importanceMaph]h/read importanceMap
gridGeometryID=1
adjointSource 24
boundingBox 12.0 10.0 5.0 -5.0 10.0 -10.0
unit=1 region=5
responseID=3
end adjointSource
end importanceMap}(hhh j4"ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j!hhubh;)}(hFor optimizing a point detector for the calculation of total photon flux,
the importance map block would look like the following:h]h/For optimizing a point detector for the calculation of total photon flux,
the importance map block would look like the following:}(hjH"h jF"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j!hhubjy)}(hread importanceMap
adjointSource 21
locationID=4
responseID=1
end adjointSource
gridGeometryID=1
end importanceMaph]h/read importanceMap
adjointSource 21
locationID=4
responseID=1
end adjointSource
gridGeometryID=1
end importanceMap}(hhh jT"ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j!hhubh;)}(hwhere location 4 is the same location used by the point detector. To calculate total photon flux, response function 1 must be defined in the definitions block similar to this response:h]h/where location 4 is the same location used by the point detector. To calculate total photon flux, response function 1 must be defined in the definitions block similar to this response:}(hjh"h jf"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j!hhubjy)}(hiread definitions
response 1
values 27r0.0 19r1. end
end response
…
end definitionsh]h/iread definitions
response 1
values 27r0.0 19r1. end
end response
…
end definitions}(hhh jt"ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j!hhubh;)}(hThis response is used for computing total photon flux for the 27 neutron/19 photon group coupled cross section library or like this responseh]h/This response is used for computing total photon flux for the 27 neutron/19 photon group coupled cross section library or like this response}(hj"h j"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j!hhubjy)}(hread definitions
response 1
photon
bounds 1000.0 2.0e7 end
values 1.0 1.0 end
end response
…
end definitionsh]h/read definitions
response 1
photon
bounds 1000.0 2.0e7 end
values 1.0 1.0 end
end response
…
end definitions}(hhh j"ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j!hhubh;)}(h2which is independent of the cross section library.h]h/2which is independent of the cross section library.}(hj"h j"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j!hhubeh}(h]#optimizing-source-detector-problemsah]h]#optimizing source/detector problemsah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(hMultiple adjoint sourcesh]h/Multiple adjoint sources}(hj"h j"hhh!NhNubah}(h]h]h]h]h]uhh(h j"hhh!h"hMubh;)}(hIf there are several tallies in very close proximity and/or several different responses being calculated by the tallies, multiple adjoint sources can be used.h]h/If there are several tallies in very close proximity and/or several different responses being calculated by the tallies, multiple adjoint sources can be used.}(hj"h j"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j"hhubjy)}(hread importanceMap
gridGeometryID=1
adjointSource 1
locationID=4 responseID=20
end adjointSource
adjointSource 2
locationID=5 responseID=21
weight=2.0
end adjointSource
end importanceMaph]h/read importanceMap
gridGeometryID=1
adjointSource 1
locationID=4 responseID=20
end adjointSource
adjointSource 2
locationID=5 responseID=21
weight=2.0
end adjointSource
end importanceMap}(hhh j"ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j"hhubh;)}(htNote that adjoint sources using point locations can be mixed with volumetric adjoint sources (using bounding boxes).h]h/tNote that adjoint sources using point locations can be mixed with volumetric adjoint sources (using bounding boxes).}(hj"h j"hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j"hhubeh}(h]multiple-adjoint-sourcesah]h]multiple adjoint sourcesah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(h+Options for Denovo :math:`S_n` calculationsh](h/Options for Denovo }(hOptions for Denovo h j#hhh!NhNubj
)}(h:math:`S_n`h]h/S_n}(hhh j#ubah}(h]h]h]h]h]uhjh j#ubh/
calculations}(h
calculationsh j#hhh!NhNubeh}(h]h]h]h]h]uhh(h j#hhh!h"hMubh;)}(hX4While the default values for various calculational parameters and settings used by Denovo for
the MAVRIC sequence should cover most applications, they can be changed if desired.
The two most basic parameters are the quadrature set used for the discrete ordinates and
the order of the Legendre polynomials used in describing the angular scattering.
The default quadrature order that MAVRIC uses is a level symmetric :math:`S_8` set, and the
default scattering order is :math:`P_3` (or the maximum number of coefficients contained in the
cross-section library if less than 3). :math:`S_8`/ :math:`P_3` is an adequate choice for many applications,
but the user is free to changes these. For complex ducts or transport over large distances at small angles,
:math:`S_{12}` may be required. :math:`S_4`/ :math:`P_1` or even :math:`S_2`/ :math:`P_0` would be useful in doing a very cursory run to confirm that the
problem was input correctly, but this would likely be inadequate for weight window generation in a problem
that is complex enough to require advanced variance reduction.h](h/XWhile the default values for various calculational parameters and settings used by Denovo for
the MAVRIC sequence should cover most applications, they can be changed if desired.
The two most basic parameters are the quadrature set used for the discrete ordinates and
the order of the Legendre polynomials used in describing the angular scattering.
The default quadrature order that MAVRIC uses is a level symmetric }(hXWhile the default values for various calculational parameters and settings used by Denovo for
the MAVRIC sequence should cover most applications, they can be changed if desired.
The two most basic parameters are the quadrature set used for the discrete ordinates and
the order of the Legendre polynomials used in describing the angular scattering.
The default quadrature order that MAVRIC uses is a level symmetric h j(#hhh!NhNubj
)}(h:math:`S_8`h]h/S_8}(hhh j1#ubah}(h]h]h]h]h]uhjh j(#ubh/* set, and the
default scattering order is }(h* set, and the
default scattering order is h j(#hhh!NhNubj
)}(h:math:`P_3`h]h/P_3}(hhh jD#ubah}(h]h]h]h]h]uhjh j(#ubh/` (or the maximum number of coefficients contained in the
cross-section library if less than 3). }(h` (or the maximum number of coefficients contained in the
cross-section library if less than 3). h j(#hhh!NhNubj
)}(h:math:`S_8`h]h/S_8}(hhh jW#ubah}(h]h]h]h]h]uhjh j(#ubh// }(h/ h j(#hhh!NhNubj
)}(h:math:`P_3`h]h/P_3}(hhh jj#ubah}(h]h]h]h]h]uhjh j(#ubh/ is an adequate choice for many applications,
but the user is free to changes these. For complex ducts or transport over large distances at small angles,
}(h is an adequate choice for many applications,
but the user is free to changes these. For complex ducts or transport over large distances at small angles,
h j(#hhh!NhNubj
)}(h:math:`S_{12}`h]h/S_{12}}(hhh j}#ubah}(h]h]h]h]h]uhjh j(#ubh/ may be required. }(h may be required. h j(#hhh!NhNubj
)}(h:math:`S_4`h]h/S_4}(hhh j#ubah}(h]h]h]h]h]uhjh j(#ubh// }(h/ h j(#ubj
)}(h:math:`P_1`h]h/P_1}(hhh j#ubah}(h]h]h]h]h]uhjh j(#ubh/ or even }(h or even h j(#hhh!NhNubj
)}(h:math:`S_2`h]h/S_2}(hhh j#ubah}(h]h]h]h]h]uhjh j(#ubh// }(hji#h j(#ubj
)}(h:math:`P_0`h]h/P_0}(hhh j#ubah}(h]h]h]h]h]uhjh j(#ubh/ would be useful in doing a very cursory run to confirm that the
problem was input correctly, but this would likely be inadequate for weight window generation in a problem
that is complex enough to require advanced variance reduction.}(h would be useful in doing a very cursory run to confirm that the
problem was input correctly, but this would likely be inadequate for weight window generation in a problem
that is complex enough to require advanced variance reduction.h j(#hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j#hhubh;)}(hThese and other Denovo options are applied to both
the forward and the adjoint calculations that are required from the
inputs given in the importance map block.h]h/These and other Denovo options are applied to both
the forward and the adjoint calculations that are required from the
inputs given in the importance map block.}(hj#h j#hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j#hhubh;)}(hXLIn problems with small sources or media that are not highly scattering,
discrete ordinates can suffer from "ray effects" :cite:`lathrop_ray_1968,lathrop_remedies_1971`
where artifacts of the discrete quadrature directions can be seen in the
computed fluxes. Denovo has a
first-collision capability to help alleviate ray effects. This method
computes the uncollided flux in each mesh cell from a point source. The
uncollided fluxes are then used as a distributed source in the main
discrete-ordinates solution. At the end of the main calculation, the
uncollided fluxes are added to the fluxes computed with the first
collision source, forming the total flux. While this helps reduce ray
effects in many problems, the first-collision capability can take a
significant amount of time to compute on a mesh with many cells or for
many point sources.h](h/}In problems with small sources or media that are not highly scattering,
discrete ordinates can suffer from “ray effects” }(hyIn problems with small sources or media that are not highly scattering,
discrete ordinates can suffer from "ray effects" h j#hhh!NhNubhp)}(hlathrop_ray_1968h]hv)}(hj#h]h/[lathrop_ray_1968]}(hhh j#ubah}(h]h]h]h]h]uhhuh j#ubah}(h]id15ah]hah]h]h] refdomainhreftypeh reftargetj#refwarnsupport_smartquotesuhhoh!h"hM
h j#hhubhp)}(hlathrop_remedies_1971h]hv)}(hj$h]h/[lathrop_remedies_1971]}(hhh j$ubah}(h]h]h]h]h]uhhuh j$ubah}(h]id16ah]hah]h]h] refdomainhreftypeh reftargetj$refwarnsupport_smartquotesuhhoh!h"hM
h j#hhubh/X
where artifacts of the discrete quadrature directions can be seen in the
computed fluxes. Denovo has a
first-collision capability to help alleviate ray effects. This method
computes the uncollided flux in each mesh cell from a point source. The
uncollided fluxes are then used as a distributed source in the main
discrete-ordinates solution. At the end of the main calculation, the
uncollided fluxes are added to the fluxes computed with the first
collision source, forming the total flux. While this helps reduce ray
effects in many problems, the first-collision capability can take a
significant amount of time to compute on a mesh with many cells or for
many point sources.}(hX
where artifacts of the discrete quadrature directions can be seen in the
computed fluxes. Denovo has a
first-collision capability to help alleviate ray effects. This method
computes the uncollided flux in each mesh cell from a point source. The
uncollided fluxes are then used as a distributed source in the main
discrete-ordinates solution. At the end of the main calculation, the
uncollided fluxes are added to the fluxes computed with the first
collision source, forming the total flux. While this helps reduce ray
effects in many problems, the first-collision capability can take a
significant amount of time to compute on a mesh with many cells or for
many point sources.h j#hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM
h j#hhubh;)}(hXAdjoint sources that use point locations will automatically use the
Denovo first-collision capability. Volumetric adjoint sources (that use
a boundingBox) will be treated without the first-collision capability.
The keywords “firstCollision” and “noFirstCollision” will be ignored by
MAVRIC for adjoint calculations. Keywords for Denovo options in the
importance map block are summarized at the end of this section, in
:numref:`denovo-op`.h](h/XAdjoint sources that use point locations will automatically use the
Denovo first-collision capability. Volumetric adjoint sources (that use
a boundingBox) will be treated without the first-collision capability.
The keywords “firstCollision” and “noFirstCollision” will be ignored by
MAVRIC for adjoint calculations. Keywords for Denovo options in the
importance map block are summarized at the end of this section, in
}(hXAdjoint sources that use point locations will automatically use the
Denovo first-collision capability. Volumetric adjoint sources (that use
a boundingBox) will be treated without the first-collision capability.
The keywords “firstCollision” and “noFirstCollision” will be ignored by
MAVRIC for adjoint calculations. Keywords for Denovo options in the
importance map block are summarized at the end of this section, in
h j=$hhh!NhNubhp)}(h:numref:`denovo-op`h]jO)}(hjH$h]h/ denovo-op}(hhh jJ$ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jF$ubah}(h]h]h]h]h]refdocj refdomainjT$reftypenumrefrefexplicitrefwarnj denovo-opuhhoh!h"hMh j=$ubh/.}(hjh j=$hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j#hhubeh}(h]#options-for-denovo-s-n-calculationsah]h]#options for denovo s_n calculationsah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(h+Starting with an existing adjoint flux fileh]h/+Starting with an existing adjoint flux file}(hj}$h j{$hhh!NhNubah}(h]h]h]h]h]uhh(h jx$hhh!h"hM!ubh;)}(hXAn importance map can be made from an existing Denovo flux file by using
the keyword “adjointFluxes=” with the appropriate file name in quotes.
The file must be a binary file using the \*.dff file format, and the
number of groups must match the number of groups in the MAVRIC cross
section library (i.e., the library entered on the third line of the
MAVRIC input file). Instead of performing an adjoint calculation, the
fluxes read from the file will be used to create both the mesh-based
importance map and the biased mesh source.h]h/XAn importance map can be made from an existing Denovo flux file by using
the keyword “adjointFluxes=” with the appropriate file name in quotes.
The file must be a binary file using the *.dff file format, and the
number of groups must match the number of groups in the MAVRIC cross
section library (i.e., the library entered on the third line of the
MAVRIC input file). Instead of performing an adjoint calculation, the
fluxes read from the file will be used to create both the mesh-based
importance map and the biased mesh source.}(hXAn importance map can be made from an existing Denovo flux file by using
the keyword “adjointFluxes=” with the appropriate file name in quotes.
The file must be a binary file using the \*.dff file format, and the
number of groups must match the number of groups in the MAVRIC cross
section library (i.e., the library entered on the third line of the
MAVRIC input file). Instead of performing an adjoint calculation, the
fluxes read from the file will be used to create both the mesh-based
importance map and the biased mesh source.h j$hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM#h jx$hhubjy)}(hsread importanceMap
adjointFluxes=”c:\mydocu~1\previousRun.adjoint.dff”
gridGeometry=7
end importanceMaph]h/sread importanceMap
adjointFluxes=”c:\mydocu~1\previousRun.adjoint.dff”
gridGeometry=7
end importanceMap}(hhh j$ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM,h jx$hhubh;)}(hIf the “adjointFluxes=” keyword is used and any adjoint sources are defined, an error will result. If a forward flux file is supplied for forward-weighting the adjoint source (see below), then an adjoint flux file cannot be specified.h]h/If the “adjointFluxes=” keyword is used and any adjoint sources are defined, an error will result. If a forward flux file is supplied for forward-weighting the adjoint source (see below), then an adjoint flux file cannot be specified.}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM3h jx$hhubh;)}(hThe grid geometry is not required when using a pre-existing flux file. If grid geometry is not supplied, one will be created from the mesh planes that are contained in the Denovo flux file (which were used to compute the fluxes in that file).h]h/The grid geometry is not required when using a pre-existing flux file. If grid geometry is not supplied, one will be created from the mesh planes that are contained in the Denovo flux file (which were used to compute the fluxes in that file).}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM5h jx$hhubeh}(h]+starting-with-an-existing-adjoint-flux-fileah]h]+starting with an existing adjoint flux fileah]h]uhh#h jhhh!h"hM!ubh$)}(hhh](h))}(h$Forward-weighting the adjoint sourceh]h/$Forward-weighting the adjoint source}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhh(h j$hhh!h"hM8ubh;)}(hXTo optimize a mesh tally or multiple region tallies/point detector
tallies over a large region, instead of a uniform weighting of the
adjoint source, a weighting based on the inverse of the forward response
can be performed. This requires an extra discrete-ordinates calculation but
can help the forward Monte Carlo calculation compute the mesh tally or
group of tallies with more uniform statistical uncertainties.h]h/XTo optimize a mesh tally or multiple region tallies/point detector
tallies over a large region, instead of a uniform weighting of the
adjoint source, a weighting based on the inverse of the forward response
can be performed. This requires an extra discrete-ordinates calculation but
can help the forward Monte Carlo calculation compute the mesh tally or
group of tallies with more uniform statistical uncertainties.}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM:h j$hhubh;)}(hThe same grid geometry will be used in both the forward calculation and
the adjoint calculation, so the user must ensure that the mesh
covers all of the forward sources and all of the adjoint sources, even
if they are point sources.h]h/The same grid geometry will be used in both the forward calculation and
the adjoint calculation, so the user must ensure that the mesh
covers all of the forward sources and all of the adjoint sources, even
if they are point sources.}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMAh j$hhubh;)}(hXTo use forward-weighted CADIS, specify either of the keywords –
“respWeighting” or “fluxWeighting”. For either, MAVRIC will run Denovo
to create an estimate of the forward flux,
:math:`\phi\left( \overrightarrow{r},E \right)`. For response weighting
(“respWeighting”), each adjoint source is inversely weighted by the
integral of the product of the response function used in that adjoint
source and the estimate of the forward flux. For an adjoint source
described by the geometric function :math:`g(\overrightarrow{r})` and
the response function :math:`\sigma_{d}\left( E \right)` (note that
:math:`\sigma_{d}\left( E \right) = 1` for computing total fluxes), the
forward-weighted adjoint source becomesh](h/To use forward-weighted CADIS, specify either of the keywords –
“respWeighting” or “fluxWeighting”. For either, MAVRIC will run Denovo
to create an estimate of the forward flux,
}(hTo use forward-weighted CADIS, specify either of the keywords –
“respWeighting” or “fluxWeighting”. For either, MAVRIC will run Denovo
to create an estimate of the forward flux,
h j$hhh!NhNubj
)}(h/:math:`\phi\left( \overrightarrow{r},E \right)`h]h/'\phi\left( \overrightarrow{r},E \right)}(hhh j%ubah}(h]h]h]h]h]uhjh j$ubh/X. For response weighting
(“respWeighting”), each adjoint source is inversely weighted by the
integral of the product of the response function used in that adjoint
source and the estimate of the forward flux. For an adjoint source
described by the geometric function }(hX. For response weighting
(“respWeighting”), each adjoint source is inversely weighted by the
integral of the product of the response function used in that adjoint
source and the estimate of the forward flux. For an adjoint source
described by the geometric function h j$hhh!NhNubj
)}(h:math:`g(\overrightarrow{r})`h]h/g(\overrightarrow{r})}(hhh j%ubah}(h]h]h]h]h]uhjh j$ubh/ and
the response function }(h and
the response function h j$hhh!NhNubj
)}(h":math:`\sigma_{d}\left( E \right)`h]h/\sigma_{d}\left( E \right)}(hhh j*%ubah}(h]h]h]h]h]uhjh j$ubh/ (note that
}(h (note that
h j$hhh!NhNubj
)}(h&:math:`\sigma_{d}\left( E \right) = 1`h]h/\sigma_{d}\left( E \right) = 1}(hhh j=%ubah}(h]h]h]h]h]uhjh j$ubh/I for computing total fluxes), the
forward-weighted adjoint source becomes}(hI for computing total fluxes), the
forward-weighted adjoint source becomesh j$hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMFh j$hhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-19uhh
h j$hhh!h"hNubj~)}(h q_{i}^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)g(\overrightarrow{r})}{\int_{}^{}{\sigma_{d}\left( E \right)\ \phi\left( \overrightarrow{r},E \right)}\ \text{dE}} \ \ .h]h/ q_{i}^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)g(\overrightarrow{r})}{\int_{}^{}{\sigma_{d}\left( E \right)\ \phi\left( \overrightarrow{r},E \right)}\ \text{dE}} \ \ .}(hhh j`%ubah}(h]j_%ah]h]h]h]docnamejnumberKlabel mavric-19nowrapjjuhj}h!h"hMRh j$hhj}j}j_%jV%subh;)}(hResponse weighting will calculate more uniform relative uncertainties of
the integral quantities of the tallies in the final Monte Carlo
calculation.h]h/Response weighting will calculate more uniform relative uncertainties of
the integral quantities of the tallies in the final Monte Carlo
calculation.}(hjw%h ju%hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMYh j$hhubh;)}(hXTo optimize the calculation of the entire group-wise flux with more
uniform relative uncertainties in each group, the adjoint source should
be weighted inversely by the forward flux,
:math:`\phi\left( \overrightarrow{r},E \right),` using the
“fluxWeighting” keyword. For an adjoint source described by the
geometric function :math:`g(\overrightarrow{r})` and the response
function :math:`\sigma_{d}\left( E \right) = 1`, the forward-weighted
adjoint source becomesh](h/To optimize the calculation of the entire group-wise flux with more
uniform relative uncertainties in each group, the adjoint source should
be weighted inversely by the forward flux,
}(hTo optimize the calculation of the entire group-wise flux with more
uniform relative uncertainties in each group, the adjoint source should
be weighted inversely by the forward flux,
h j%hhh!NhNubj
)}(h0:math:`\phi\left( \overrightarrow{r},E \right),`h]h/(\phi\left( \overrightarrow{r},E \right),}(hhh j%ubah}(h]h]h]h]h]uhjh j%ubh/b using the
“fluxWeighting” keyword. For an adjoint source described by the
geometric function }(hb using the
“fluxWeighting” keyword. For an adjoint source described by the
geometric function h j%hhh!NhNubj
)}(h:math:`g(\overrightarrow{r})`h]h/g(\overrightarrow{r})}(hhh j%ubah}(h]h]h]h]h]uhjh j%ubh/ and the response
function }(h and the response
function h j%hhh!NhNubj
)}(h&:math:`\sigma_{d}\left( E \right) = 1`h]h/\sigma_{d}\left( E \right) = 1}(hhh j%ubah}(h]h]h]h]h]uhjh j%ubh/-, the forward-weighted
adjoint source becomes}(h-, the forward-weighted
adjoint source becomesh j%hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM]h j$hhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-20uhh
h j$hhh!h"hNubj~)}(hq_{i}^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)g(\overrightarrow{r})}{\phi\left( \overrightarrow{r},E \right)}\ .h]h/q_{i}^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)g(\overrightarrow{r})}{\phi\left( \overrightarrow{r},E \right)}\ .}(hhh j%ubah}(h]j%ah]h]h]h]docnamejnumberKlabel mavric-20nowrapjjuhj}h!h"hMfh j$hhj}j}j%j%subh;)}(hXFor example, consider a problem with a single source and two detectors,
one near the source that measures flux and one far from the source that
measures some response. In a standard Monte Carlo calculation, it is
expected that since more Monte Carlo particles cross the near detector,
it will have a much lower relative uncertainty than the far detector.
Standard CADIS could be used to optimize the calculation of each in
separate simulations:h]h/XFor example, consider a problem with a single source and two detectors,
one near the source that measures flux and one far from the source that
measures some response. In a standard Monte Carlo calculation, it is
expected that since more Monte Carlo particles cross the near detector,
it will have a much lower relative uncertainty than the far detector.
Standard CADIS could be used to optimize the calculation of each in
separate simulations:}(hj%h j%hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMlh j$hhubj)}(hhh]j)}(hhh](j)}(hhh]h}(h]h]h]h]h]jK2uhjh j%ubj)}(hhh]h}(h]h]h]h]h]jK2uhjh j%ubj)}(hhh](j8)}(hhh](j=)}(hhh]h;)}(h)To optimize the flux in the near detectorh]h/)To optimize the flux in the near detector}(hj&h j&ubah}(h]h]h]h]h]uhh:h!h"hMvh j&ubah}(h]h]h]h]h]uhj<h j&ubj=)}(hhh]h;)}(h,To optimize the response in the far detectorh]h/,To optimize the response in the far detector}(hj2&h j0&ubah}(h]h]h]h]h]uhh:h!h"hMxh j-&ubah}(h]h]h]h]h]uhj<h j&ubeh}(h]h]h]h]h]uhj7h j&ubj8)}(hhh](j=)}(hhh]jy)}(hread importanceMap
gridGeometryID=1
adjointSource 1
boundingBox x1 x2 y1 y2 z1 z2
responseID=1
end adjointSource
end importanceMaph]h/read importanceMap
gridGeometryID=1
adjointSource 1
boundingBox x1 x2 y1 y2 z1 z2
responseID=1
end adjointSource
end importanceMap}(hhh jP&ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMzh jM&ubah}(h]h]h]h]h]uhj<h jJ&ubj=)}(hhh]jy)}(hread importanceMap
gridGeometryID=1
adjointSource 2
boundingBox u1 u2 v1 v2 w1 w2
responseID=6
end adjointSource
end importanceMaph]h/read importanceMap
gridGeometryID=1
adjointSource 2
boundingBox u1 u2 v1 v2 w1 w2
responseID=6
end adjointSource
end importanceMap}(hhh jk&ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh jh&ubah}(h]h]h]h]h]uhj<h jJ&ubeh}(h]h]h]h]h]uhj7h j&ubeh}(h]h]h]h]h]uhjh j%ubeh}(h]h]h]h]h]colsKuhjh j%ubah}(h]h]h]h]h]jjuhj
h j$hhh!NhNubh;)}(hXwhere response 1 was defined as :math:`\sigma_{1}\left( E \right) = 1`
and response 6 was defined as :math:`\sigma_{6}\left( E \right) =`
flux-to-response conversion factors. The two options for
forward weighting allow the tallies for both detectors to be calculated
in the same MAVRIC simulation. Using “fluxWeighting”, the importance map
and biased source will be made to help distribute Monte Carlo particles
evenly through each energy group and every voxel in both detectors,
making the relative uncertainties close to uniform. With
“respWeighting”, the importance map and biased source will optimize the
total integrated response of each tally.h](h/ where response 1 was defined as }(h where response 1 was defined as h j&hhh!NhNubj
)}(h&:math:`\sigma_{1}\left( E \right) = 1`h]h/\sigma_{1}\left( E \right) = 1}(hhh j&ubah}(h]h]h]h]h]uhjh j&ubh/
and response 6 was defined as }(h
and response 6 was defined as h j&hhh!NhNubj
)}(h$:math:`\sigma_{6}\left( E \right) =`h]h/\sigma_{6}\left( E \right) =}(hhh j&ubah}(h]h]h]h]h]uhjh j&ubh/X
flux-to-response conversion factors. The two options for
forward weighting allow the tallies for both detectors to be calculated
in the same MAVRIC simulation. Using “fluxWeighting”, the importance map
and biased source will be made to help distribute Monte Carlo particles
evenly through each energy group and every voxel in both detectors,
making the relative uncertainties close to uniform. With
“respWeighting”, the importance map and biased source will optimize the
total integrated response of each tally.}(hX
flux-to-response conversion factors. The two options for
forward weighting allow the tallies for both detectors to be calculated
in the same MAVRIC simulation. Using “fluxWeighting”, the importance map
and biased source will be made to help distribute Monte Carlo particles
evenly through each energy group and every voxel in both detectors,
making the relative uncertainties close to uniform. With
“respWeighting”, the importance map and biased source will optimize the
total integrated response of each tally.h j&hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j$hhubj)}(hhh]j)}(hhh](j)}(hhh]h}(h]h]h]h]h]jK2uhjh j&ubj)}(hhh]h}(h]h]h]h]h]jK2uhjh j&ubj)}(hhh](j8)}(hhh](j=)}(hhh]h;)}(hLTo optimize :math:`\phi\left( \overrightarrow{r},E \right)` in each detectorh](h/To optimize }(hTo optimize h j&ubj
)}(h/:math:`\phi\left( \overrightarrow{r},E \right)`h]h/'\phi\left( \overrightarrow{r},E \right)}(hhh j&ubah}(h]h]h]h]h]uhjh j&ubh/ in each detector}(h in each detectorh j&ubeh}(h]h]h]h]h]uhh:h!h"hMh j&ubah}(h]h]h]h]h]uhj<h j&ubj=)}(hhh]h;)}(hTo optimize a total response :math:`\int_{}^{}{\sigma_{d}\left ( E \right) \phi \left( \overrightarrow{r},E \right)} dE` (either total flux or total dose)h](h/To optimize a total response }(hTo optimize a total response h j'ubj
)}(h[:math:`\int_{}^{}{\sigma_{d}\left ( E \right) \phi \left( \overrightarrow{r},E \right)} dE`h]h/S\int_{}^{}{\sigma_{d}\left ( E \right) \phi \left( \overrightarrow{r},E \right)} dE}(hhh j&'ubah}(h]h]h]h]h]uhjh j'ubh/" (either total flux or total dose)}(h" (either total flux or total dose)h j'ubeh}(h]h]h]h]h]uhh:h!h"hMh j'ubah}(h]h]h]h]h]uhj<h j&ubeh}(h]h]h]h]h]uhj7h j&ubj8)}(hhh](j=)}(hhh]jy)}(hX> read importanceMap
gridGeometryID=1
‘ near detector
adjointSource 1
boundingBox x1 x2 y1 y2 z1 z2
responseID=1
end adjointSource
‘ far detector
adjointSource 2
boundingBox u1 u2 v1 v2 w1 w2
responseID=6
end adjointSource
fluxWeighting
end importanceMaph]h/X> read importanceMap
gridGeometryID=1
‘ near detector
adjointSource 1
boundingBox x1 x2 y1 y2 z1 z2
responseID=1
end adjointSource
‘ far detector
adjointSource 2
boundingBox u1 u2 v1 v2 w1 w2
responseID=6
end adjointSource
fluxWeighting
end importanceMap}(hhh jQ'ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh jN'ubah}(h]h]h]h]h]uhj<h jK'ubj=)}(hhh]jy)}(hX<read importanceMap
gridGeometryID=1
‘ near detector
adjointSource 1
boundingBox x1 x2 y1 y2 z1 z2
responseID=1
end adjointSource
‘ far detector
adjointSource 2
boundingBox u1 u2 v1 v2 w1 w2
responseID=6
end adjointSource
respWeighting
end importanceMaph]h/X<read importanceMap
gridGeometryID=1
‘ near detector
adjointSource 1
boundingBox x1 x2 y1 y2 z1 z2
responseID=1
end adjointSource
‘ far detector
adjointSource 2
boundingBox u1 u2 v1 v2 w1 w2
responseID=6
end adjointSource
respWeighting
end importanceMap}(hhh jl'ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh ji'ubah}(h]h]h]h]h]uhj<h jK'ubeh}(h]h]h]h]h]uhj7h j&ubeh}(h]h]h]h]h]uhjh j&ubeh}(h]h]h]h]h]colsKuhjh j&ubah}(h]h]h]h]h]jjuhj
h j$hhh!NhNubh;)}(h0Using flux weighting, the adjoint source will beh]h/0Using flux weighting, the adjoint source will be}(hj'h j'hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j$hhubj
)}(hhh](h)}(hhh]h}(h]h]h]h]h]hequation-mavric-21uhh
h j'ubj~)}(hXq^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{1}\left( E \right)g_{\mathrm{\text{near}}}(\overrightarrow{r})}{\phi\left( \overrightarrow{r},E \right)} + \frac{\sigma_{6}\left( E \right)g_{\mathrm{\text{far}}}(\overrightarrow{r})}{\phi\left( \overrightarrow{r},E \right)}\ ,h]h/Xq^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{1}\left( E \right)g_{\mathrm{\text{near}}}(\overrightarrow{r})}{\phi\left( \overrightarrow{r},E \right)} + \frac{\sigma_{6}\left( E \right)g_{\mathrm{\text{far}}}(\overrightarrow{r})}{\phi\left( \overrightarrow{r},E \right)}\ ,}(hhh j'ubah}(h]j'ah]h]h]h]docnamejnumberKlabel mavric-21nowrapjjuhj}h!h"hMh j'j}j}j'j'subeh}(h]h]h]h]h]uhj
h j$hhh!NhNubh;)}(h7or using response weighting, the adjoint source will beh]h/7or using response weighting, the adjoint source will be}(hj'h j'hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j$hhubj
)}(hhh](h)}(hhh]h}(h]h]h]h]h]hequation-mavric-22uhh
h j'ubj~)}(hXLq^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{1}\left( E \right)g_{1}(\overrightarrow{r})}{\int_{}^{}{\sigma_{1}\left( E \right)\phi \left(\overrightarrow{r},E \right)}\ dE} + \frac{\sigma_{6}\left( E \right)g_{2}(\overrightarrow{r})}{\int_{}^{}{\sigma_{6}\left(E \right)\phi \left( \overrightarrow{r},E \right)}\ dE} \ .h]h/XLq^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{1}\left( E \right)g_{1}(\overrightarrow{r})}{\int_{}^{}{\sigma_{1}\left( E \right)\phi \left(\overrightarrow{r},E \right)}\ dE} + \frac{\sigma_{6}\left( E \right)g_{2}(\overrightarrow{r})}{\int_{}^{}{\sigma_{6}\left(E \right)\phi \left( \overrightarrow{r},E \right)}\ dE} \ .}(hhh j'ubah}(h]j'ah]h]h]h]docnamejnumberKlabel mavric-22nowrapjjuhj}h!h"hMh j'j}j}j'j'subeh}(h]h]h]h]h]uhj
h j$hhh!NhNubh;)}(hXThis implementation is slightly different from the original MAVRIC in
SCALE 6. The current approach is simpler for the user and allows the
importance parameters to optimize the final Monte Carlo calculation for
the calculation of two different responses in two different areas.h]h/XThis implementation is slightly different from the original MAVRIC in
SCALE 6. The current approach is simpler for the user and allows the
importance parameters to optimize the final Monte Carlo calculation for
the calculation of two different responses in two different areas.}(hj(h j (hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j$hhubh;)}(hXIf the number of mesh cells containing the true source is less than 10,
then MAVRIC will convert these source voxels to point sources and Denovo
will automatically use its first-collision capability to help reduce ray
effects in the forward calculation. The user can easily override the
MAVRIC defaults—to force the calculation of a first-collision source no
matter how many voxels contain source; this can be done by using the keyword
“firstCollision”. To prevent the calculation of a first-collision
source, the keyword “noFirstCollision” can be used. If the keywords
“firstCollision” or “noFirstCollision” are used, then they will only apply to
the forward calculation, not the subsequent adjoint calculation.h]h/XIf the number of mesh cells containing the true source is less than 10,
then MAVRIC will convert these source voxels to point sources and Denovo
will automatically use its first-collision capability to help reduce ray
effects in the forward calculation. The user can easily override the
MAVRIC defaults—to force the calculation of a first-collision source no
matter how many voxels contain source; this can be done by using the keyword
“firstCollision”. To prevent the calculation of a first-collision
source, the keyword “noFirstCollision” can be used. If the keywords
“firstCollision” or “noFirstCollision” are used, then they will only apply to
the forward calculation, not the subsequent adjoint calculation.}(hj(h j(hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j$hhubh;)}(hXThe keyword “saveExtraMaps” will save extra files that can be viewed by
the Mesh File Viewer. The source used by the forward Denovo calculation
is stored in “\ *outputName.*\ dofs.3dmap”, where *outputName* is the
name the user chose for his output file.h](h/The keyword “saveExtraMaps” will save extra files that can be viewed by
the Mesh File Viewer. The source used by the forward Denovo calculation
is stored in “ }(hThe keyword “saveExtraMaps” will save extra files that can be viewed by
the Mesh File Viewer. The source used by the forward Denovo calculation
is stored in “\ h j%(hhh!NhNubhA)}(h
*outputName.*h]h/outputName.}(hhh j.(ubah}(h]h]h]h]h]uhh@h j%(ubh/ dofs.3dmap”, where }(h\ dofs.3dmap”, where h j%(hhh!NhNubhA)}(h*outputName*h]h/
outputName}(hhh jA(ubah}(h]h]h]h]h]uhh@h j%(ubh/0 is the
name the user chose for his output file.}(h0 is the
name the user chose for his output file.h j%(hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j$hhubeh}(h]$forward-weighting-the-adjoint-sourceah]h]$forward-weighting the adjoint sourceah]h]uhh#h jhhh!h"hM8ubh$)}(hhh](h))}(h4Forward weighting with an existing forward flux fileh]h/4Forward weighting with an existing forward flux file}(hjg(h je(hhh!NhNubah}(h]h]h]h]h]uhh(h jb(hhh!h"hMubh;)}(hXOSimilar to the capability of using pre-existing adjoint flux files,
MAVRIC can use a pre-existing forward flux file to create a
forward-weighted adjoint source without performing the forward Denovo
calculation. The user may specify the \*.dff file containing the forward
fluxes using the keyword “forwardFluxes=”. The filename should be
enclosed in quotes, and the file must be a binary file using the Denovo
flux file format. The number of groups must match the number of groups
in the MAVRIC cross section library (i.e., the library entered on the
third line of the MAVRIC input file).h]h/XOSimilar to the capability of using pre-existing adjoint flux files,
MAVRIC can use a pre-existing forward flux file to create a
forward-weighted adjoint source without performing the forward Denovo
calculation. The user may specify the *.dff file containing the forward
fluxes using the keyword “forwardFluxes=”. The filename should be
enclosed in quotes, and the file must be a binary file using the Denovo
flux file format. The number of groups must match the number of groups
in the MAVRIC cross section library (i.e., the library entered on the
third line of the MAVRIC input file).}(hXOSimilar to the capability of using pre-existing adjoint flux files,
MAVRIC can use a pre-existing forward flux file to create a
forward-weighted adjoint source without performing the forward Denovo
calculation. The user may specify the \*.dff file containing the forward
fluxes using the keyword “forwardFluxes=”. The filename should be
enclosed in quotes, and the file must be a binary file using the Denovo
flux file format. The number of groups must match the number of groups
in the MAVRIC cross section library (i.e., the library entered on the
third line of the MAVRIC input file).h js(hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jb(hhubjy)}(hread importanceMap
forwardFluxes=”c:\mydocu~1\previousRun.forward.dff”
gridGeometry=7
adjointSource 1
...
end adjointSource
respWeighting
end importanceMaph]h/read importanceMap
forwardFluxes=”c:\mydocu~1\previousRun.forward.dff”
gridGeometry=7
adjointSource 1
...
end adjointSource
respWeighting
end importanceMap}(hhh j(ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh jb(hhubh;)}(hwWhen using a pre-existing forward flux file, either “respWeighting” or “fluxWeighting” must still be specified.h]h/wWhen using a pre-existing forward flux file, either “respWeighting” or “fluxWeighting” must still be specified.}(hj(h j(hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jb(hhubeh}(h]4forward-weighting-with-an-existing-forward-flux-fileah]h]4forward weighting with an existing forward flux fileah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(hUsing the importance maph]h/Using the importance map}(hj(h j(hhh!NhNubah}(h]h]h]h]h]uhh(h j(hhh!h"hMubh;)}(hXAn importance map produced by the importance map block consists of the target
weight values as a function of position and energy. The upper weight window used
for splitting and the lower weight window used for Russian roulette are set by the
window ratio. The window ratio is simply the ratio of the weight window's upper bound to
the weight window lower bound, with the target weight being the average of the upper and lower bounds.h]h/XAn importance map produced by the importance map block consists of the target
weight values as a function of position and energy. The upper weight window used
for splitting and the lower weight window used for Russian roulette are set by the
window ratio. The window ratio is simply the ratio of the weight window’s upper bound to
the weight window lower bound, with the target weight being the average of the upper and lower bounds.}(hj(h j(hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j(hhubh;)}(hXdThe keyword “windowRatio=” can be used within the importance map block to specify what
window ratio will be used with the importance map that is passed to the Monaco forward
Monte Carlo calculation. For a windowRatio of :math:`r`, the upper weights for
splitting, :math:`w_{max}`, and the lower weights for Russian roulette, :math:`w_{min}`, are set ash](h/The keyword “windowRatio=” can be used within the importance map block to specify what
window ratio will be used with the importance map that is passed to the Monaco forward
Monte Carlo calculation. For a windowRatio of }(hThe keyword “windowRatio=” can be used within the importance map block to specify what
window ratio will be used with the importance map that is passed to the Monaco forward
Monte Carlo calculation. For a windowRatio of h j(hhh!NhNubj
)}(h :math:`r`h]h/r}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/#, the upper weights for
splitting, }(h#, the upper weights for
splitting, h j(hhh!NhNubj
)}(h:math:`w_{max}`h]h/w_{max}}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/., and the lower weights for Russian roulette, }(h., and the lower weights for Russian roulette, h j(hhh!NhNubj
)}(h:math:`w_{min}`h]h/w_{min}}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/, are set as}(h, are set ash j(hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j(hhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-23uhh
h j(hhh!h"hNubj~)}(h/w_{\mathrm{\min}} = \frac{2}{r + 1}\overline{w}h]h//w_{\mathrm{\min}} = \frac{2}{r + 1}\overline{w}}(hhh j)ubah}(h]j)ah]h]h]h]docnamejnumberKlabel mavric-23nowrapjjuhj}h!h"hMh j(hhj}j}j)j)subh;)}(handh]h/and}(hj2)h j0)hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j(hhubh)}(hhh]h}(h]h]h]h]h]hequation-mavric-24uhh
h j(hhh!h"hNubj~)}(h0w_{\mathrm{\max}} = \frac{2r}{r + 1}\overline{w}h]h/0w_{\mathrm{\max}} = \frac{2r}{r + 1}\overline{w}}(hhh jH)ubah}(h]jG)ah]h]h]h]docnamejnumberKlabel mavric-24nowrapjjuhj}h!h"hMh j(hhj}j}jG)j>)subh;)}(hfor the target weight :math:`\overline{w}` in each mesh cell and for
each energy of the importance map. The default value for the windowRatio
is 5.0.h](h/for the target weight }(hfor the target weight h j])hhh!NhNubj
)}(h:math:`\overline{w}`h]h/\overline{w}}(hhh jf)ubah}(h]h]h]h]h]uhjh j])ubh/k in each mesh cell and for
each energy of the importance map. The default value for the windowRatio
is 5.0.}(hk in each mesh cell and for
each energy of the importance map. The default value for the windowRatio
is 5.0.h j])hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h j(hhubeh}(h]using-the-importance-mapah]h]using the importance mapah]h]uhh#h jhhh!h"hMubh$)}(hhh](h))}(h*Other notes on importance map calculationsh]h/*Other notes on importance map calculations}(hj)h j)hhh!NhNubah}(h]h]h]h]h]uhh(h j)hhh!h"hM%ubh;)}(hXdSince the importance map calculations all take place using mesh
geometry, one of the first steps that occurs is to create a mesh
representation of the true source (the forward source) on the same grid.
This procedure uses the same two methods as the Monaco mesh source saver
routine. Mesh cells can be subdivided and tested to see if they are
within the defined source, or a set number of points can be sampled from
the source. The keywords “subCells=” and “sourceTrials=” are used in the
importance map block to change the default settings for constructing the
mesh representation of the forward source.h]h/XdSince the importance map calculations all take place using mesh
geometry, one of the first steps that occurs is to create a mesh
representation of the true source (the forward source) on the same grid.
This procedure uses the same two methods as the Monaco mesh source saver
routine. Mesh cells can be subdivided and tested to see if they are
within the defined source, or a set number of points can be sampled from
the source. The keywords “subCells=” and “sourceTrials=” are used in the
importance map block to change the default settings for constructing the
mesh representation of the forward source.}(hj)h j)hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM'h j)hhubh;)}(hIf macromaterials are used (“mmTolerance<1”) and the adjoint source is
limited to a particular material, then the amount of adjoint source in a mesh
voxel will be weighted by the material amount in that voxel.h]h/If macromaterials are used (“mmTolerance<1”) and the adjoint source is
limited to a particular material, then the amount of adjoint source in a mesh
voxel will be weighted by the material amount in that voxel.}(hj)h j)hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM1h j)hhubh;)}(hXIn SCALE/MAVRIC, Denovo is called as a fixed-source S\ :sub:`N` solver
and cannot model multiplying media. Neither forward nor adjoint neutron
calculations from Denovo will be accurate when neutron multiplication is
a major source component. If neutron multiplication is not turned off in
the parameters block of the MAVRIC input (using “fissionMult=0”), a
warning will be generated to remind the user of this limitation.h](h/7In SCALE/MAVRIC, Denovo is called as a fixed-source S }(h7In SCALE/MAVRIC, Denovo is called as a fixed-source S\ h j)hhh!NhNubj )}(h:sub:`N`h]h/N}(hhh j)ubah}(h]h]h]h]h]uhj h j)ubh/Xj solver
and cannot model multiplying media. Neither forward nor adjoint neutron
calculations from Denovo will be accurate when neutron multiplication is
a major source component. If neutron multiplication is not turned off in
the parameters block of the MAVRIC input (using “fissionMult=0”), a
warning will be generated to remind the user of this limitation.}(hXj solver
and cannot model multiplying media. Neither forward nor adjoint neutron
calculations from Denovo will be accurate when neutron multiplication is
a major source component. If neutron multiplication is not turned off in
the parameters block of the MAVRIC input (using “fissionMult=0”), a
warning will be generated to remind the user of this limitation.h j)hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM5h j)hhubh;)}(hXgBy default, MAVRIC instructs Denovo not to perform outer iterations for
neutron problems if the cross section library contains upscatter groups.
This is because the time required calculating the fluxes using upscatter
can be significantly longer than without. For problems in which thermal
neutrons are an important part of the transport or tallies, the user
should specify the keyword “upScatter=1” in the importance map block.
This will instruct Denovo to perform the outer iterations for the
upscatter groups, giving more accurate results but taking a much longer
time for the discrete-ordinates calculation.h]h/XgBy default, MAVRIC instructs Denovo not to perform outer iterations for
neutron problems if the cross section library contains upscatter groups.
This is because the time required calculating the fluxes using upscatter
can be significantly longer than without. For problems in which thermal
neutrons are an important part of the transport or tallies, the user
should specify the keyword “upScatter=1” in the importance map block.
This will instruct Denovo to perform the outer iterations for the
upscatter groups, giving more accurate results but taking a much longer
time for the discrete-ordinates calculation.}(hj)h j)hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM<h j)hhubh;)}(hXlWhen performing a MAVRIC calculation using a coarse-group energy structure
for Denovo (for example with the 27/19 library) but a fine-group energy
structure (with the 200/47 library) for the final Monaco calculation,
the source biasing parameters are determined on the coarse-group
structure. The importance map (*.mim) file and the biased mesh source
(*.msm) files all use the coarse-group structure. The source biasing
information is then applied to fine-group mesh versions of the sources,
resulting in the \*.sampling.*.msm files. This way, the biased sources
used in the final Monaco calculation retain their fine-group resolution.
This can be especially important in representing the high-energy portion
of the fission neutron distribution for example. When using CE-Monaco,
the source sampling routines first use the \*.msm files to determine the
source particle’s voxel and energy group. From that voxel and energy
group, the user-given source distributions are used to sample the
specific starting location and specific energy of the source particle.
This way, the CE-Monaco calculation samples the true CE distributions.h](h/X9When performing a MAVRIC calculation using a coarse-group energy structure
for Denovo (for example with the 27/19 library) but a fine-group energy
structure (with the 200/47 library) for the final Monaco calculation,
the source biasing parameters are determined on the coarse-group
structure. The importance map (}(hX9When performing a MAVRIC calculation using a coarse-group energy structure
for Denovo (for example with the 27/19 library) but a fine-group energy
structure (with the 200/47 library) for the final Monaco calculation,
the source biasing parameters are determined on the coarse-group
structure. The importance map (h j)hhh!NhNubhA)}(h)*.mim) file and the biased mesh source
(*h]h/'.mim) file and the biased mesh source
(}(hhh j)ubah}(h]h]h]h]h]uhh@h j)ubh/X
.msm) files all use the coarse-group structure. The source biasing
information is then applied to fine-group mesh versions of the sources,
resulting in the *.sampling.*.msm files. This way, the biased sources
used in the final Monaco calculation retain their fine-group resolution.
This can be especially important in representing the high-energy portion
of the fission neutron distribution for example. When using CE-Monaco,
the source sampling routines first use the *.msm files to determine the
source particle’s voxel and energy group. From that voxel and energy
group, the user-given source distributions are used to sample the
specific starting location and specific energy of the source particle.
This way, the CE-Monaco calculation samples the true CE distributions.}(hX
.msm) files all use the coarse-group structure. The source biasing
information is then applied to fine-group mesh versions of the sources,
resulting in the \*.sampling.*.msm files. This way, the biased sources
used in the final Monaco calculation retain their fine-group resolution.
This can be especially important in representing the high-energy portion
of the fission neutron distribution for example. When using CE-Monaco,
the source sampling routines first use the \*.msm files to determine the
source particle’s voxel and energy group. From that voxel and energy
group, the user-given source distributions are used to sample the
specific starting location and specific energy of the source particle.
This way, the CE-Monaco calculation samples the true CE distributions.h j)hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMFh j)hhubj)}(hhh](h))}(h%Keywords for the importance map blockh]h/%Keywords for the importance map block}(hj*h j *ubah}(h]h]h]h]h]uhh(h!h"hMXh j*ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh j*ubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h#.. image:: figs/MAVRIC/table4-5.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/table4-5.pngjY}j[j7*suhjKh j)*h!h"hKubah}(h]h]h]h]h]uhj<h j&*ubah}(h]h]h]h]h]uhj7h j#*ubah}(h]h]h]h]h]uhjh j*ubeh}(h]h]h]h]h]colsKuhjh j*ubeh}(h]keywords-importanceah]h]keywords-importanceah]h]jcenteruhj
h j)hhh!NhNubj)}(hhh](h))}(h+Denovo options for the importance map blockh]h/+Denovo options for the importance map block}(hj`*h j^*ubah}(h]h]h]h]h]uhh(h!h"hM`h j[*ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jl*ubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h#.. image:: figs/MAVRIC/table4-6.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/table4-6.pngjY}j[j*suhjKh j~*h!h"hKubah}(h]h]h]h]h]uhj<h j{*ubah}(h]h]h]h]h]uhj7h jx*ubah}(h]h]h]h]h]uhjh jl*ubeh}(h]h]h]h]h]colsKuhjh j[*ubeh}(h] denovo-opah]h] denovo-opah]h]jcenteruhj
h j)hhh!NhNubeh}(h]*other-notes-on-importance-map-calculationsah]h]*other notes on importance map calculationsah]h]uhh#h jhhh!h"hM%ubeh}(h]importance-map-blockah]h]importance map blockah]h]uhh#h jIhhh!h"hMtubeh}(h]mavric-inputah]h]mavric inputah]h]uhh#h h%hhh!h"hMaubh$)}(hhh](h))}(h
MAVRIC outputh]h/
MAVRIC output}(hj*h j*hhh!NhNubah}(h]h]h]h]h]uhh(h j*hhh!h"hMiubh$)}(hhh](h))}(hMain text output fileh]h/Main text output file}(hj*h j*hhh!NhNubah}(h]h]h]h]h]uhh(h j*hhh!h"hMlubh;)}(hX"Similar to other SCALE sequences, MAVRIC returns a text output file
containing the output from the SCALE driver, the sequence itself, and
all of the functional modules called. The SCALE driver output first
displays the problem input file, and then the first reading of the input file
by the MAVRIC sequence is shown (which includes some material processing
information). If there are any errors or warnings about the input file,
they will be shown next. Next in the output file are the different
passes through the MAVRIC sequence---up to 10 parts. If any errors or
warning messages (such as lack of memory) are generated during
processing, they will be displayed here. Finally, the output files from
each functional module are concatenated to the above output and shows
the files returned to the user.h]h/X"Similar to other SCALE sequences, MAVRIC returns a text output file
containing the output from the SCALE driver, the sequence itself, and
all of the functional modules called. The SCALE driver output first
displays the problem input file, and then the first reading of the input file
by the MAVRIC sequence is shown (which includes some material processing
information). If there are any errors or warnings about the input file,
they will be shown next. Next in the output file are the different
passes through the MAVRIC sequence—up to 10 parts. If any errors or
warning messages (such as lack of memory) are generated during
processing, they will be displayed here. Finally, the output files from
each functional module are concatenated to the above output and shows
the files returned to the user.}(hj*h j*hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMnh j*hhubh;)}(hXsFirst, the Monaco section of output first reviews the input it received. First
the geometry is reviewed, showing which materials are used in each
region and the volume of that region, if input or calculated. Then a
detailed list of other Monaco input is reviewed: cross section parameters, data
definitions, the source description, the tallies, the Monte Carlo
parameters, and the biasing parameters. For MAVRIC calculations, if an
importance map is used, then its summary is also given. The “Mesh
Importance Map Characterization” shows where the importance map may be
changing too rapidly and may require more refinement.h]h/XsFirst, the Monaco section of output first reviews the input it received. First
the geometry is reviewed, showing which materials are used in each
region and the volume of that region, if input or calculated. Then a
detailed list of other Monaco input is reviewed: cross section parameters, data
definitions, the source description, the tallies, the Monte Carlo
parameters, and the biasing parameters. For MAVRIC calculations, if an
importance map is used, then its summary is also given. The “Mesh
Importance Map Characterization” shows where the importance map may be
changing too rapidly and may require more refinement.}(hj*h j*hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM{h j*hhubh;)}(hXFor each Monaco batch, the output file lists the batch time and the
starting random number for the next batch, which may be useful in
rerunning only a portion of a problem. Once all of the batches are
completed, a list of the various tally files that have been created is
given. Finally, the tallies are summarized in a section entitled “Final
Tally Results Summary.” For each point detector, the total neutron and
photon fluxes (uncollided and total) are given as well as the final
response values for each response function. For each region tally, the
total neutron and photon fluxes (both track-length and collision density
estimates) are listed, followed by the final response values for each
response function. Group‑by‑group details are saved to separate files
for each tally.h]h/XFor each Monaco batch, the output file lists the batch time and the
starting random number for the next batch, which may be useful in
rerunning only a portion of a problem. Once all of the batches are
completed, a list of the various tally files that have been created is
given. Finally, the tallies are summarized in a section entitled “Final
Tally Results Summary.” For each point detector, the total neutron and
photon fluxes (uncollided and total) are given as well as the final
response values for each response function. For each region tally, the
total neutron and photon fluxes (both track-length and collision density
estimates) are listed, followed by the final response values for each
response function. Group‑by‑group details are saved to separate files
for each tally.}(hj+h j+hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j*hhubeh}(h]main-text-output-fileah]h]main text output fileah]h]uhh#h j*hhh!h"hMlubh$)}(hhh](h))}(hAdditional output filesh]h/Additional output files}(hj!+h j+hhh!NhNubah}(h]h]h]h]h]uhh(h j+hhh!h"hMubh;)}(hX In addition to the generous amount of data contained in the MAVRIC text
output file, many other files are created containing the intermediate
data used by the sequence and the final tally data. Many of the files
produced can be viewed using the Mesh File Viewer or the Interactive
Plotter capabilities of Fulcrum, which is distributed with SCALE. (Note
that most of the images in this document were taken from the Mesh File
Viewer from SCALE 6.1.) :numref:`output-files` lists the other output files, based
on the name of the main output file (here called *outputName)*, that are
available to the user. These files will be copied back to the directory
where the input file was located. Many of the files come from Monaco and
are discussed in the Monaco chapter of the SCALE manual (SECTIONREFERENCE).h](h/XIn addition to the generous amount of data contained in the MAVRIC text
output file, many other files are created containing the intermediate
data used by the sequence and the final tally data. Many of the files
produced can be viewed using the Mesh File Viewer or the Interactive
Plotter capabilities of Fulcrum, which is distributed with SCALE. (Note
that most of the images in this document were taken from the Mesh File
Viewer from SCALE 6.1.) }(hXIn addition to the generous amount of data contained in the MAVRIC text
output file, many other files are created containing the intermediate
data used by the sequence and the final tally data. Many of the files
produced can be viewed using the Mesh File Viewer or the Interactive
Plotter capabilities of Fulcrum, which is distributed with SCALE. (Note
that most of the images in this document were taken from the Mesh File
Viewer from SCALE 6.1.) h j-+hhh!NhNubhp)}(h:numref:`output-files`h]jO)}(hj8+h]h/output-files}(hhh j:+ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j6+ubah}(h]h]h]h]h]refdocj refdomainjD+reftypenumrefrefexplicitrefwarnjoutput-filesuhhoh!h"hMh j-+ubh/V lists the other output files, based
on the name of the main output file (here called }(hV lists the other output files, based
on the name of the main output file (here called h j-+hhh!NhNubhA)}(h
*outputName)*h]h/outputName)}(hhh j[+ubah}(h]h]h]h]h]uhh@h j-+ubh/, that are
available to the user. These files will be copied back to the directory
where the input file was located. Many of the files come from Monaco and
are discussed in the Monaco chapter of the SCALE manual (SECTIONREFERENCE).}(h, that are
available to the user. These files will be copied back to the directory
where the input file was located. Many of the files come from Monaco and
are discussed in the Monaco chapter of the SCALE manual (SECTIONREFERENCE).h j-+hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j+hhubh;)}(hXOther files that the user may be interested in are listed in
:numref:`intermediate-files`. These files are kept in the temporary directory where SCALE
executes and are not copied back to the directory where the input file
was located, unless specifically requested using a SCALE “``shell``”
command. Curious users may also be interested in viewing the various
input files (i_*) that the MAVRIC sequence writes in order to run the
SCALE functional modules.h](h/=Other files that the user may be interested in are listed in
}(h=Other files that the user may be interested in are listed in
h jt+hhh!NhNubhp)}(h:numref:`intermediate-files`h]jO)}(hj+h]h/intermediate-files}(hhh j+ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j}+ubah}(h]h]h]h]h]refdocj refdomainj+reftypenumrefrefexplicitrefwarnjintermediate-filesuhhoh!h"hMh jt+ubh/. These files are kept in the temporary directory where SCALE
executes and are not copied back to the directory where the input file
was located, unless specifically requested using a SCALE “}(h. These files are kept in the temporary directory where SCALE
executes and are not copied back to the directory where the input file
was located, unless specifically requested using a SCALE “h jt+hhh!NhNubjO)}(h ``shell``h]h/shell}(hhh j+ubah}(h]h]h]h]h]uhjNh jt+ubh/”
command. Curious users may also be interested in viewing the various
input files (i_*) that the MAVRIC sequence writes in order to run the
SCALE functional modules.}(h”
command. Curious users may also be interested in viewing the various
input files (i_*) that the MAVRIC sequence writes in order to run the
SCALE functional modules.h jt+hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j+hhubh)}(h.. _output-files:h]h}(h]h]h]h]h]houtput-filesuhh
hMh j+hhh!h"ubj)}(hhh](h))}(hWOutput files that are copied back to user’s area when the sequence finishes\ :sup:`a`h](h/OOutput files that are copied back to user’s area when the sequence finishes }(hOOutput files that are copied back to user’s area when the sequence finishes\ h j+ubh superscript)}(h:sup:`a`h]h/a}(hhh j+ubah}(h]h]h]h]h]uhj+h j+ubeh}(h]h]h]h]h]uhh(h!h"hMh j+ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]colwidthK uhjh j+ubj)}(hhh]h}(h]h]h]h]h]colwidthKuhjh j+ubj)}(hhh]h}(h]h]h]h]h]colwidthKfuhjh j+ubj3)}(hhh]j8)}(hhh](j=)}(hhh]h;)}(hFilenameh]h/Filename}(hj,h j,ubah}(h]h]h]h]h]uhh:h!h"hMh j,ubah}(h]h]h]h]h]uhj<h j,ubj=)}(hhh]h;)}(hViewerh]h/Viewer}(hj+,h j),ubah}(h]h]h]h]h]uhh:h!h"hMh j&,ubah}(h]h]h]h]h]uhj<h j,ubj=)}(hhh]h;)}(hDescriptionh]h/Description}(hjB,h j@,ubah}(h]h]h]h]h]uhh:h!h"hMh j=,ubah}(h]h]h]h]h]uhj<h j,ubeh}(h]h]h]h]h]uhj7h j ,ubah}(h]h]h]h]h]uhj2h j+ubj)}(hhh](j8)}(hhh](j=)}(hhh]h;)}(hOutput Summaryh]h/Output Summary}(hjk,h ji,ubah}(h]h]h]h]h]uhh:h!h"hMh jf,ubah}(h]h]h]h]h]uhj<h jc,ubj=)}(hhh]h}(h]h]h]h]h]uhj<h jc,ubj=)}(hhh]h}(h]h]h]h]h]uhj<h jc,ubeh}(h]h]h]h]h]uhj7h j`,ubj8)}(hhh](j=)}(hhh]h;)}(h*outputName*.outh](hA)}(h*outputName*h]h/
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sections for Denovo}(hj38h j18ubah}(h]h]h]h]h]uhh:h!h"hMh j.8ubah}(h]h]h]h]h]uhj<h j8ubeh}(h]h]h]h]h]uhj7h j8ubj8)}(hhh](j=)}(hhh]h;)}(hfort.51h]h/fort.51}(hjS8h jQ8ubah}(h]h]h]h]h]uhh:h!h"hMh jN8ubah}(h]h]h]h]h]uhj<h jK8ubj=)}(hhh]h;)}(h2text file, listings
of the mixing table
for Monacoh]h/2text file, listings
of the mixing table
for Monaco}(hjj8h jh8ubah}(h]h]h]h]h]uhh:h!h"hMh je8ubah}(h]h]h]h]h]uhj<h jK8ubeh}(h]h]h]h]h]uhj7h j8ubj8)}(hhh](j=)}(hhh]h;)}(hfort.52h]h/fort.52}(hj8h j8ubah}(h]h]h]h]h]uhh:h!h"hMh j8ubah}(h]h]h]h]h]uhj<h j8ubj=)}(hhh]h;)}(h4text file, review of
MAVRIC sequence input
variablesh]h/4text file, review of
MAVRIC sequence input
variables}(hj8h j8ubah}(h]h]h]h]h]uhh:h!h"hMh j8ubah}(h]h]h]h]h]uhj<h j8ubeh}(h]h]h]h]h]uhj7h j8ubj8)}(hhh](j=)}(hhh]h;)}(hfort.54h]h/fort.54}(hj8h j8ubah}(h]h]h]h]h]uhh:h!h"hM h j8ubah}(h]h]h]h]h]uhj<h j8ubj=)}(hhh]h;)}(h;energy bin boundaries
for the current cross
section libraryh]h/;energy bin boundaries
for the current cross
section library}(hj8h j8ubah}(h]h]h]h]h]uhh:h!h"hM h j8ubah}(h]h]h]h]h]uhj<h j8ubeh}(h]h]h]h]h]uhj7h j8ubj8)}(hhh](j=)}(hhh]h;)}(h
xkba_b.inph]h/
xkba_b.inp}(hj8h j8ubah}(h]h]h]h]h]uhh:h!h"hM
h j8ubah}(h]h]h]h]h]uhj<h j8ubj=)}(hhh](h;)}(h/binary input file for
Denovo – rename to
haveh]h//binary input file for
Denovo – rename to
have}(hj9h j
9ubah}(h]h]h]h]h]uhh:h!h"hM
h j
9ubh;)}(hJa \*.dsi extension
(Denovo simple input)
to be viewed via Mesh
File Viewerh]h/Ja *.dsi extension
(Denovo simple input)
to be viewed via Mesh
File Viewer}(hJa \*.dsi extension
(Denovo simple input)
to be viewed via Mesh
File Viewerh j9ubah}(h]h]h]h]h]uhh:h!h"hMh j
9ubeh}(h]h]h]h]h]uhj<h j8ubeh}(h]h]h]h]h]uhj7h j8ubeh}(h]h]h]h]h]uhjh j7ubeh}(h]h]h]h]h]colsKuhjh j7ubeh}(h](id32j7eh]h]intermediate-filesah]h]jjuhj
h j+hhh!h"hNj}jH9j7sj}j7j7subeh}(h]additional-output-filesah]h]additional output filesah]h]uhh#h j*hhh!h"hMubeh}(h]
mavric-outputah]h]
mavric outputah]h]uhh#h h%hhh!h"hMiubh$)}(hhh](h))}(hSample problemsh]h/Sample problems}(hjb9h j`9hhh!NhNubah}(h]h]h]h]h]uhh(h j]9hhh!h"hMubh$)}(hhh](h))}(h*Graphite shielding measurements with CADISh]h/*Graphite shielding measurements with CADIS}(hjs9h jq9hhh!NhNubah}(h]h]h]h]h]uhh(h jn9hhh!h"hMubh;)}(hXKAs shown in the Monaco sample problem for simulating the Ueki shielding experiments
(Monaco chapter Graphite Shielding Measurements) (SECTIONREFERENCE),
as the amount of shielding material between a source and detector increases,
the time required to reach a certain level of relative uncertainty increases quickly.
This example will use the MAVRIC automated variance reduction capability to optimize the
calculation of the dose rate at the detector location by specifying an importance map block
with an adjoint source made from the detector response function and the detector location.h]h/XKAs shown in the Monaco sample problem for simulating the Ueki shielding experiments
(Monaco chapter Graphite Shielding Measurements) (SECTIONREFERENCE),
as the amount of shielding material between a source and detector increases,
the time required to reach a certain level of relative uncertainty increases quickly.
This example will use the MAVRIC automated variance reduction capability to optimize the
calculation of the dose rate at the detector location by specifying an importance map block
with an adjoint source made from the detector response function and the detector location.}(hj9h j9hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh jn9hhubh$)}(hhh](h))}(h
Input fileh]h/
Input file}(hj9h j9hhh!NhNubah}(h]h]h]h]h]uhh(h j9hhh!h"hM&ubh;)}(hX*The following is a listing of the file ``mavric.graphiteCADIS.inp`` located
in the SCALE ``samples\input`` directory. This calculation will use the
coarse-group shielding library (27n19g) for all of the importance map
calculations and the fine-group library (200n47g) for the final Monaco
step. Additions, compared to the file ``monaco.graphite.inp``, include a
grid geometry for the Denovo computational mesh, a mesh tally to better
visualize the particle flow, and the importance map block to optimize
the Monte Carlo calculation of the point detector.h](h/'The following is a listing of the file }(h'The following is a listing of the file h j9hhh!NhNubjO)}(h``mavric.graphiteCADIS.inp``h]h/mavric.graphiteCADIS.inp}(hhh j9ubah}(h]h]h]h]h]uhjNh j9ubh/ located
in the SCALE }(h located
in the SCALE h j9hhh!NhNubjO)}(h``samples\input``h]h/
samples\input}(hhh j9ubah}(h]h]h]h]h]uhjNh j9ubh/ directory. This calculation will use the
coarse-group shielding library (27n19g) for all of the importance map
calculations and the fine-group library (200n47g) for the final Monaco
step. Additions, compared to the file }(h directory. This calculation will use the
coarse-group shielding library (27n19g) for all of the importance map
calculations and the fine-group library (200n47g) for the final Monaco
step. Additions, compared to the file h j9hhh!NhNubjO)}(h``monaco.graphite.inp``h]h/monaco.graphite.inp}(hhh j9ubah}(h]h]h]h]h]uhjNh j9ubh/, include a
grid geometry for the Denovo computational mesh, a mesh tally to better
visualize the particle flow, and the importance map block to optimize
the Monte Carlo calculation of the point detector.}(h, include a
grid geometry for the Denovo computational mesh, a mesh tally to better
visualize the particle flow, and the importance map block to optimize
the Monte Carlo calculation of the point detector.h j9hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM(h j9hhubjy)}(hX(=mavric
Monaco/MAVRIC Training - Exercise 3. Graphite Shielding Measurements Revisited
v7-27n19g
'-------------------------------------------------------------------------------
' Composition Block - standard SCALE input
'-------------------------------------------------------------------------------
read composition
para(h2o) 1 1.0 293.0 end
carbon 2 den=1.7 1.0 300.0 end
end composition
'-------------------------------------------------------------------------------
' Geometry Block - SCALE standard geometry package (SGGP)
'-------------------------------------------------------------------------------
read geometry
global unit 1
cuboid 1 25.0 -25.0 25.0 -25.0 25.0 -25.0
cone 2 10.35948 25.01 0.0 0.0 rotate a1=-90 a2=-90 a3=0
cuboid 3 90.0 70.0 40.0 -40.0 40.0 -40.0
cuboid 99 120.0 -30.0 50.0 -50.0 50.0 -50.0
media 1 1 1 -2
media 0 1 2
media 2 1 3
media 0 1 99 -1 -2 -3
boundary 99
end geometry
'-------------------------------------------------------------------------------
' Definitions Block
'-------------------------------------------------------------------------------
read definitions
location 1
position 110 0 0
end location
response 5
title="ANSI standard (1977) neutron flux-to-dose-rate factors"
specialDose=9029
end response
distribution 1
title="Cf-252 neutrons, Watt spectrum a=1.025 MeV and b=2.926/MeV"
special="wattSpectrum"
parameters 1.025 2.926 end
end distribution
gridGeometry 7
title="large meshes in paraffin, 5 cm mesh for shield thicknesses"
xLinear 5 -25 25
xLinear 12 30 90
xplanes 100 110 120 -30 end
yplanes -50 -40 40 50 end
yLinear 7 -35 35
zplanes -50 -40 40 50 end
zLinear 7 -35 35
end gridGeometry
end definitions
'-------------------------------------------------------------------------------
' Sources Block
' Cf-252 neutrons, Watt fission spectrum model
' with a=1.025 MeV and b=2.926/MeV
'-------------------------------------------------------------------------------
read sources
src 1
title="Cf-252 neutrons, Watt fission spectrum model"
strength=4.05E+07
cuboid 0.01 0.01 0 0 0 0
neutrons
eDistributionID=1
end src
end sources
'-------------------------------------------------------------------------------
' Tallies Block
'-------------------------------------------------------------------------------
read tallies
pointDetector 1
title="center of detector"
locationID=1
responseID=5
end pointDetector
meshTally 1
title="example mesh tally"
gridGeometryID=7
responseID=5
noGroupFluxes
end meshTally
end tallies
'-------------------------------------------------------------------------------
' Parameters Block
'-------------------------------------------------------------------------------
read parameters
randomSeed=00003ecd7b4e3e8b
library="v7-200n47g"
perBatch=10000 batches=10
fissionMult=0 noPhotons
end parameters
'-------------------------------------------------------------------------------
' Importance Map Block
'-------------------------------------------------------------------------------
read importanceMap
adjointSource 1
locationID=1
responseID=5
end adjointSource
gridGeometryID=7
macromaterial
mmTolerance=0.01
end macromaterial
end importanceMap
end data
endh]h/X(=mavric
Monaco/MAVRIC Training - Exercise 3. Graphite Shielding Measurements Revisited
v7-27n19g
'-------------------------------------------------------------------------------
' Composition Block - standard SCALE input
'-------------------------------------------------------------------------------
read composition
para(h2o) 1 1.0 293.0 end
carbon 2 den=1.7 1.0 300.0 end
end composition
'-------------------------------------------------------------------------------
' Geometry Block - SCALE standard geometry package (SGGP)
'-------------------------------------------------------------------------------
read geometry
global unit 1
cuboid 1 25.0 -25.0 25.0 -25.0 25.0 -25.0
cone 2 10.35948 25.01 0.0 0.0 rotate a1=-90 a2=-90 a3=0
cuboid 3 90.0 70.0 40.0 -40.0 40.0 -40.0
cuboid 99 120.0 -30.0 50.0 -50.0 50.0 -50.0
media 1 1 1 -2
media 0 1 2
media 2 1 3
media 0 1 99 -1 -2 -3
boundary 99
end geometry
'-------------------------------------------------------------------------------
' Definitions Block
'-------------------------------------------------------------------------------
read definitions
location 1
position 110 0 0
end location
response 5
title="ANSI standard (1977) neutron flux-to-dose-rate factors"
specialDose=9029
end response
distribution 1
title="Cf-252 neutrons, Watt spectrum a=1.025 MeV and b=2.926/MeV"
special="wattSpectrum"
parameters 1.025 2.926 end
end distribution
gridGeometry 7
title="large meshes in paraffin, 5 cm mesh for shield thicknesses"
xLinear 5 -25 25
xLinear 12 30 90
xplanes 100 110 120 -30 end
yplanes -50 -40 40 50 end
yLinear 7 -35 35
zplanes -50 -40 40 50 end
zLinear 7 -35 35
end gridGeometry
end definitions
'-------------------------------------------------------------------------------
' Sources Block
' Cf-252 neutrons, Watt fission spectrum model
' with a=1.025 MeV and b=2.926/MeV
'-------------------------------------------------------------------------------
read sources
src 1
title="Cf-252 neutrons, Watt fission spectrum model"
strength=4.05E+07
cuboid 0.01 0.01 0 0 0 0
neutrons
eDistributionID=1
end src
end sources
'-------------------------------------------------------------------------------
' Tallies Block
'-------------------------------------------------------------------------------
read tallies
pointDetector 1
title="center of detector"
locationID=1
responseID=5
end pointDetector
meshTally 1
title="example mesh tally"
gridGeometryID=7
responseID=5
noGroupFluxes
end meshTally
end tallies
'-------------------------------------------------------------------------------
' Parameters Block
'-------------------------------------------------------------------------------
read parameters
randomSeed=00003ecd7b4e3e8b
library="v7-200n47g"
perBatch=10000 batches=10
fissionMult=0 noPhotons
end parameters
'-------------------------------------------------------------------------------
' Importance Map Block
'-------------------------------------------------------------------------------
read importanceMap
adjointSource 1
locationID=1
responseID=5
end adjointSource
gridGeometryID=7
macromaterial
mmTolerance=0.01
end macromaterial
end importanceMap
end data
end}(hhh j9ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM1h j9hhubeh}(h]
input-fileah]h]h]
input fileah]uhh#h jn9hhh!h"hM&
referencedKubh$)}(hhh](h))}(hOutputh]h/Output}(hj:h j:hhh!NhNubah}(h]h]h]h]h]uhh(h j:hhh!h"hMubh;)}(hnMAVRIC results for the point detector response for the 20 cm case are shown below and in :numref:`mesh-tally`.h](h/YMAVRIC results for the point detector response for the 20 cm case are shown below and in }(hYMAVRIC results for the point detector response for the 20 cm case are shown below and in h j:hhh!NhNubhp)}(h:numref:`mesh-tally`h]jO)}(hj:h]h/
mesh-tally}(hhh j:ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j:ubah}(h]h]h]h]h]refdocj refdomainj):reftypenumrefrefexplicitrefwarnj
mesh-tallyuhhoh!h"hMh j:ubh/.}(hjh j:hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j:hhubjy)}(hXLNeutron Point Detector 1. center of detector
average standard relat FOM stat checks
tally/quantity value deviation uncert (/min) 1 2 3 4 5 6
------------------ ----------- ----------- ------- -------- -----------
uncollided flux 1.06384E+01 1.88744E-02 0.00177
total flux 2.36367E+02 5.47276E+00 0.02315 8.10E+02 X - X - X -
response 5 1.28632E-02 1.74351E-04 0.01355 2.36E+03 X X X X X X
------------------ ----------- ----------- ------- -------- -----------h]h/XLNeutron Point Detector 1. center of detector
average standard relat FOM stat checks
tally/quantity value deviation uncert (/min) 1 2 3 4 5 6
------------------ ----------- ----------- ------- -------- -----------
uncollided flux 1.06384E+01 1.88744E-02 0.00177
total flux 2.36367E+02 5.47276E+00 0.02315 8.10E+02 X - X - X -
response 5 1.28632E-02 1.74351E-04 0.01355 2.36E+03 X X X X X X
------------------ ----------- ----------- ------- -------- -----------}(hhh jE:ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j:hhubh;)}(hXFThis problem took only ~2.5 minutes (0.2 in Denovo and 2.3 minutes in
Monaco) on the same processor as the 20 minute analog case. (The figure
of merit [FOM] is 15 times higher than the analog.) Note that the point
detector dose rate is the same as the Monaco analog sample problem, but
the relative uncertainty is smaller with less computation time. CADIS
has optimized the calculation by focusing on neutrons that contribute to
the dose rate at the detector location at the expense of neutrons in
the paraffin block. This is demonstrated by the mesh tally of dose rates
where the values for the dose rate are lower in the paraffin block and
the relative uncertainties are higher. Since the calculation was
optimized for the position of the detector, dose rates in other parts of
the problem are underestimated and should not be believed.h]h/XFThis problem took only ~2.5 minutes (0.2 in Denovo and 2.3 minutes in
Monaco) on the same processor as the 20 minute analog case. (The figure
of merit [FOM] is 15 times higher than the analog.) Note that the point
detector dose rate is the same as the Monaco analog sample problem, but
the relative uncertainty is smaller with less computation time. CADIS
has optimized the calculation by focusing on neutrons that contribute to
the dose rate at the detector location at the expense of neutrons in
the paraffin block. This is demonstrated by the mesh tally of dose rates
where the values for the dose rate are lower in the paraffin block and
the relative uncertainties are higher. Since the calculation was
optimized for the position of the detector, dose rates in other parts of
the problem are underestimated and should not be believed.}(hjY:h jW:hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j:hhubh;)}(hX+The mesh tally shows that the CADIS calculation did not follow as many
particles deep into the paraffin block, so the uncertainties are greater
there, but that is what this problem was supposed to do—reduce the
uncertainty at the point detector at the expense of the other portions
of the problem.h]h/X+The mesh tally shows that the CADIS calculation did not follow as many
particles deep into the paraffin block, so the uncertainties are greater
there, but that is what this problem was supposed to do—reduce the
uncertainty at the point detector at the expense of the other portions
of the problem.}(hjg:h je:hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j:hhubh)}(h.. _mesh-tally:h]h}(h]h]h]h]h]h
mesh-tallyuhh
hMh j:hhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/mesh-tally.png
Mesh tally showing neutron dose rate (rem/hr) and uncertainties for the analog case and the CADIS case.
h]h}(h]h]h]h]h]urifigs/MAVRIC/mesh-tally.pngjY}j[j:suhjKh j~:h!h"hMubj)}(hgMesh tally showing neutron dose rate (rem/hr) and uncertainties for the analog case and the CADIS case.h]h/gMesh tally showing neutron dose rate (rem/hr) and uncertainties for the analog case and the CADIS case.}(hj:h j:ubah}(h]h]h]h]h]uhjh!h"hMh j~:ubeh}(h](id33j}:eh]h]
mesh-tallyah]h]jjuhjhMh j:hhh!h"j}j:js:sj}j}:js:subeh}(h]outputah]h]h]outputah]uhh#h jn9hhh!h"hMj:Kubeh}(h]*graphite-shielding-measurements-with-cadisah]h]*graphite shielding measurements with cadisah]h]uhh#h j]9hhh!h"hMubh$)}(hhh](h))}(h#Dose rates outside of a simple caskh]h/#Dose rates outside of a simple cask}(hj:h j:hhh!NhNubah}(h]h]h]h]h]uhh(h j:hhh!h"hMubh;)}(hXThis example problem is a full-size cylindrical cask model, which consists of an inner steel liner,
a thick section of concrete, and an outer steel cover. This problem is intended to be used as a tool to
teach users how to build MAVRIC input files. This is not a completely realistic shipping cask; it has been
simplified greatly for this purpose. The goal of this example it to show how to quickly calculate neutron
and photon does rates at six points outside of the cask, including in front of the vent port.h]h/XThis example problem is a full-size cylindrical cask model, which consists of an inner steel liner,
a thick section of concrete, and an outer steel cover. This problem is intended to be used as a tool to
teach users how to build MAVRIC input files. This is not a completely realistic shipping cask; it has been
simplified greatly for this purpose. The goal of this example it to show how to quickly calculate neutron
and photon does rates at six points outside of the cask, including in front of the vent port.}(hj:h j:hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j:hhubh$)}(hhh](h))}(hGeometry and materialsh]h/Geometry and materials}(hj:h j:hhh!NhNubah}(h]h]h]h]h]uhh(h j:hhh!h"hMubh;)}(hXThe simple model of a cask is shown in :numref:`cask-geom2`.
Vent ports at the top and bottom of the cask are modeled as void all of the way around the cask.
The interior of the cask was modeled using materials from about 20 typical pressurized water reactor
(PWR) fuel assemblies (including the UO2, Zr, Fe, Ni, Cr, Sn, and other constituents),
homogenized over the interior volume. The total mass of the fuel/assembly hardware in this
region is 10.6 metric tonnes. Separate end regions of the assemblies are not modeled in this
simple example. Also note that the fuel material is based on fresh fuel, not spent fuel with
its hundreds of fission products.h](h/'The simple model of a cask is shown in }(h'The simple model of a cask is shown in h j:hhh!NhNubhp)}(h:numref:`cask-geom2`h]jO)}(hj:h]h/
cask-geom2}(hhh j:ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j:ubah}(h]h]h]h]h]refdocj refdomainj:reftypenumrefrefexplicitrefwarnj
cask-geom2uhhoh!h"hMh j:ubh/XU.
Vent ports at the top and bottom of the cask are modeled as void all of the way around the cask.
The interior of the cask was modeled using materials from about 20 typical pressurized water reactor
(PWR) fuel assemblies (including the UO2, Zr, Fe, Ni, Cr, Sn, and other constituents),
homogenized over the interior volume. The total mass of the fuel/assembly hardware in this
region is 10.6 metric tonnes. Separate end regions of the assemblies are not modeled in this
simple example. Also note that the fuel material is based on fresh fuel, not spent fuel with
its hundreds of fission products.}(hXU.
Vent ports at the top and bottom of the cask are modeled as void all of the way around the cask.
The interior of the cask was modeled using materials from about 20 typical pressurized water reactor
(PWR) fuel assemblies (including the UO2, Zr, Fe, Ni, Cr, Sn, and other constituents),
homogenized over the interior volume. The total mass of the fuel/assembly hardware in this
region is 10.6 metric tonnes. Separate end regions of the assemblies are not modeled in this
simple example. Also note that the fuel material is based on fresh fuel, not spent fuel with
its hundreds of fission products.h j:hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j:hhubh)}(h.. _cask-geom2:h]h}(h]h]h]h]h]h
cask-geom2uhh
hMh j:hhh!h"ubj)}(hhh](jL)}(hg.. figure:: figs/MAVRIC/cask-geom2.png
:align: center
Cask geometry and detector locations.
h]h}(h]h]h]h]h]urifigs/MAVRIC/cask-geom2.pngjY}j[j3;suhjKh j%;h!h"hMubj)}(h%Cask geometry and detector locations.h]h/%Cask geometry and detector locations.}(hj7;h j5;ubah}(h]h]h]h]h]uhjh!h"hMh j%;ubeh}(h](id34j$;eh]h]
cask-geom2ah]h]jcenteruhjhMh j:hhh!h"j}jH;j;sj}j$;j;subeh}(h]geometry-and-materialsah]h]geometry and materialsah]h]uhh#h j:hhh!h"hMubh$)}(hhh](h))}(hSources and responsesh]h/Sources and responses}(hj[;h jY;hhh!NhNubah}(h]h]h]h]h]uhh(h jV;hhh!h"hMubh;)}(hXSpent fuel from a typical mid-sized PWR was used to determine the source
term. ORIGEN was used to deplete a full core (46.1 metric tonnes of
uranium, 4.2% enriched, with O, Zr, Fe, Ni, Cr, Sn, and other
constituents) to 55,000 MWdays/MTU. The contents of the modeled fuel
represent typical values for PWR fuel. ORIGEN then computed the neutron
and photon spectra in 27-group and 19-group energy structures for the
fuel following a 10-year cooling period after the last irradiation. The
total neutron source strength for the cask (1/6 of a full core, or about
20 assemblies) was 8.577×10\ :sup:`9` neutrons/s. The total photon
source strength was 7.155 × 10\ :sup:`16` photons/s.h](h/XNSpent fuel from a typical mid-sized PWR was used to determine the source
term. ORIGEN was used to deplete a full core (46.1 metric tonnes of
uranium, 4.2% enriched, with O, Zr, Fe, Ni, Cr, Sn, and other
constituents) to 55,000 MWdays/MTU. The contents of the modeled fuel
represent typical values for PWR fuel. ORIGEN then computed the neutron
and photon spectra in 27-group and 19-group energy structures for the
fuel following a 10-year cooling period after the last irradiation. The
total neutron source strength for the cask (1/6 of a full core, or about
20 assemblies) was 8.577×10 }(hXNSpent fuel from a typical mid-sized PWR was used to determine the source
term. ORIGEN was used to deplete a full core (46.1 metric tonnes of
uranium, 4.2% enriched, with O, Zr, Fe, Ni, Cr, Sn, and other
constituents) to 55,000 MWdays/MTU. The contents of the modeled fuel
represent typical values for PWR fuel. ORIGEN then computed the neutron
and photon spectra in 27-group and 19-group energy structures for the
fuel following a 10-year cooling period after the last irradiation. The
total neutron source strength for the cask (1/6 of a full core, or about
20 assemblies) was 8.577×10\ h jg;hhh!NhNubj+)}(h:sup:`9`h]h/9}(hhh jp;ubah}(h]h]h]h]h]uhj+h jg;ubh/B neutrons/s. The total photon
source strength was 7.155 × 10 }(hB neutrons/s. The total photon
source strength was 7.155 × 10\ h jg;hhh!NhNubj+)}(h :sup:`16`h]h/16}(hhh j;ubah}(h]h]h]h]h]uhj+h jg;ubh/ photons/s.}(h photons/s.h jg;hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jV;hhubh;)}(hX%Two cases will be done for this example: one for calculating the neutron
dose rates from the spent fuel neutrons and the other for calculating
the photon dose rates from the spent fuel photons. The source spectra
and response functions are shown in :numref:`spent-neutron` through :numref:`ANSI-photon`
and listed in :numref:`source-and-response`. Note that in this example, the neutron source
shown in :numref:`spent-neutron` and :numref:`source-and-response` is considered the final neutron
source: no further neutron multiplication is considered.h](h/Two cases will be done for this example: one for calculating the neutron
dose rates from the spent fuel neutrons and the other for calculating
the photon dose rates from the spent fuel photons. The source spectra
and response functions are shown in }(hTwo cases will be done for this example: one for calculating the neutron
dose rates from the spent fuel neutrons and the other for calculating
the photon dose rates from the spent fuel photons. The source spectra
and response functions are shown in h j;hhh!NhNubhp)}(h:numref:`spent-neutron`h]jO)}(hj;h]h/
spent-neutron}(hhh j;ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j;ubah}(h]h]h]h]h]refdocj refdomainj;reftypenumrefrefexplicitrefwarnj
spent-neutronuhhoh!h"hMh j;ubh/ through }(h through h j;hhh!NhNubhp)}(h:numref:`ANSI-photon`h]jO)}(hj;h]h/ANSI-photon}(hhh j;ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j;ubah}(h]h]h]h]h]refdocj refdomainj;reftypenumrefrefexplicitrefwarnjansi-photonuhhoh!h"hMh j;ubh/
and listed in }(h
and listed in h j;hhh!NhNubhp)}(h:numref:`source-and-response`h]jO)}(hj;h]h/source-and-response}(hhh j;ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j;ubah}(h]h]h]h]h]refdocj refdomainj;reftypenumrefrefexplicitrefwarnjsource-and-responseuhhoh!h"hMh j;ubh/9. Note that in this example, the neutron source
shown in }(h9. Note that in this example, the neutron source
shown in h j;hhh!NhNubhp)}(h:numref:`spent-neutron`h]jO)}(hj<h]h/
spent-neutron}(hhh j<ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j<ubah}(h]h]h]h]h]refdocj refdomainj"<reftypenumrefrefexplicitrefwarnj
spent-neutronuhhoh!h"hMh j;ubh/ and }(h and h j;hhh!NhNubhp)}(h:numref:`source-and-response`h]jO)}(hj;<h]h/source-and-response}(hhh j=<ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j9<ubah}(h]h]h]h]h]refdocj refdomainjG<reftypenumrefrefexplicitrefwarnjsource-and-responseuhhoh!h"hMh j;ubh/Y is considered the final neutron
source: no further neutron multiplication is considered.}(hY is considered the final neutron
source: no further neutron multiplication is considered.h j;hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jV;hhubh)}(h.. _spent-neutron:h]h}(h]h]h]h]h]h
spent-neutronuhh
hMh jV;hhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/fig4.1.08_caskSrcRespn.dist1.png
:align: center
Spent fuel neutron source spectrum with strength 8.577 × 10\ :sup:`9`/second.
h]h}(h]h]h]h]h]uri,figs/MAVRIC/fig4.1.08_caskSrcRespn.dist1.pngjY}j[j}<suhjKh jo<h!h"hM
ubj)}(hPSpent fuel neutron source spectrum with strength 8.577 × 10\ :sup:`9`/second.h](h/@Spent fuel neutron source spectrum with strength 8.577 × 10 }(h@Spent fuel neutron source spectrum with strength 8.577 × 10\ h j<ubj+)}(h:sup:`9`h]h/9}(hhh j<ubah}(h]h]h]h]h]uhj+h j<ubh//second.}(h/second.h j<ubeh}(h]h]h]h]h]uhjh!h"hM
h jo<ubeh}(h](id35jn<eh]h]
spent-neutronah]h]jcenteruhjhM
h jV;hhh!h"j}j<jd<sj}jn<jd<subh)}(h.. _ANSI-neutron:h]h}(h]h]h]h]h]hansi-neutronuhh
hMh jV;hhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/fig4.1.09_caskSrcRespn.resp1.png
:align: center
ANSI-1977/ flux-to-dose-rate factors (rem/hr)/(neutrons/\cm :sup:`2`/sec).
h]h}(h]h]h]h]h]uri,figs/MAVRIC/fig4.1.09_caskSrcRespn.resp1.pngjY}j[j<suhjKh j<h!h"hMubj)}(hJANSI-1977/ flux-to-dose-rate factors (rem/hr)/(neutrons/\cm :sup:`2`/sec).h](h/h j>hhh!NhNubah}(h]h]h]h]h]uhh(h j>hhh!h"hM(ubh;)}(hX(The analog model for this problem starts with the problem title and the cross section library name,
which in this example is the ENDF/B-VII.0 27 neutron group / 19 photon group library.
This is in the SCALE ``samples\input`` directory as ``mavric.caskAnalogn.inp`` and ``mavric.caskAnalogp.inp``.h](h/The analog model for this problem starts with the problem title and the cross section library name,
which in this example is the ENDF/B-VII.0 27 neutron group / 19 photon group library.
This is in the SCALE }(hThe analog model for this problem starts with the problem title and the cross section library name,
which in this example is the ENDF/B-VII.0 27 neutron group / 19 photon group library.
This is in the SCALE h j>hhh!NhNubjO)}(h``samples\input``h]h/
samples\input}(hhh j>ubah}(h]h]h]h]h]uhjNh j>ubh/ directory as }(h directory as h j>hhh!NhNubjO)}(h``mavric.caskAnalogn.inp``h]h/mavric.caskAnalogn.inp}(hhh j/>ubah}(h]h]h]h]h]uhjNh j>ubh/ and }(h and h j>hhh!NhNubjO)}(h``mavric.caskAnalogp.inp``h]h/mavric.caskAnalogp.inp}(hhh jB>ubah}(h]h]h]h]h]uhjNh j>ubh/.}(hjh j>hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM*h j>hhubjy)}(h'=mavric
Simplified cask model
v7-27n19gh]h/'=mavric
Simplified cask model
v7-27n19g}(hhh jZ>ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM.h j>hhubh;)}(hNThen the material compositions are listed for fresh fuel, concrete, and steel.h]h/NThen the material compositions are listed for fresh fuel, concrete, and steel.}(hjn>h jl>hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM4h j>hhubjy)}(hXpread composition
wtptFuel 1 0.913717475 18 6000 0.00939719 7014 0.00528993
8016 9.73397641 13000 0.00715715 14000 0.01031670
15000 0.02227505 22000 0.00780567 24000 0.36655141
25000 0.01716839 26000 0.72041451 27000 0.00523824
28000 0.68955526 40000 15.78990702 41000 0.05130153
42000 0.02844690 50118 0.25877903 92235 3.03560962
92238 69.24080999
1.0 293.0 end
orconcrete 2 1.0 293.0 end
ss304 3 1.0 293.0 end
end compositionh]h/Xpread composition
wtptFuel 1 0.913717475 18 6000 0.00939719 7014 0.00528993
8016 9.73397641 13000 0.00715715 14000 0.01031670
15000 0.02227505 22000 0.00780567 24000 0.36655141
25000 0.01716839 26000 0.72041451 27000 0.00523824
28000 0.68955526 40000 15.78990702 41000 0.05130153
42000 0.02844690 50118 0.25877903 92235 3.03560962
92238 69.24080999
1.0 293.0 end
orconcrete 2 1.0 293.0 end
ss304 3 1.0 293.0 end
end composition}(hhh jz>ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM6h j>hhubh;)}(heThen the SGGP geometry is listed, with the origin of the coordinate system at the center of the cask.h]h/eThen the SGGP geometry is listed, with the origin of the coordinate system at the center of the cask.}(hj>h j>hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMEh j>hhubjy)}(hXread geometry
global unit 1
zcylinder 1 95.0 228.6 -228.6
zcylinder 2 170.0 255.2 -255.2
zcylinder 3 90.0 240.6 -240.6
zcylinder 4 90.0 280.6 -280.6
zcylinder 5 170.0 280.6 -280.6
zcylinder 6 170.0 285.6 -285.6
zcylinder 7 95.0 255.2 -255.2
zcylinder 8 100.0 255.2 -255.2
zcylinder 9 168.0 255.2 -255.2
sphere 10 999.0
media 1 1 1 vol=1.29629E+07
media 3 1 8 -7 vol=1.56338E+06
media 2 1 9 -8 vol=2.92216E+07
media 3 1 2 -9 vol=1.08394E+06
media 3 1 3 -1 vol=6.10726E+05
media 2 1 4 -3 vol=2.03575E+06
media 3 1 6 -5 vol=9.07920E+05
media 0 1 5 -4 -2 vol=3.31953E+06
media 0 1 7 -4 -1 vol=1.54598E+05
media 0 1 10 -6 vol=4.12429E+09
boundary 10
end geometryh]h/Xread geometry
global unit 1
zcylinder 1 95.0 228.6 -228.6
zcylinder 2 170.0 255.2 -255.2
zcylinder 3 90.0 240.6 -240.6
zcylinder 4 90.0 280.6 -280.6
zcylinder 5 170.0 280.6 -280.6
zcylinder 6 170.0 285.6 -285.6
zcylinder 7 95.0 255.2 -255.2
zcylinder 8 100.0 255.2 -255.2
zcylinder 9 168.0 255.2 -255.2
sphere 10 999.0
media 1 1 1 vol=1.29629E+07
media 3 1 8 -7 vol=1.56338E+06
media 2 1 9 -8 vol=2.92216E+07
media 3 1 2 -9 vol=1.08394E+06
media 3 1 3 -1 vol=6.10726E+05
media 2 1 4 -3 vol=2.03575E+06
media 3 1 6 -5 vol=9.07920E+05
media 0 1 5 -4 -2 vol=3.31953E+06
media 0 1 7 -4 -1 vol=1.54598E+05
media 0 1 10 -6 vol=4.12429E+09
boundary 10
end geometry}(hhh j>ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMGh j>hhubh;)}(hThe definitions block contains locations, response functions, grid geometries, and a distribution used by the source input block. For the neutron source/neutron dose problem, the definitions block is listed below.h]h/The definitions block contains locations, response functions, grid geometries, and a distribution used by the source input block. For the neutron source/neutron dose problem, the definitions block is listed below.}(hj>h j>hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMbh j>hhubjy)}(hXread definitions
location 1 position 180.0 0.0 0.0 end location
location 2 position 0.0 0.0 295.6 end location
location 3 position 180.0 0.0 267.9 end location
location 4 position 270.0 0.0 0.0 end location
location 5 position 0.0 0.0 385.6 end location
location 6 position 270.0 0.0 385.6 end location
response 1 specialDose=9029 end response
distribution 1
title="kewaunee core, 3 cycles and then 10 years"
neutronGroups
truePDF 2.040E-02 2.147E-01 2.365E-01 1.267E-01 1.586E-01
1.587E-01 7.281E-02 1.073E-02 7.688E-04 5.694E-05
4.479E-06 3.148E-07 4.983E-08 9.864E-09 1.117E-09
3.286E-10 1.060E-10 9.203E-11 9.135E-11 1.755E-10
2.590E-11 3.024E-11 3.451E-11 3.269E-12 5.447E-12
4.089E-14 4.916E-14 end
end distribution
end definitionsh]h/Xread definitions
location 1 position 180.0 0.0 0.0 end location
location 2 position 0.0 0.0 295.6 end location
location 3 position 180.0 0.0 267.9 end location
location 4 position 270.0 0.0 0.0 end location
location 5 position 0.0 0.0 385.6 end location
location 6 position 270.0 0.0 385.6 end location
response 1 specialDose=9029 end response
distribution 1
title="kewaunee core, 3 cycles and then 10 years"
neutronGroups
truePDF 2.040E-02 2.147E-01 2.365E-01 1.267E-01 1.586E-01
1.587E-01 7.281E-02 1.073E-02 7.688E-04 5.694E-05
4.479E-06 3.148E-07 4.983E-08 9.864E-09 1.117E-09
3.286E-10 1.060E-10 9.203E-11 9.135E-11 1.755E-10
2.590E-11 3.024E-11 3.451E-11 3.269E-12 5.447E-12
4.089E-14 4.916E-14 end
end distribution
end definitions}(hhh j>ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMdh j>hhubh;)}(h6The neutron source from the spent fuel is then listed.h]h/6The neutron source from the spent fuel is then listed.}(hj>h j>hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMzh j>hhubjy)}(hread sources
src 1
title="1/6 of kewaunee core, ~ 0.25 Ci"
strength=8.577E+09
neutrons
zCylinder 95.0 228.6 -228.6
eDistributionID=1
end src
end sourcesh]h/read sources
src 1
title="1/6 of kewaunee core, ~ 0.25 Ci"
strength=8.577E+09
neutrons
zCylinder 95.0 228.6 -228.6
eDistributionID=1
end src
end sources}(hhh j>ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM|h j>hhubh;)}(h^Six point detectors are used to evaluate dose rates radially, axially, and near the vent port.h]h/^Six point detectors are used to evaluate dose rates radially, axially, and near the vent port.}(hj>h j>hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j>hhubjy)}(hXread tallies
pointDetector 1 locationID=1 responseID=1 end pointDetector
pointDetector 2 locationID=2 responseID=1 end pointDetector
pointDetector 3 locationID=3 responseID=1 end pointDetector
pointDetector 4 locationID=4 responseID=1 end pointDetector
pointDetector 5 locationID=5 responseID=1 end pointDetector
pointDetector 6 locationID=6 responseID=1 end pointDetector
end talliesh]h/Xread tallies
pointDetector 1 locationID=1 responseID=1 end pointDetector
pointDetector 2 locationID=2 responseID=1 end pointDetector
pointDetector 3 locationID=3 responseID=1 end pointDetector
pointDetector 4 locationID=4 responseID=1 end pointDetector
pointDetector 5 locationID=5 responseID=1 end pointDetector
pointDetector 6 locationID=6 responseID=1 end pointDetector
end tallies}(hhh j>ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j>hhubh;)}(hThe Monte Carlo parameters were tailored for the neutron problem to be 1-minute batches
on a 2 GHz Linux computer. For the photon problem, the number per batch would be 91,000 for 1-minute batches.h]h/The Monte Carlo parameters were tailored for the neutron problem to be 1-minute batches
on a 2 GHz Linux computer. For the photon problem, the number per batch would be 91,000 for 1-minute batches.}(hj?h j?hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j>hhubjy)}(h|read parameters
randomSeed=8655745280030001
perBatch=25400 batches=600
fissionMult=0 noPhotons
end parametersh]h/|read parameters
randomSeed=8655745280030001
perBatch=25400 batches=600
fissionMult=0 noPhotons
end parameters}(hhh j?ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j>hhubh;)}(hXNo biasing is specified, which will use the default weight window target value of 1 for every energy
group in every region. To allow the neutrons to penetrate into the cask wall before being rouletted,
a larger window ratio is used, making the lower weight window bound 0.01.h]h/XNo biasing is specified, which will use the default weight window target value of 1 for every energy
group in every region. To allow the neutrons to penetrate into the cask wall before being rouletted,
a larger window ratio is used, making the lower weight window bound 0.01.}(hj.?h j,?hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j>hhubjy)}(h.read biasing
windowRatio=199.0
end biasingh]h/.read biasing
windowRatio=199.0
end biasing}(hhh j:?ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j>hhubh;)}(hThe Monaco input is then ended.h]h/The Monaco input is then ended.}(hjN?h jL?hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j>hhubjy)}(hend data
endh]h/end data
end}(hhh jZ?ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j>hhubh;)}(hFor the photon source/photon dose rate problem, the definitions block would instead contain a photon flux-to-dose-rate response function and the energy distribution for the source.h]h/For the photon source/photon dose rate problem, the definitions block would instead contain a photon flux-to-dose-rate response function and the energy distribution for the source.}(hjn?h jl?hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j>hhubjy)}(hXread definitions
response 1
specialDose=9504
end response
…
distribution 1
title="kewaunee core, 3 cycles and then 10 years"
photonGroups
truePDF 1.320E-12 7.185E-11 3.281E-10 1.672E-09 4.167E-09
8.086E-08 7.937E-07 1.164E-05 3.331E-05 8.160E-03
3.511E-02 2.478E-02 4.827E-01 4.641E-02 9.736E-03
1.514E-02 5.182E-02 7.015E-02 2.560E-01 end
end distribution
end definitionsh]h/Xread definitions
response 1
specialDose=9504
end response
…
distribution 1
title="kewaunee core, 3 cycles and then 10 years"
photonGroups
truePDF 1.320E-12 7.185E-11 3.281E-10 1.672E-09 4.167E-09
8.086E-08 7.937E-07 1.164E-05 3.331E-05 8.160E-03
3.511E-02 2.478E-02 4.827E-01 4.641E-02 9.736E-03
1.514E-02 5.182E-02 7.015E-02 2.560E-01 end
end distribution
end definitions}(hhh jz?ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j>hhubh;)}(h>The sources block would contain the photon source information.h]h/>The sources block would contain the photon source information.}(hj?h j?hhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j>hhubjy)}(hread sources
src 1
title="1/6 of kewaunee core, ~ 2e6 Ci"
strength=7.155e+16
photons
zCylinder 95.0 228.6 -228.6
eDistributionID=1
end src
end sourcesh]h/read sources
src 1
title="1/6 of kewaunee core, ~ 2e6 Ci"
strength=7.155e+16
photons
zCylinder 95.0 228.6 -228.6
eDistributionID=1
end src
end sources}(hhh j?ubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh j>hhubh;)}(hX2Each of the two analog problems in the ``samples\input`` directory will run for
about 10 minutes. In this time, no meaningful results will be generated
due to the difficulty of the problem. Analog results for each case
running 110 hr are listed in :numref:`analog-neutron` for the neutron source/neutron
dose problem, while results for the photon problem are listed in
:numref:`analog-photon`. Note that after 110 hr, some of the relative uncertainties
in the point detector tallies are still quite high, and only one of the
six tallies in each problem passed all of the statistical checks.
:numref:`neutron-dose-plot` is the convergence plot for the neutron dose rate at point
detector 1, showing that the tally is not well converged and that some
batches contain rare events that change the tally value a great deal.h](h/'Each of the two analog problems in the }(h'Each of the two analog problems in the h j?hhh!NhNubjO)}(h``samples\input``h]h/
samples\input}(hhh j?ubah}(h]h]h]h]h]uhjNh j?ubh/ directory will run for
about 10 minutes. In this time, no meaningful results will be generated
due to the difficulty of the problem. Analog results for each case
running 110 hr are listed in }(h directory will run for
about 10 minutes. In this time, no meaningful results will be generated
due to the difficulty of the problem. Analog results for each case
running 110 hr are listed in h j?hhh!NhNubhp)}(h:numref:`analog-neutron`h]jO)}(hj?h]h/analog-neutron}(hhh j?ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j?ubah}(h]h]h]h]h]refdocj refdomainj?reftypenumrefrefexplicitrefwarnjanalog-neutronuhhoh!h"hMh j?ubh/a for the neutron source/neutron
dose problem, while results for the photon problem are listed in
}(ha for the neutron source/neutron
dose problem, while results for the photon problem are listed in
h j?hhh!NhNubhp)}(h:numref:`analog-photon`h]jO)}(hj?h]h/
analog-photon}(hhh j?ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j?ubah}(h]h]h]h]h]refdocj refdomainj?reftypenumrefrefexplicitrefwarnj
analog-photonuhhoh!h"hMh j?ubh/. Note that after 110 hr, some of the relative uncertainties
in the point detector tallies are still quite high, and only one of the
six tallies in each problem passed all of the statistical checks.
}(h. Note that after 110 hr, some of the relative uncertainties
in the point detector tallies are still quite high, and only one of the
six tallies in each problem passed all of the statistical checks.
h j?hhh!NhNubhp)}(h:numref:`neutron-dose-plot`h]jO)}(hj@h]h/neutron-dose-plot}(hhh j@ubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j@ubah}(h]h]h]h]h]refdocj refdomainj @reftypenumrefrefexplicitrefwarnjneutron-dose-plotuhhoh!h"hMh j?ubh/ is the convergence plot for the neutron dose rate at point
detector 1, showing that the tally is not well converged and that some
batches contain rare events that change the tally value a great deal.}(h is the convergence plot for the neutron dose rate at point
detector 1, showing that the tally is not well converged and that some
batches contain rare events that change the tally value a great deal.h j?hhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j>hhubj)}(hhh](h))}(hWAnalog Monaco results for the simplified cask model—neutron source/neutron dose rate.h]h/WAnalog Monaco results for the simplified cask model—neutron source/neutron dose rate.}(hjB@h j@@ubah}(h]h]h]h]h]uhh(h!h"hMh j=@ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jN@ubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab10.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab10.pngjY}j[jn@suhjKh j`@h!h"hKubah}(h]h]h]h]h]uhj<h j]@ubah}(h]h]h]h]h]uhj7h jZ@ubah}(h]h]h]h]h]uhjh jN@ubeh}(h]h]h]h]h]colsKuhjh j=@ubeh}(h]analog-neutronah]h]analog-neutronah]h]jcenteruhj
h j>hhh!NhNubj)}(hhh](h))}(hUAnalog Monaco results for the simplified cask model—photon source/photon dose rate.h]h/UAnalog Monaco results for the simplified cask model—photon source/photon dose rate.}(hj@h j@ubah}(h]h]h]h]h]uhh(h!h"hMh j@ubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh j@ubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab11.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab11.pngjY}j[j@suhjKh j@h!h"hKubah}(h]h]h]h]h]uhj<h j@ubah}(h]h]h]h]h]uhj7h j@ubah}(h]h]h]h]h]uhjh j@ubeh}(h]h]h]h]h]colsKuhjh j@ubeh}(h]
analog-photonah]h]
analog-photonah]h]jcenteruhj
h j>hhh!NhNubh)}(h.. _neutron-dose-plot:h]h}(h]h]h]h]h]hneutron-dose-plotuhh
hMh j>hhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/fig4.1.12_mavric.caskAnalogn.pd1.png
:align: center
:width: 500
Convergence plot for the neutron dose rate at point detector 1 (error bars show the 1-sigma tally uncertainties).
h]h}(h]h]h]h]h]width500uri0figs/MAVRIC/fig4.1.12_mavric.caskAnalogn.pd1.pngjY}j[jAsuhjKh j@h!h"hMubj)}(hqConvergence plot for the neutron dose rate at point detector 1 (error bars show the 1-sigma tally uncertainties).h]h/qConvergence plot for the neutron dose rate at point detector 1 (error bars show the 1-sigma tally uncertainties).}(hjAh jAubah}(h]h]h]h]h]uhjh!h"hMh j@ubeh}(h](id39j@eh]h]neutron-dose-plotah]h]jcenteruhjhMh j>hhh!h"j}jAj@sj}j@j@subeh}(h]analog-calculationah]h]analog calculationah]h]uhh#h j:hhh!h"hM(ubh$)}(hhh](h))}(hSAS4 calculationsh]h/SAS4 calculations}(hj*Ah j(Ahhh!NhNubah}(h]h]h]h]h]uhh(h j%Ahhh!h"hMubh;)}(hXCalculations for these two problems were also done using the SAS4
sequence in SCALE 5.1. SAS4 was specifically designed for cask
geometries and used a one-dimensional discrete-ordinates calculation
(either radially or axially) to determine weight windows. Results for
the neutron problem are shown in :numref:`neutron-problem`, and results for the
photon problem are shown in :numref:`photon-problem`. Note that SAS4 using radial
biasing is only expected to do well for the two radial point detector
locations. Similarly, only the two axial point detectors are expected to
do well when using axial biasing. SAS4 was not intended to do well for
the points near the vent port, but the results using the axial biasing
seem reasonable.h](h/X-Calculations for these two problems were also done using the SAS4
sequence in SCALE 5.1. SAS4 was specifically designed for cask
geometries and used a one-dimensional discrete-ordinates calculation
(either radially or axially) to determine weight windows. Results for
the neutron problem are shown in }(hX-Calculations for these two problems were also done using the SAS4
sequence in SCALE 5.1. SAS4 was specifically designed for cask
geometries and used a one-dimensional discrete-ordinates calculation
(either radially or axially) to determine weight windows. Results for
the neutron problem are shown in h j6Ahhh!NhNubhp)}(h:numref:`neutron-problem`h]jO)}(hjAAh]h/neutron-problem}(hhh jCAubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j?Aubah}(h]h]h]h]h]refdocj refdomainjMAreftypenumrefrefexplicitrefwarnjneutron-problemuhhoh!h"hMh j6Aubh/2, and results for the
photon problem are shown in }(h2, and results for the
photon problem are shown in h j6Ahhh!NhNubhp)}(h:numref:`photon-problem`h]jO)}(hjfAh]h/photon-problem}(hhh jhAubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jdAubah}(h]h]h]h]h]refdocj refdomainjrAreftypenumrefrefexplicitrefwarnjphoton-problemuhhoh!h"hMh j6Aubh/XK. Note that SAS4 using radial
biasing is only expected to do well for the two radial point detector
locations. Similarly, only the two axial point detectors are expected to
do well when using axial biasing. SAS4 was not intended to do well for
the points near the vent port, but the results using the axial biasing
seem reasonable.}(hXK. Note that SAS4 using radial
biasing is only expected to do well for the two radial point detector
locations. Similarly, only the two axial point detectors are expected to
do well when using axial biasing. SAS4 was not intended to do well for
the points near the vent port, but the results using the axial biasing
seem reasonable.h j6Ahhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j%Ahhubj)}(hhh](h))}(hSAS4 results using radial biasing (361 minutes) and axial biasing (361 minutes), for the simplified cask model—neutron source/neutron dose rateh]h/SAS4 results using radial biasing (361 minutes) and axial biasing (361 minutes), for the simplified cask model—neutron source/neutron dose rate}(hjAh jAubah}(h]h]h]h]h]uhh(h!h"hM h jAubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jAubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab12.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab12.pngjY}j[jAsuhjKh jAh!h"hKubah}(h]h]h]h]h]uhj<h jAubah}(h]h]h]h]h]uhj7h jAubah}(h]h]h]h]h]uhjh jAubeh}(h]h]h]h]h]colsKuhjh jAubeh}(h]neutron-problemah]h]neutron-problemah]h]jcenteruhj
h j%Ahhh!NhNubj)}(hhh](h))}(hSAS4 results using radial biasing (361 minutes) and axial biasing (361 minutes), for the simplified cask model—photon source/photon dose rateh]h/SAS4 results using radial biasing (361 minutes) and axial biasing (361 minutes), for the simplified cask model—photon source/photon dose rate}(hjAh jAubah}(h]h]h]h]h]uhh(h!h"hM h jAubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jAubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab13.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab13.pngjY}j[jBsuhjKh jBh!h"hKubah}(h]h]h]h]h]uhj<h jBubah}(h]h]h]h]h]uhj7h jBubah}(h]h]h]h]h]uhjh jAubeh}(h]h]h]h]h]colsKuhjh jAubeh}(h]photon-problemah]h]photon-problemah]h]jcenteruhj
h j%Ahhh!NhNubeh}(h]sas4-calculationsah]h]sas4 calculationsah]h]uhh#h j:hhh!h"hMubh$)}(hhh](h))}(hCalculations using CADISh]h/Calculations using CADIS}(hjFBh jDBhhh!NhNubah}(h]h]h]h]h]uhh(h jABhhh!h"hM ubh;)}(hXwIn the analog calculations, the dose rates at all six points could be
calculated at the same time. With MAVRIC and using CADIS, the importance
map will optimize the transport of particles towards only the selected
detector. Hence, each detector will have a separate calculation with an
importance map tailored to reduce the variance for only that detector.
Calculations for close detectors could be performed at the same time. For example, detectors 1
and 4 both need to push particles out of the cask in the positive
*x* direction, towards the *z*\ =0 plane. In this example, all six
detectors will use separate importance maps.h](h/XIn the analog calculations, the dose rates at all six points could be
calculated at the same time. With MAVRIC and using CADIS, the importance
map will optimize the transport of particles towards only the selected
detector. Hence, each detector will have a separate calculation with an
importance map tailored to reduce the variance for only that detector.
Calculations for close detectors could be performed at the same time. For example, detectors 1
and 4 both need to push particles out of the cask in the positive
}(hXIn the analog calculations, the dose rates at all six points could be
calculated at the same time. With MAVRIC and using CADIS, the importance
map will optimize the transport of particles towards only the selected
detector. Hence, each detector will have a separate calculation with an
importance map tailored to reduce the variance for only that detector.
Calculations for close detectors could be performed at the same time. For example, detectors 1
and 4 both need to push particles out of the cask in the positive
h jRBhhh!NhNubhA)}(h*x*h]h/x}(hhh j[Bubah}(h]h]h]h]h]uhh@h jRBubh/ direction, towards the }(h direction, towards the h jRBhhh!NhNubhA)}(h*z*h]h/z}(hhh jnBubah}(h]h]h]h]h]uhh@h jRBubh/Q =0 plane. In this example, all six
detectors will use separate importance maps.}(hQ\ =0 plane. In this example, all six
detectors will use separate importance maps.h jRBhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h jABhhubh;)}(hXiFor the importance map, in the input, the user lists what planes to use
for the adjoint discrete-ordinates calculation. These planes define
cells, which are treated as homogenous parallelpipeds by Denovo, made of
a macro material corresponding to a mixture of materials that are in the
cell in the true geometry. Users should try to bound as many materials
as possible with their selection of mesh planes. More mesh planes should
be used where the importance (adjoint flux) varies quickly, such as
near the adjoint sources (the detector positions). It is also important
to have planes on the true source bounding box.h]h/XiFor the importance map, in the input, the user lists what planes to use
for the adjoint discrete-ordinates calculation. These planes define
cells, which are treated as homogenous parallelpipeds by Denovo, made of
a macro material corresponding to a mixture of materials that are in the
cell in the true geometry. Users should try to bound as many materials
as possible with their selection of mesh planes. More mesh planes should
be used where the importance (adjoint flux) varies quickly, such as
near the adjoint sources (the detector positions). It is also important
to have planes on the true source bounding box.}(hjBh jBhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM h jABhhubh;)}(hXZIn this example problem, different sets of mesh planes will be used for
the different detector positions. For detector positions 1 and 4, the
mesh planes are shown in :numref:`importance-1` and :numref:`importance-2`. Note that
there are more planes closer to the detectors. Also note that in the
*z* dimension, it is quite easy to place mesh planes at every material
boundary, but it is a bit more difficult to do so in the *x* and *y* dimensions
due to the curved surfaces. Users need not worry about getting things
perfect—an approximate importance map can still reduce Monte Carlo
variances a great deal. The meshes used for detector positions 2/5 and
positions 3/6 are also shown in :numref:`importance-1` and :numref:`importance-2`. Mesh
parameters are listed in :numref:`mesh-param-xyz`, and the mesh planes are listed in
:numref:`mesh-planes`.h](h/In this example problem, different sets of mesh planes will be used for
the different detector positions. For detector positions 1 and 4, the
mesh planes are shown in }(hIn this example problem, different sets of mesh planes will be used for
the different detector positions. For detector positions 1 and 4, the
mesh planes are shown in h jBhhh!NhNubhp)}(h:numref:`importance-1`h]jO)}(hjBh]h/importance-1}(hhh jBubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jBubah}(h]h]h]h]h]refdocj refdomainjBreftypenumrefrefexplicitrefwarnjimportance-1uhhoh!h"hM% h jBubh/ and }(h and h jBhhh!NhNubhp)}(h:numref:`importance-2`h]jO)}(hjBh]h/importance-2}(hhh jBubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jBubah}(h]h]h]h]h]refdocj refdomainjBreftypenumrefrefexplicitrefwarnjimportance-2uhhoh!h"hM% h jBubh/Q. Note that
there are more planes closer to the detectors. Also note that in the
}(hQ. Note that
there are more planes closer to the detectors. Also note that in the
h jBhhh!NhNubhA)}(h*z*h]h/z}(hhh jBubah}(h]h]h]h]h]uhh@h jBubh/~ dimension, it is quite easy to place mesh planes at every material
boundary, but it is a bit more difficult to do so in the }(h~ dimension, it is quite easy to place mesh planes at every material
boundary, but it is a bit more difficult to do so in the h jBhhh!NhNubhA)}(h*x*h]h/x}(hhh jBubah}(h]h]h]h]h]uhh@h jBubh/ and }(h and h jBubhA)}(h*y*h]h/y}(hhh jCubah}(h]h]h]h]h]uhh@h jBubh/X dimensions
due to the curved surfaces. Users need not worry about getting things
perfect—an approximate importance map can still reduce Monte Carlo
variances a great deal. The meshes used for detector positions 2/5 and
positions 3/6 are also shown in }(hX dimensions
due to the curved surfaces. Users need not worry about getting things
perfect—an approximate importance map can still reduce Monte Carlo
variances a great deal. The meshes used for detector positions 2/5 and
positions 3/6 are also shown in h jBhhh!NhNubhp)}(h:numref:`importance-1`h]jO)}(hj#Ch]h/importance-1}(hhh j%Cubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j!Cubah}(h]h]h]h]h]refdocj refdomainj/Creftypenumrefrefexplicitrefwarnjimportance-1uhhoh!h"hM% h jBubh/ and }(hjBh jBubhp)}(h:numref:`importance-2`h]jO)}(hjGCh]h/importance-2}(hhh jICubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jECubah}(h]h]h]h]h]refdocj refdomainjSCreftypenumrefrefexplicitrefwarnjimportance-2uhhoh!h"hM% h jBubh/ . Mesh
parameters are listed in }(h . Mesh
parameters are listed in h jBhhh!NhNubhp)}(h:numref:`mesh-param-xyz`h]jO)}(hjlCh]h/mesh-param-xyz}(hhh jnCubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jjCubah}(h]h]h]h]h]refdocj refdomainjxCreftypenumrefrefexplicitrefwarnjmesh-param-xyzuhhoh!h"hM% h jBubh/$, and the mesh planes are listed in
}(h$, and the mesh planes are listed in
h jBhhh!NhNubhp)}(h:numref:`mesh-planes`h]jO)}(hjCh]h/mesh-planes}(hhh jCubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jCubah}(h]h]h]h]h]refdocj refdomainjCreftypenumrefrefexplicitrefwarnjmesh-planesuhhoh!h"hM% h jBubh/.}(hjh jBhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM% h jABhhubh)}(h.. _importance-1:h]h}(h]h]h]h]h]himportance-1uhh
hM2 h jABhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/fig1.13.jpg
:width: 99 %
:align: center
Importance map mesh planes in the x and z dimensions for detector positions 1/4, 2/5, and 3/6.
h]h}(h]h]h]h]h]width99%urifigs/MAVRIC/fig1.13.jpgjY}j[jCsuhjKh jCh!h"hM8 ubj)}(h^Importance map mesh planes in the x and z dimensions for detector positions 1/4, 2/5, and 3/6.h]h/^Importance map mesh planes in the x and z dimensions for detector positions 1/4, 2/5, and 3/6.}(hjCh jCubah}(h]h]h]h]h]uhjh!h"hM8 h jCubeh}(h](id40jCeh]h]importance-1ah]h]jcenteruhjhM8 h jABhhh!h"j}jCjCsj}jCjCsubh)}(h.. _importance-2:h]h}(h]h]h]h]h]himportance-2uhh
hM: h jABhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/fig1.14.jpg
:width: 99 %
:align: center
Importance map mesh planes in the x and y dimensions for detector positions 1/4, 2/5, and 3/6.
h]h}(h]h]h]h]h]width99%urifigs/MAVRIC/fig1.14.jpgjY}j[j
DsuhjKh jCh!h"hM@ ubj)}(h^Importance map mesh planes in the x and y dimensions for detector positions 1/4, 2/5, and 3/6.h]h/^Importance map mesh planes in the x and y dimensions for detector positions 1/4, 2/5, and 3/6.}(hjDh jDubah}(h]h]h]h]h]uhjh!h"hM@ h jCubeh}(h](id41jCeh]h]importance-2ah]h]jcenteruhjhM@ h jABhhh!h"j}jDjCsj}jCjCsubj)}(hhh](h))}(hMesh parametersh]h/Mesh parameters}(hj*Dh j(Dubah}(h]h]h]h]h]uhh(h!h"hMB h j%Dubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKuhjh j6Dubj)}(hhh]h}(h]h]h]h]h]jKuhjh j6Dubj)}(hhh]h}(h]h]h]h]h]jKuhjh j6Dubj)}(hhh]h}(h]h]h]h]h]jKuhjh j6Dubj)}(hhh]h}(h]h]h]h]h]jKuhjh j6Dubj3)}(hhh]j8)}(hhh](j=)}(hhh]h;)}(hDetector positionh]h/Detector position}(hjqDh joDubah}(h]h]h]h]h]uhh:h!h"hMG h jlDubah}(h]h]h]h]h]uhj<h jiDubj=)}(hhh]h;)}(hNumberh]h/Number}(hjDh jDubah}(h]h]h]h]h]uhh:h!h"hMH h jDubah}(h]h]h]h]h]uhj<h jiDubj=)}(hhh]h;)}(hofh]h/of}(hjDh jDubah}(h]h]h]h]h]uhh:h!h"hMI h jDubah}(h]h]h]h]h]uhj<h jiDubj=)}(hhh]h;)}(hcellsh]h/cells}(hjDh jDubah}(h]h]h]h]h]uhh:h!h"hMJ h jDubah}(h]h]h]h]h]uhj<h jiDubj=)}(hhh]h;)}(hTotal cellsh]h/Total cells}(hjDh jDubah}(h]h]h]h]h]uhh:h!h"hMK h jDubah}(h]h]h]h]h]uhj<h jiDubeh}(h]h]h]h]h]uhj7h jfDubah}(h]h]h]h]h]uhj2h j6Dubj)}(hhh](j8)}(hhh](j=)}(hhh]h}(h]h]h]h]h]uhj<h jDubj=)}(hhh]h;)}(hxh]h/x}(hjDh jDubah}(h]h]h]h]h]uhh:h!h"hMM h jDubah}(h]h]h]h]h]uhj<h jDubj=)}(hhh]h;)}(hyh]h/y}(hjEh jEubah}(h]h]h]h]h]uhh:h!h"hMN h jEubah}(h]h]h]h]h]uhj<h jDubj=)}(hhh]h;)}(hzh]h/z}(hj-Eh j+Eubah}(h]h]h]h]h]uhh:h!h"hMO h j(Eubah}(h]h]h]h]h]uhj<h jDubj=)}(hhh]h}(h]h]h]h]h]uhj<h jDubeh}(h]h]h]h]h]uhj7h jDubj8)}(hhh](j=)}(hhh]h;)}(h1/4h]h/1/4}(hjVEh jTEubah}(h]h]h]h]h]uhh:h!h"hMQ h jQEubah}(h]h]h]h]h]uhj<h jNEubj=)}(hhh]h;)}(h46h]h/46}(hjmEh jkEubah}(h]h]h]h]h]uhh:h!h"hMR h jhEubah}(h]h]h]h]h]uhj<h jNEubj=)}(hhh]h;)}(h35h]h/35}(hjEh jEubah}(h]h]h]h]h]uhh:h!h"hMS h jEubah}(h]h]h]h]h]uhj<h jNEubj=)}(hhh]h;)}(h35h]h/35}(hjEh jEubah}(h]h]h]h]h]uhh:h!h"hMT h jEubah}(h]h]h]h]h]uhj<h jNEubj=)}(hhh]h;)}(h56350h]h/56350}(hjEh jEubah}(h]h]h]h]h]uhh:h!h"hMU h jEubah}(h]h]h]h]h]uhj<h jNEubeh}(h]h]h]h]h]uhj7h jDubj8)}(hhh](j=)}(hhh]h;)}(h2/5h]h/2/5}(hjEh jEubah}(h]h]h]h]h]uhh:h!h"hMV h jEubah}(h]h]h]h]h]uhj<h jEubj=)}(hhh]h;)}(h35h]h/35}(hjEh jEubah}(h]h]h]h]h]uhh:h!h"hMW h jEubah}(h]h]h]h]h]uhj<h jEubj=)}(hhh]h;)}(h35h]h/35}(hjFh jEubah}(h]h]h]h]h]uhh:h!h"hMX h jEubah}(h]h]h]h]h]uhj<h jEubj=)}(hhh]h;)}(h49h]h/49}(hjFh jFubah}(h]h]h]h]h]uhh:h!h"hMY h jFubah}(h]h]h]h]h]uhj<h jEubj=)}(hhh]h;)}(h60025h]h/60025}(hj.Fh j,Fubah}(h]h]h]h]h]uhh:h!h"hMZ h j)Fubah}(h]h]h]h]h]uhj<h jEubeh}(h]h]h]h]h]uhj7h jDubj8)}(hhh](j=)}(hhh]h;)}(h3/6h]h/3/6}(hjNFh jLFubah}(h]h]h]h]h]uhh:h!h"hM[ h jIFubah}(h]h]h]h]h]uhj<h jFFubj=)}(hhh]h;)}(h46h]h/46}(hjeFh jcFubah}(h]h]h]h]h]uhh:h!h"hM\ h j`Fubah}(h]h]h]h]h]uhj<h jFFubj=)}(hhh]h;)}(h35h]h/35}(hj|Fh jzFubah}(h]h]h]h]h]uhh:h!h"hM] h jwFubah}(h]h]h]h]h]uhj<h jFFubj=)}(hhh]h;)}(h49h]h/49}(hjFh jFubah}(h]h]h]h]h]uhh:h!h"hM^ h jFubah}(h]h]h]h]h]uhj<h jFFubj=)}(hhh]h;)}(h78890h]h/78890}(hjFh jFubah}(h]h]h]h]h]uhh:h!h"hM_ h jFubah}(h]h]h]h]h]uhj<h jFFubeh}(h]h]h]h]h]uhj7h jDubeh}(h]h]h]h]h]uhjh j6Dubeh}(h]h]h]h]h]colsKuhjh j%Dubeh}(h]mesh-param-xyzah]h]mesh-param-xyzah]h]jcenteruhj
h jABhhh!NhNubj)}(hhh](h))}(hnList of the various sets of mesh planes used for the importance calculations for six different point detectorsh]h/nList of the various sets of mesh planes used for the importance calculations for six different point detectors}(hjFh jFubah}(h]h]h]h]h]uhh(h!h"hMa h jFubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jFubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab15.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab15.pngjY}j[j GsuhjKh jFh!h"hKubah}(h]h]h]h]h]uhj<h jFubah}(h]h]h]h]h]uhj7h jFubah}(h]h]h]h]h]uhjh jFubeh}(h]h]h]h]h]colsKuhjh jFubeh}(h]mesh-planesah]h]mesh-planesah]h]jcenteruhj
h jABhhh!NhNubeh}(h]calculations-using-cadisah]h]calculations using cadisah]h]uhh#h j:hhh!h"hM ubh$)}(hhh](h))}(hMAVRIC input filesh]h/MAVRIC input files}(hj:Gh j8Ghhh!NhNubah}(h]h]h]h]h]uhh(h j5Ghhh!h"hMj ubh;)}(hXnWith two sources and six detectors, this example problem will require 12
separate input files. Starting with the two input files for the analog
calculations, these 12 input files will share most of the same features
and will differ only in blocks related to the importance map calculation: the
location of the adjoint source and the planes used in the grid geometry.h]h/XnWith two sources and six detectors, this example problem will require 12
separate input files. Starting with the two input files for the analog
calculations, these 12 input files will share most of the same features
and will differ only in blocks related to the importance map calculation: the
location of the adjoint source and the planes used in the grid geometry.}(hjHGh jFGhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMl h j5Ghhubh;)}(hX'To change the input for the neutron problem from an analog calculation
to one using CADIS, the user first adds the mesh planes for the
discrete-ordinates calculation as a grid geometry to the definitions
block. This set of planes is tailored for the vent port direction
toward detectors 3 and 6.h]h/X'To change the input for the neutron problem from an analog calculation
to one using CADIS, the user first adds the mesh planes for the
discrete-ordinates calculation as a grid geometry to the definitions
block. This set of planes is tailored for the vent port direction
toward detectors 3 and 6.}(hjVGh jTGhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMr h j5Ghhubjy)}(hXgridGeometry 3
title="for importance map for detectors 3,6"
xplanes -170 -168 -146 -122 -100
-95 -90 -60 -40 -20 -5
5 15 25 35 45 55 65 75 85 90 95 100
104 108 112 116 120 124 128 132 136 140 144 148 152
156 158 160 162
164 165 166 167
168 169 170 end
yplanes -170 -168 -155 -141 -127 -113 -100
-95 -90 -85 -75 -65 -55 -45 -35 -25 -15 -5
5 15 25 35 45 55 65 75 85 90 95 100
113 127 141 155 168 170 end
zplanes -285.6 -280.6 -255.2 -240.6 -228.6 -210
-190 -170 -150 -130 -110 -90 -70 -50 -30 -10
10 30 50 70 90 110 130 150 170 190
210 216.2 222.4
228.6 232.6 236.6
240.6 245.1 249.7 254.2
255.2 256.2 260.1 264 267.9 271.8 275.7 279.6
280.6 281.6 282.6 283.6 284.6 285.6 end
end gridGeometryh]h/XgridGeometry 3
title="for importance map for detectors 3,6"
xplanes -170 -168 -146 -122 -100
-95 -90 -60 -40 -20 -5
5 15 25 35 45 55 65 75 85 90 95 100
104 108 112 116 120 124 128 132 136 140 144 148 152
156 158 160 162
164 165 166 167
168 169 170 end
yplanes -170 -168 -155 -141 -127 -113 -100
-95 -90 -85 -75 -65 -55 -45 -35 -25 -15 -5
5 15 25 35 45 55 65 75 85 90 95 100
113 127 141 155 168 170 end
zplanes -285.6 -280.6 -255.2 -240.6 -228.6 -210
-190 -170 -150 -130 -110 -90 -70 -50 -30 -10
10 30 50 70 90 110 130 150 170 190
210 216.2 222.4
228.6 232.6 236.6
240.6 245.1 249.7 254.2
255.2 256.2 260.1 264 267.9 271.8 275.7 279.6
280.6 281.6 282.6 283.6 284.6 285.6 end
end gridGeometry}(hhh jbGubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMx h j5Ghhubh;)}(hXTo help the mesh-based biased source represent the true source,
“mixture=1” can be added to the source definition. This will ensure that
particles sampled from the mesh source that are not in the fuel are
rejected. Then an importance map block replaces the standard biasing
block. In this case, the importance map will optimize the flow of
particles to location 3 (where point detector 3 is defined).h]h/XTo help the mesh-based biased source represent the true source,
“mixture=1” can be added to the source definition. This will ensure that
particles sampled from the mesh source that are not in the fuel are
rejected. Then an importance map block replaces the standard biasing
block. In this case, the importance map will optimize the flow of
particles to location 3 (where point detector 3 is defined).}(hjvGh jtGhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM h j5Ghhubjy)}(hread importanceMap
adjointSource 1
locationID=3
responseID=1
end adjointSource
gridGeometryID=3
macromaterial
mmTolerance=0.01
end macromaterial
end importanceMaph]h/read importanceMap
adjointSource 1
locationID=3
responseID=1
end adjointSource
gridGeometryID=3
macromaterial
mmTolerance=0.01
end macromaterial
end importanceMap}(hhh jGubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM h j5Ghhubh;)}(hDA mesh tally could be added with the following in the tallies block.h]h/DA mesh tally could be added with the following in the tallies block.}(hjGh jGhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM h j5Ghhubjy)}(hmeshTally 1
title="Shows how importance map changes the transport of particles"
gridGeometryID=3
responseID=1
end meshTallyh]h/meshTally 1
title="Shows how importance map changes the transport of particles"
gridGeometryID=3
responseID=1
end meshTally}(hhh jGubah}(h]h]h]h]h]jjuhjxh!h"hM h j5Ghhubh;)}(hXThe above mesh tally uses the same grid geometry as the CADIS
calculations, but a different grid (or grids) could be used. The files
``mavric.caskCADISn.inp`` and ``mavric.caskCADISp.inp`` are available in the
SCALE ``samples\input`` directory. These are for calculating the dose rates
at detector position 3, but they can be modified for the other five positions
(by changing the geometry grid planes and the adjoint source location).h](h/The above mesh tally uses the same grid geometry as the CADIS
calculations, but a different grid (or grids) could be used. The files
}(hThe above mesh tally uses the same grid geometry as the CADIS
calculations, but a different grid (or grids) could be used. The files
h jGhhh!NhNubjO)}(h``mavric.caskCADISn.inp``h]h/mavric.caskCADISn.inp}(hhh jGubah}(h]h]h]h]h]uhjNh jGubh/ and }(h and h jGhhh!NhNubjO)}(h``mavric.caskCADISp.inp``h]h/mavric.caskCADISp.inp}(hhh jGubah}(h]h]h]h]h]uhjNh jGubh/ are available in the
SCALE }(h are available in the
SCALE h jGhhh!NhNubjO)}(h``samples\input``h]h/
samples\input}(hhh jGubah}(h]h]h]h]h]uhjNh jGubh/ directory. These are for calculating the dose rates
at detector position 3, but they can be modified for the other five positions
(by changing the geometry grid planes and the adjoint source location).}(h directory. These are for calculating the dose rates
at detector position 3, but they can be modified for the other five positions
(by changing the geometry grid planes and the adjoint source location).h jGhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h j5Ghhubeh}(h]mavric-input-filesah]h]mavric input filesah]h]uhh#h j:hhh!h"hMj ubh$)}(hhh](h))}(h'Neutron source/neutron response resultsh]h/'Neutron source/neutron response results}(hjHh jHhhh!NhNubah}(h]h]h]h]h]uhh(h jHhhh!h"hM ubh;)}(hX:The above MAVRIC input file first performed the discrete-ordinates
calculation to determine the adjoint flux from detector position 3. The
adjoint Denovo flux file (\*.adjoint.dff) produced can be viewed using
the Mesh File Viewer and is shown in :numref:`adjoint-denovo` for several of the
neutron energy groups.h](h/The above MAVRIC input file first performed the discrete-ordinates
calculation to determine the adjoint flux from detector position 3. The
adjoint Denovo flux file (*.adjoint.dff) produced can be viewed using
the Mesh File Viewer and is shown in }(hThe above MAVRIC input file first performed the discrete-ordinates
calculation to determine the adjoint flux from detector position 3. The
adjoint Denovo flux file (\*.adjoint.dff) produced can be viewed using
the Mesh File Viewer and is shown in h jHhhh!NhNubhp)}(h:numref:`adjoint-denovo`h]jO)}(hjHh]h/adjoint-denovo}(hhh jHubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jHubah}(h]h]h]h]h]refdocj refdomainj(Hreftypenumrefrefexplicitrefwarnjadjoint-denovouhhoh!h"hM h jHubh/* for several of the
neutron energy groups.}(h* for several of the
neutron energy groups.h jHhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h jHhhubh;)}(hXlMAVRIC then combined a mesh representation of the true source (space and
energy) with the adjoint fluxes to create the importance map and
mesh-based biased source. These are shown in :numref:`fifth-neutron` for the fifth
neutron group, covering the energy range of 0.9 to 1.4 MeV. Notice how
the most important region (lowest target weights) is right around the
vent port near detector position 3. This is something we know
qualitatively, but quantitative values for exactly how the importance
changes with space and energy are difficult to guess. Also notice the
“consistent” part of CADIS—--the source particles---are born with a weight
that matches the target weight for the position they are born into. The
biased source sampling distribution is depicted in :numref:`biased-source`, showing
how the source particles nearest to detector 3 will be sampled more
often.h](h/MAVRIC then combined a mesh representation of the true source (space and
energy) with the adjoint fluxes to create the importance map and
mesh-based biased source. These are shown in }(hMAVRIC then combined a mesh representation of the true source (space and
energy) with the adjoint fluxes to create the importance map and
mesh-based biased source. These are shown in h jEHhhh!NhNubhp)}(h:numref:`fifth-neutron`h]jO)}(hjPHh]h/
fifth-neutron}(hhh jRHubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jNHubah}(h]h]h]h]h]refdocj refdomainj\Hreftypenumrefrefexplicitrefwarnj
fifth-neutronuhhoh!h"hM h jEHubh/X4 for the fifth
neutron group, covering the energy range of 0.9 to 1.4 MeV. Notice how
the most important region (lowest target weights) is right around the
vent port near detector position 3. This is something we know
qualitatively, but quantitative values for exactly how the importance
changes with space and energy are difficult to guess. Also notice the
“consistent” part of CADIS—–the source particles—are born with a weight
that matches the target weight for the position they are born into. The
biased source sampling distribution is depicted in }(hX3 for the fifth
neutron group, covering the energy range of 0.9 to 1.4 MeV. Notice how
the most important region (lowest target weights) is right around the
vent port near detector position 3. This is something we know
qualitatively, but quantitative values for exactly how the importance
changes with space and energy are difficult to guess. Also notice the
“consistent” part of CADIS—--the source particles---are born with a weight
that matches the target weight for the position they are born into. The
biased source sampling distribution is depicted in h jEHhhh!NhNubhp)}(h:numref:`biased-source`h]jO)}(hjuHh]h/
biased-source}(hhh jwHubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jsHubah}(h]h]h]h]h]refdocj refdomainjHreftypenumrefrefexplicitrefwarnj
biased-sourceuhhoh!h"hM h jEHubh/T, showing
how the source particles nearest to detector 3 will be sampled more
often.}(hT, showing
how the source particles nearest to detector 3 will be sampled more
often.h jEHhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h jHhhubh;)}(hThe biased source distribution and the importance map are then used by
Monaco to compute the dose equivalent rate response at detector 3.h]h/The biased source distribution and the importance map are then used by
Monaco to compute the dose equivalent rate response at detector 3.}(hjHh jHhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM h jHhhubj)}(hhh]jL)}(hK.. figure:: figs/MAVRIC/fig4.1.15g_caskn.adjoint.scale.png
:align: centerh]h}(h]h]h]h]h]uri.figs/MAVRIC/fig4.1.15g_caskn.adjoint.scale.pngjY}j[jHsuhjKh jHh!h"hNubah}(h]h]h]h]h]jcenteruhjh jHhhh!h"hNubh)}(h.. _adjoint-denovo:h]h}(h]h]h]h]h]hadjoint-denovouhh
hM h jHhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/1.15.jpg
:align: center
:width: 100 %
Adjoint neutron fluxes (/cm :sup:`2`/s) for groups 5 (0.9–1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV) calculated by Denovo.
h]h}(h]h]h]h]h]width100%urifigs/MAVRIC/1.15.jpgjY}j[jHsuhjKh jHh!h"hM ubj)}(hAdjoint neutron fluxes (/cm :sup:`2`/s) for groups 5 (0.9–1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV) calculated by Denovo.h](h/Adjoint neutron fluxes (/cm }(hAdjoint neutron fluxes (/cm h jHubj+)}(h:sup:`2`h]h/2}(hhh jHubah}(h]h]h]h]h]uhj+h jHubh/b/s) for groups 5 (0.9–1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV) calculated by Denovo.}(hb/s) for groups 5 (0.9–1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV) calculated by Denovo.h jHubeh}(h]h]h]h]h]uhjh!h"hM h jHubeh}(h](id42jHeh]h]adjoint-denovoah]h]jcenteruhjhM h jHhhh!h"j}jIjHsj}jHjHsubj)}(hhh]jL)}(hL.. figure:: figs/MAVRIC/fig4.1.16e_caskn.targets.scale.png
:align: center
h]h}(h]h]h]h]h]uri.figs/MAVRIC/fig4.1.16e_caskn.targets.scale.pngjY}j[jIsuhjKh j
Ih!h"hNubah}(h]h]h]h]h]jcenteruhjh jHhhh!h"hNubh)}(h.. _fifth-neutron:h]h}(h]h]h]h]h]h
fifth-neutronuhh
hM h jHhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/1.16.jpg
:align: center
:width: 80 %
Neutron target weights from the importance map and source weights (at birth) for neutron group 5 (0.9 to 1.4 MeV).
h]h}(h]h]h]h]h]width80%urifigs/MAVRIC/1.16.jpgjY}j[j?IsuhjKh j/Ih!h"hM ubj)}(huNeutron target weights from the importance map and source weights (at birth) for neutron group 5 (0.9 to 1.4 MeV).h]h/uNeutron target weights from the importance map and source weights (at birth) for neutron group 5 (0.9 to 1.4 MeV).|}(hjCIh jAIubah}(h]h]h]h]h]uhjh!h"hM h j/Iubeh}(h](id43j.Ieh]h]
fifth-neutronah]h]jcenteruhjhM h jHhhh!h"j}jTIj$Isj}j.Ij$Isubj)}(hhh]jL)}(hI.. figure:: figs/MAVRIC/fig4.1.17g_caskn.prob.scale.png
:align: center
h]h}(h]h]h]h]h]uri+figs/MAVRIC/fig4.1.17g_caskn.prob.scale.pngjY}j[jhIsuhjKh jZIh!h"hNubah}(h]h]h]h]h]jcenteruhjh jHhhh!h"hNubh)}(h.. _biased-source:h]h}(h]h]h]h]h]h
biased-sourceuhh
hM h jHhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/1.17.jpg
:align: center
:width: 100 %
Biased source sampling probability (neutrons/cm3) for neutron groups 5 (0.9‑1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV).
h]h}(h]h]h]h]h]width100%urifigs/MAVRIC/1.17.jpgjY}j[jIsuhjKh j|Ih!h"hM ubj)}(hBiased source sampling probability (neutrons/cm3) for neutron groups 5 (0.9‑1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV).h]h/Biased source sampling probability (neutrons/cm3) for neutron groups 5 (0.9‑1.4 MeV), 10 (0.58–3.0 keV), and 19 (0.8–1 eV).}(hjIh jIubah}(h]h]h]h]h]uhjh!h"hM h j|Iubeh}(h](id44j{Ieh]h]
biased-sourceah]h]jcenteruhjhM h jHhhh!h"j}jIjqIsj}j{IjqIsubh;)}(hThe results for all six neutron cases, each using their own importance
map and biased source, are shown in :numref:`MAVRIC-final`.h](h/kThe results for all six neutron cases, each using their own importance
map and biased source, are shown in }(hkThe results for all six neutron cases, each using their own importance
map and biased source, are shown in h jIhhh!NhNubhp)}(h:numref:`MAVRIC-final`h]jO)}(hjIh]h/MAVRIC-final}(hhh jIubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jIubah}(h]h]h]h]h]refdocj refdomainjIreftypenumrefrefexplicitrefwarnjmavric-finaluhhoh!h"hM h jIubh/.}(hjh jIhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h jHhhubh;)}(hXThis example shows that MAVRIC using CADIS obtains the
correct answer much faster than the analog calculations. This is shown
with a comparison to the results from the analog Monaco and SAS4
calculations, all of which are listed in :numref:`MAVRIC-CADIS-results`.h](h/This example shows that MAVRIC using CADIS obtains the
correct answer much faster than the analog calculations. This is shown
with a comparison to the results from the analog Monaco and SAS4
calculations, all of which are listed in }(hThis example shows that MAVRIC using CADIS obtains the
correct answer much faster than the analog calculations. This is shown
with a comparison to the results from the analog Monaco and SAS4
calculations, all of which are listed in h jIhhh!NhNubhp)}(h:numref:`MAVRIC-CADIS-results`h]jO)}(hjIh]h/MAVRIC-CADIS-results}(hhh jIubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jIubah}(h]h]h]h]h]refdocj refdomainjIreftypenumrefrefexplicitrefwarnjmavric-cadis-resultsuhhoh!h"hM h jIubh/.}(hjh jIhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h jHhhubh;)}(hXTo account for the time it takes to achieve a given level of
uncertainties, the calculation figure-of-merit---FOM=1/time/(relative
uncertainty)\ :sup:`2`---can be calculated for each of the codes. The
ratios of each code FOM to the FOM of analog Monaco (speedup) are listed
in :numref:`figure-of-merit` to show how much faster MAVRIC and SAS4 are compared to
analog Monaco. The FOMs for MAVRIC include the Denovo calculation times.
The FOMs for analog Monaco and SAS4 were modified to account for
calculating all six detectors at once.h](h/To account for the time it takes to achieve a given level of
uncertainties, the calculation figure-of-merit—FOM=1/time/(relative
uncertainty) }(hTo account for the time it takes to achieve a given level of
uncertainties, the calculation figure-of-merit---FOM=1/time/(relative
uncertainty)\ h j
Jhhh!NhNubj+)}(h:sup:`2`h]h/2}(hhh jJubah}(h]h]h]h]h]uhj+h j
Jubh/|—can be calculated for each of the codes. The
ratios of each code FOM to the FOM of analog Monaco (speedup) are listed
in }(h|---can be calculated for each of the codes. The
ratios of each code FOM to the FOM of analog Monaco (speedup) are listed
in h j
Jhhh!NhNubhp)}(h:numref:`figure-of-merit`h]jO)}(hj+Jh]h/figure-of-merit}(hhh j-Jubah}(h]h](jstd
std-numrefeh]h]h]uhjNh j)Jubah}(h]h]h]h]h]refdocj refdomainj7Jreftypenumrefrefexplicitrefwarnjfigure-of-merituhhoh!h"hM h j
Jubh/ to show how much faster MAVRIC and SAS4 are compared to
analog Monaco. The FOMs for MAVRIC include the Denovo calculation times.
The FOMs for analog Monaco and SAS4 were modified to account for
calculating all six detectors at once.}(h to show how much faster MAVRIC and SAS4 are compared to
analog Monaco. The FOMs for MAVRIC include the Denovo calculation times.
The FOMs for analog Monaco and SAS4 were modified to account for
calculating all six detectors at once.h j
Jhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM h jHhhubj)}(hhh](h))}(heFinal MAVRIC results (rem/hr) for each point detector in the neutron source/neutron dose rate problemh]h/eFinal MAVRIC results (rem/hr) for each point detector in the neutron source/neutron dose rate problem}(hjYJh jWJubah}(h]h]h]h]h]uhh(h!h"hM
h jTJubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jeJubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab16.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab16.pngjY}j[jJsuhjKh jwJh!h"hKubah}(h]h]h]h]h]uhj<h jtJubah}(h]h]h]h]h]uhj7h jqJubah}(h]h]h]h]h]uhjh jeJubeh}(h]h]h]h]h]colsKuhjh jTJubeh}(h]mavric-finalah]h]mavric-finalah]h]jcenteruhj
h jHhhh!NhNubj)}(hhh](h))}(h>Comparison of neutron dose rates (rem/hr) to other SCALE codesh]h/>Comparison of neutron dose rates (rem/hr) to other SCALE codes}(hjJh jJubah}(h]h]h]h]h]uhh(h!h"hM
h jJubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKuhjh jJubj)}(hhh]h}(h]h]h]h]h]jKuhjh jJubj)}(hhh]h}(h]h]h]h]h]jKuhjh jJubj)}(hhh]h}(h]h]h]h]h]jKuhjh jJubj)}(hhh]h}(h]h]h]h]h]jKuhjh jJubj)}(hhh](j8)}(hhh](j=)}(hhh]h}(h]h]h]h]h]uhj<h jJubj=)}(hhh]h;)}(h
Analog Monacoh]h/
Analog Monaco}(hjJh jJubah}(h]h]h]h]h]uhh:h!h"hM
h jJubah}(h]h]h]h]h]uhj<h jJubj=)}(hhh]h;)}(hSAS4 radialh]h/SAS4 radial}(hjKh jKubah}(h]h]h]h]h]uhh:h!h"hM
h jKubah}(h]h]h]h]h]uhj<h jJubj=)}(hhh]h;)}(h
SAS4 axialh]h/
SAS4 axial}(hj,Kh j*Kubah}(h]h]h]h]h]uhh:h!h"hM
h j'Kubah}(h]h]h]h]h]uhj<h jJubj=)}(hhh]h;)}(hMAVRICh]h/MAVRIC}(hjCKh jAKubah}(h]h]h]h]h]uhh:h!h"hM
h j>Kubah}(h]h]h]h]h]uhj<h jJubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(hdetectorh]h/detector}(hjcKh jaKubah}(h]h]h]h]h]uhh:h!h"hM
h j^Kubah}(h]h]h]h]h]uhj<h j[Kubj=)}(hhh]h;)}(h6595 minh]h/6595 min}(hjzKh jxKubah}(h]h]h]h]h]uhh:h!h"hM
h juKubah}(h]h]h]h]h]uhj<h j[Kubj=)}(hhh]h;)}(h360 minh]h/360 min}(hjKh jKubah}(h]h]h]h]h]uhh:h!h"hM
h jKubah}(h]h]h]h]h]uhj<h j[Kubj=)}(hhh]h;)}(h361 minh]h/361 min}(hjKh jKubah}(h]h]h]h]h]uhh:h!h"hM
h jKubah}(h]h]h]h]h]uhj<h j[Kubj=)}(hhh]h;)}(h556 minh]h/556 min}(hjKh jKubah}(h]h]h]h]h]uhh:h!h"hM
h jKubah}(h]h]h]h]h]uhj<h j[Kubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(h1h]h/1}(hjKh jKubah}(h]h]h]h]h]uhh:h!h"hM
h jKubah}(h]h]h]h]h]uhj<h jKubj=)}(hhh]h;)}(h8.78E-04 ± 19%h]h/8.78E-04 ± 19%}(hjKh jKubah}(h]h]h]h]h]uhh:h!h"hM
h jKubah}(h]h]h]h]h]uhj<h jKubj=)}(hhh]h;)}(h7.67E-04 ± 0.8%h]h/7.67E-04 ± 0.8%}(hj
Lh jLubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jKubj=)}(hhh]h;)}(h1.32E-05 ± 45%h]h/1.32E-05 ± 45%}(hj$Lh j"Lubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jKubj=)}(hhh]h;)}(h7.65E-04 ± 0.8%h]h/7.65E-04 ± 0.8%}(hj;Lh j9Lubah}(h]h]h]h]h]uhh:h!h"hM
h j6Lubah}(h]h]h]h]h]uhj<h jKubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(h2h]h/2}(hj[Lh jYLubah}(h]h]h]h]h]uhh:h!h"hM
h jVLubah}(h]h]h]h]h]uhj<h jSLubj=)}(hhh]h;)}(h7.35E-03 ± 4.1%h]h/7.35E-03 ± 4.1%}(hjrLh jpLubah}(h]h]h]h]h]uhh:h!h"hM
h jmLubah}(h]h]h]h]h]uhj<h jSLubj=)}(hhh]h;)}(h2.67E-02 ± 86%h]h/2.67E-02 ± 86%}(hjLh jLubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jSLubj=)}(hhh]h;)}(h7.80E-03 ± 0.4%h]h/7.80E-03 ± 0.4%}(hjLh jLubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jSLubj=)}(hhh]h;)}(h7.83E-03 ± 0.3%h]h/7.83E-03 ± 0.3%}(hjLh jLubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jSLubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(h3h]h/3}(hjLh jLubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jLubj=)}(hhh]h;)}(h1.54E-02 ± 1.2%h]h/1.54E-02 ± 1.2%}(hjLh jLubah}(h]h]h]h]h]uhh:h!h"hM
h jLubah}(h]h]h]h]h]uhj<h jLubj=)}(hhh]h;)}(h1.27E-02 ± 14%h]h/1.27E-02 ± 14%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM
h jMubah}(h]h]h]h]h]uhj<h jLubj=)}(hhh]h;)}(h1.53E-02 ± 0.8%h]h/1.53E-02 ± 0.8%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM!
h jMubah}(h]h]h]h]h]uhj<h jLubj=)}(hhh]h;)}(h1.54E-02 ± 0.3%h]h/1.54E-02 ± 0.3%}(hj3Mh j1Mubah}(h]h]h]h]h]uhh:h!h"hM"
h j.Mubah}(h]h]h]h]h]uhj<h jLubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(h4h]h/4}(hjSMh jQMubah}(h]h]h]h]h]uhh:h!h"hM#
h jNMubah}(h]h]h]h]h]uhj<h jKMubj=)}(hhh]h;)}(h4.47E-04 ± 3.1%h]h/4.47E-04 ± 3.1%}(hjjMh jhMubah}(h]h]h]h]h]uhh:h!h"hM$
h jeMubah}(h]h]h]h]h]uhj<h jKMubj=)}(hhh]h;)}(h4.54E-04 ± 0.8%h]h/4.54E-04 ± 0.8%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM%
h j|Mubah}(h]h]h]h]h]uhj<h jKMubj=)}(hhh]h;)}(h2.34E-04 ± 68%h]h/2.34E-04 ± 68%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM&
h jMubah}(h]h]h]h]h]uhj<h jKMubj=)}(hhh]h;)}(h4.57E-04 ± 0.3%h]h/4.57E-04 ± 0.3%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM'
h jMubah}(h]h]h]h]h]uhj<h jKMubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(h5h]h/5}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM(
h jMubah}(h]h]h]h]h]uhj<h jMubj=)}(hhh]h;)}(h1.36E-02 ± 0.6%h]h/1.36E-02 ± 0.6%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM)
h jMubah}(h]h]h]h]h]uhj<h jMubj=)}(hhh]h;)}(h1.43E-02 ± 13%h]h/1.43E-02 ± 13%}(hjMh jMubah}(h]h]h]h]h]uhh:h!h"hM*
h jMubah}(h]h]h]h]h]uhj<h jMubj=)}(hhh]h;)}(h1.35E-02 ± 0.4%h]h/1.35E-02 ± 0.4%}(hjNh jNubah}(h]h]h]h]h]uhh:h!h"hM+
h jNubah}(h]h]h]h]h]uhj<h jMubj=)}(hhh]h;)}(h1.36E-02 ± 0.3%h]h/1.36E-02 ± 0.3%}(hj+Nh j)Nubah}(h]h]h]h]h]uhh:h!h"hM,
h j&Nubah}(h]h]h]h]h]uhj<h jMubeh}(h]h]h]h]h]uhj7h jJubj8)}(hhh](j=)}(hhh]h;)}(h6h]h/6}(hjKNh jINubah}(h]h]h]h]h]uhh:h!h"hM-
h jFNubah}(h]h]h]h]h]uhj<h jCNubj=)}(hhh]h;)}(h2.92E-03 ± 0.7%h]h/2.92E-03 ± 0.7%}(hjbNh j`Nubah}(h]h]h]h]h]uhh:h!h"hM.
h j]Nubah}(h]h]h]h]h]uhj<h jCNubj=)}(hhh]h;)}(h2.81E-03 ± 12.7%h]h/2.81E-03 ± 12.7%}(hjyNh jwNubah}(h]h]h]h]h]uhh:h!h"hM/
h jtNubah}(h]h]h]h]h]uhj<h jCNubj=)}(hhh]h;)}(h2.86E-03 ± 0.5%h]h/2.86E-03 ± 0.5%}(hjNh jNubah}(h]h]h]h]h]uhh:h!h"hM0
h jNubah}(h]h]h]h]h]uhj<h jCNubj=)}(hhh]h;)}(h2.93E-03 ± 0.2%h]h/2.93E-03 ± 0.2%}(hjNh jNubah}(h]h]h]h]h]uhh:h!h"hM1
h jNubah}(h]h]h]h]h]uhj<h jCNubeh}(h]h]h]h]h]uhj7h jJubeh}(h]h]h]h]h]uhjh jJubeh}(h]h]h]h]h]colsKuhjh jJubeh}(h]mavric-cadis-resultsah]h]mavric-cadis-resultsah]h]jcenteruhj
h jHhhh!NhNubj)}(hhh](h))}(hTRatio of the figure-of-merit (speed-up) of MAVRIC and SAS4 compared to analog Monacoh]h/TRatio of the figure-of-merit (speed-up) of MAVRIC and SAS4 compared to analog Monaco}(hjNh jNubah}(h]h]h]h]h]uhh(h!h"hM4
h jNubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jNubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab18.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab18.pngjY}j[jOsuhjKh jNh!h"hKubah}(h]h]h]h]h]uhj<h jNubah}(h]h]h]h]h]uhj7h jNubah}(h]h]h]h]h]uhjh jNubeh}(h]h]h]h]h]colsKuhjh jNubeh}(h]figure-of-meritah]h]figure-of-meritah]h]jcenteruhj
h jHhhh!NhNubeh}(h]'neutron-source-neutron-response-resultsah]h]'neutron source/neutron response resultsah]h]uhh#h j:hhh!h"hM ubh$)}(hhh](h))}(h%Photon source/photon response resultsh]h/%Photon source/photon response results}(hj7Oh j5Ohhh!NhNubah}(h]h]h]h]h]uhh(h j2Ohhh!h"hM<
ubh;)}(hXThe results for the photon source/photon response are similar to the
results of the neutron source/neutron response. For the MAVRIC
calculation using the photon importance map made from an adjoint source
located at detector position 3, :numref:`fig4-18` details the adjoint photon
flux. :numref:`fig4-19` compares the target weights from the importance map
and the source birth weights. :numref:`fig4-20` shows the distribution of
the sampled source positions from the biased source.h](h/The results for the photon source/photon response are similar to the
results of the neutron source/neutron response. For the MAVRIC
calculation using the photon importance map made from an adjoint source
located at detector position 3, }(hThe results for the photon source/photon response are similar to the
results of the neutron source/neutron response. For the MAVRIC
calculation using the photon importance map made from an adjoint source
located at detector position 3, h jCOhhh!NhNubhp)}(h:numref:`fig4-18`h]jO)}(hjNOh]h/fig4-18}(hhh jPOubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jLOubah}(h]h]h]h]h]refdocj refdomainjZOreftypenumrefrefexplicitrefwarnjfig4-18uhhoh!h"hM>
h jCOubh/" details the adjoint photon
flux. }(h" details the adjoint photon
flux. h jCOhhh!NhNubhp)}(h:numref:`fig4-19`h]jO)}(hjsOh]h/fig4-19}(hhh juOubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jqOubah}(h]h]h]h]h]refdocj refdomainjOreftypenumrefrefexplicitrefwarnjfig4-19uhhoh!h"hM>
h jCOubh/S compares the target weights from the importance map
and the source birth weights. }(hS compares the target weights from the importance map
and the source birth weights. h jCOhhh!NhNubhp)}(h:numref:`fig4-20`h]jO)}(hjOh]h/fig4-20}(hhh jOubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jOubah}(h]h]h]h]h]refdocj refdomainjOreftypenumrefrefexplicitrefwarnjfig4-20uhhoh!h"hM>
h jCOubh/O shows the distribution of
the sampled source positions from the biased source.}(hO shows the distribution of
the sampled source positions from the biased source.h jCOhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM>
h j2Ohhubh;)}(hy:numref:`tab4-19` shows the results from all six photon MAVRIC runs, each
using its own importance map and biased source.h](hp)}(h:numref:`tab4-19`h]jO)}(hjOh]h/tab4-19}(hhh jOubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jOubah}(h]h]h]h]h]refdocj refdomainjOreftypenumrefrefexplicitrefwarnjtab4-19uhhoh!h"hMF
h jOubh/h shows the results from all six photon MAVRIC runs, each
using its own importance map and biased source.}(hh shows the results from all six photon MAVRIC runs, each
using its own importance map and biased source.h jOhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMF
h j2Ohhubh;)}(hThe MAVRIC results of the photon problem compare well against SAS4 and
analog Monaco, as shown in :numref:`tab4-20` and :numref:`tab4-21`.h](h/bThe MAVRIC results of the photon problem compare well against SAS4 and
analog Monaco, as shown in }(hbThe MAVRIC results of the photon problem compare well against SAS4 and
analog Monaco, as shown in h jOhhh!NhNubhp)}(h:numref:`tab4-20`h]jO)}(hjOh]h/tab4-20}(hhh jOubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jOubah}(h]h]h]h]h]refdocj refdomainjPreftypenumrefrefexplicitrefwarnjtab4-20uhhoh!h"hMI
h jOubh/ and }(h and h jOhhh!NhNubhp)}(h:numref:`tab4-21`h]jO)}(hj Ph]h/tab4-21}(hhh j"Pubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jPubah}(h]h]h]h]h]refdocj refdomainj,Preftypenumrefrefexplicitrefwarnjtab4-21uhhoh!h"hMI
h jOubh/.}(hjh jOhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMI
h j2Ohhubj)}(hhh]jL)}(hL.. figure:: figs/MAVRIC/fig4.1.18g_caskp.adjoint.scale.png
:align: center
h]h}(h]h]h]h]h]uri.figs/MAVRIC/fig4.1.18g_caskp.adjoint.scale.pngjY}j[jVPsuhjKh jHPh!h"hNubah}(h]h]h]h]h]jcenteruhjh j2Ohhh!h"hNubh)}(h.. _fig4-18:h]h}(h]h]h]h]h]hfig4-18uhh
hMO
h j2Ohhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/4.18.jpg
:align: center
Adjoint photon fluxes (/cm: sup:`2`/s) for groups 2 (8–10 MeV), 2 (0.8–1.0 MeV), and 18 (45–100 keV) calculated by Denovo.
h]h}(h]h]h]h]h]urifigs/MAVRIC/4.18.jpgjY}j[jxPsuhjKh jjPh!h"hMT
ubj)}(hAdjoint photon fluxes (/cm: sup:`2`/s) for groups 2 (8–10 MeV), 2 (0.8–1.0 MeV), and 18 (45–100 keV) calculated by Denovo.h](h/ Adjoint photon fluxes (/cm: sup:}(h Adjoint photon fluxes (/cm: sup:h jzPubh title_reference)}(h`2`h]h/2}(hhh jPubah}(h]h]h]h]h]uhjPh jzPubh/_/s) for groups 2 (8–10 MeV), 2 (0.8–1.0 MeV), and 18 (45–100 keV) calculated by Denovo.}(h_/s) for groups 2 (8–10 MeV), 2 (0.8–1.0 MeV), and 18 (45–100 keV) calculated by Denovo.h jzPubeh}(h]h]h]h]h]uhjh!h"hMT
h jjPubeh}(h](id45jiPeh]h]fig4-18ah]h]jcenteruhjhMT
h j2Ohhh!h"j}jPj_Psj}jiPj_Psubj)}(hhh](h))}(hbFinal MAVRIC results (rem/hr) for each point detectorin the photon source/photon dose rate problemh]h/bFinal MAVRIC results (rem/hr) for each point detectorin the photon source/photon dose rate problem}(hjPh jPubah}(h]h]h]h]h]uhh(h!h"hMV
h jPubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jPubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab18.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab18.pngjY}j[jPsuhjKh jPh!h"hKubah}(h]h]h]h]h]uhj<h jPubah}(h]h]h]h]h]uhj7h jPubah}(h]h]h]h]h]uhjh jPubeh}(h]h]h]h]h]colsKuhjh jPubeh}(h]tab4-19ah]h]tab4-19ah]h]jcenteruhj
h j2Ohhh!NhNubj)}(hhh]jL)}(hL.. figure:: figs/MAVRIC/fig4.1.19e_caskp.targets.scale.png
:align: center
h]h}(h]h]h]h]h]uri.figs/MAVRIC/fig4.1.19e_caskp.targets.scale.pngjY}j[jQsuhjKh jPh!h"hNubah}(h]h]h]h]h]jcenteruhjh j2Ohhh!h"hNubh)}(h.. _fig4-19:h]h}(h]h]h]h]h]hfig4-19uhh
hM_
h j2Ohhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/4.19.jpg
:align: center
:width: 80 %
Photon target weights from the importance map and source weights (at birth) for photon group 12 (0.8–1.0 MeV).
h]h}(h]h]h]h]h]width80%urifigs/MAVRIC/4.19.jpgjY}j[j0QsuhjKh j Qh!h"hMe
ubj)}(hrPhoton target weights from the importance map and source weights (at birth) for photon group 12 (0.8–1.0 MeV).h]h/rPhoton target weights from the importance map and source weights (at birth) for photon group 12 (0.8–1.0 MeV).}(hj4Qh j2Qubah}(h]h]h]h]h]uhjh!h"hMe
h j Qubeh}(h](id46jQeh]h]fig4-19ah]h]jcenteruhjhMe
h j2Ohhh!h"j}jEQjQsj}jQjQsubj)}(hhh](h))}(hAComparison of the photon dose rates (rem/hr) to other SCALE codesh]h/AComparison of the photon dose rates (rem/hr) to other SCALE codes}(hjPQh jNQubah}(h]h]h]h]h]uhh(h!h"hMg
h jKQubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh j\Qubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab20.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab20.pngjY}j[j|QsuhjKh jnQh!h"hKubah}(h]h]h]h]h]uhj<h jkQubah}(h]h]h]h]h]uhj7h jhQubah}(h]h]h]h]h]uhjh j\Qubeh}(h]h]h]h]h]colsKuhjh jKQubeh}(h]tab4-20ah]h]tab4-20ah]h]jcenteruhj
h j2Ohhh!NhNubh)}(h.. _fig4-20:h]h}(h]h]h]h]h]hfig4-20uhh
hMm
h j2Ohhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/fig4-20.png
:align: center
Biased source sampling probability (photons/cm3) for groups 2 (8–10 MeV), 12 (0.8–1.0 MeV), and 18 (45–100 keV).
h]h}(h]h]h]h]h]urifigs/MAVRIC/fig4-20.pngjY}j[jQsuhjKh jQh!h"hMr
ubj)}(hxBiased source sampling probability (photons/cm3) for groups 2 (8–10 MeV), 12 (0.8–1.0 MeV), and 18 (45–100 keV).h]h/xBiased source sampling probability (photons/cm3) for groups 2 (8–10 MeV), 12 (0.8–1.0 MeV), and 18 (45–100 keV).}(hjQh jQubah}(h]h]h]h]h]uhjh!h"hMr
h jQubeh}(h](id47jQeh]h]fig4-20ah]h]jcenteruhjhMr
h j2Ohhh!h"j}jQjQsj}jQjQsubj)}(hhh](h))}(hHRatio of the FOM (speed-up) of MAVRIC and SAS4 compared to analog Monacoh]h/HRatio of the FOM (speed-up) of MAVRIC and SAS4 compared to analog Monaco}(hjQh jQubah}(h]h]h]h]h]uhh(h!h"hMt
h jQubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jQubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab21.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab21.pngjY}j[jRsuhjKh jQh!h"hKubah}(h]h]h]h]h]uhj<h jQubah}(h]h]h]h]h]uhj7h jQubah}(h]h]h]h]h]uhjh jQubeh}(h]h]h]h]h]colsKuhjh jQubeh}(h]tab4-21ah]h]tab4-21ah]h]jcenteruhj
h j2Ohhh!NhNubeh}(h]%photon-source-photon-response-resultsah]h]%photon source/photon response resultsah]h]uhh#h j:hhh!h"hM<
ubeh}(h]#dose-rates-outside-of-a-simple-caskah]h]#dose rates outside of a simple caskah]h]uhh#h j]9hhh!h"hMubh$)}(hhh](h))}(h3Gamma-ray litho-density logging tool using FW-CADISh]h/3Gamma-ray litho-density logging tool using FW-CADIS}(hj>Rh jS' = S\left( \frac{661.7}{0.5}\left( 700 + 600 \right) \right)}(hhh jTubah}(h]h]h]h]h]uhjh jvTubh/i,
which uses the ratio of the line energy to the energy at the center of
the group in the 200/47 library.}(hi,
which uses the ratio of the line energy to the energy at the center of
the group in the 200/47 library.h jvThhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh jShhubjy)}(hread sources
src 1
title="Cs-137 Source: 661.7 keV"
strength=1.0e11
photons
sphere 0.0 origin x=5.0
eDistributionID=1
end src
end sourcesh]h/read sources
src 1
title="Cs-137 Source: 661.7 keV"
strength=1.0e11
photons
sphere 0.0 origin x=5.0
eDistributionID=1
end src
end sources}(hhh jTubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMh jShhubh;)}(hlEach detector is represented by a region tally. A mesh tally is made for one slice in *y* for visualization.h](h/VEach detector is represented by a region tally. A mesh tally is made for one slice in }(hVEach detector is represented by a region tally. A mesh tally is made for one slice in h jThhh!NhNubhA)}(h*y*h]h/y}(hhh jTubah}(h]h]h]h]h]uhh@h jTubh/ for visualization.}(h for visualization.h jThhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM"h jShhubjy)}(hXread tallies
regionTally 1
photon unit=1 region=2
end regionTally
regionTally 2
photon unit=1 region=4
end regionTally
meshTally 1
title="mesh tally in just the y=0 plane"
photon
gridGeometryID=2
noGroupFluxes
end meshTally
end tallies
read parameters
library="v7-200n47g"
randomSeed=00003ecd7b4e3e8b
perBatch=466000 batches=24
noNeutrons
end parametersh]h/Xread tallies
regionTally 1
photon unit=1 region=2
end regionTally
regionTally 2
photon unit=1 region=4
end regionTally
meshTally 1
title="mesh tally in just the y=0 plane"
photon
gridGeometryID=2
noGroupFluxes
end meshTally
end tallies
read parameters
library="v7-200n47g"
randomSeed=00003ecd7b4e3e8b
perBatch=466000 batches=24
noNeutrons
end parameters}(hhh jTubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hM$h jShhubh;)}(hXThe importance map defines two adjoint sources that correspond to the two
tallies. Forward weighting, based on the response integrated over energy
(“respWeighting”), is used. Because the true source is a point source,
the subcell method of making a mesh source will fail, so the number of
source trials is input. This number is small since the source is a
monoenergetic point source. The Denovo calculations used the default
S\ :sub:`8` quadrature and the P\ :sub:`3` Legendre order.h](h/XThe importance map defines two adjoint sources that correspond to the two
tallies. Forward weighting, based on the response integrated over energy
(“respWeighting”), is used. Because the true source is a point source,
the subcell method of making a mesh source will fail, so the number of
source trials is input. This number is small since the source is a
monoenergetic point source. The Denovo calculations used the default
S }(hXThe importance map defines two adjoint sources that correspond to the two
tallies. Forward weighting, based on the response integrated over energy
(“respWeighting”), is used. Because the true source is a point source,
the subcell method of making a mesh source will fail, so the number of
source trials is input. This number is small since the source is a
monoenergetic point source. The Denovo calculations used the default
S\ h jThhh!NhNubj )}(h:sub:`8`h]h/8}(hhh jTubah}(h]h]h]h]h]uhj h jTubh/ quadrature and the P }(h quadrature and the P\ h jThhh!NhNubj )}(h:sub:`3`h]h/3}(hhh jTubah}(h]h]h]h]h]uhj h jTubh/ Legendre order.}(h Legendre order.h jThhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hM;h jShhubjy)}(hXread importanceMap
gridGeometryID=1
' near detector
adjointSource 1
boundingBox 6 4 1 -1 21 19
unit=1 region=2
responseID=1
end adjointSource
' far detector
adjointSource 2
boundingBox 7 3 2 -2 42 38
unit=1 region=4
responseID=1
end adjointSource
respWeighting
sourceTrials=100
end importanceMap
end data
endh]h/Xread importanceMap
gridGeometryID=1
' near detector
adjointSource 1
boundingBox 6 4 1 -1 21 19
unit=1 region=2
responseID=1
end adjointSource
' far detector
adjointSource 2
boundingBox 7 3 2 -2 42 38
unit=1 region=4
responseID=1
end adjointSource
respWeighting
sourceTrials=100
end importanceMap
end data
end}(hhh jUubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMCh jShhubeh}(h]id19ah]h]h]j9ah]uhh#h j9Rhhh!h"hM
j:Kubh$)}(hhh](h))}(hOutputh]h/Output}(hj1Uh j/Uhhh!NhNubah}(h]h]h]h]h]uhh(h j,Uhhh!h"hM]ubh;)}(hThe results for the two region tallies, the first for the near detector and the second for the far detector after 60 minutes of computations (3 forward Denovo, 4 adjoint Denovo and 52 Monaco), were as follows.h]h/The results for the two region tallies, the first for the near detector and the second for the far detector after 60 minutes of computations (3 forward Denovo, 4 adjoint Denovo and 52 Monaco), were as follows.}(hj?Uh j=Uhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hM_h j,Uhhubjy)}(hXPhoton Region Tally 1.
average standard relat FOM stat checks
tally/quantity value deviation uncert (/min) 1 2 3 4 5 6
------------------ ----------- ----------- ------- -------- -----------
total flux (tl) 1.47918E+03 1.57461E+01 0.01065 1.70E+02 X - X X X X
total flux (cd) 1.47936E+03 1.56963E+01 0.01061 1.71E+02 X - X - X X
------------------ ----------- ----------- ------- -------- -----------
Photon Region Tally 2.
average standard relat FOM stat checks
tally/quantity value deviation uncert (/min) 1 2 3 4 5 6
------------------ ----------- ----------- ------- -------- -----------
total flux (tl) 4.57691E+01 2.81778E-01 0.00616 5.07E+02 X X X X X X
total flux (cd) 4.57825E+01 2.80714E-01 0.00613 5.11E+02 X X X X X X
------------------ ----------- ----------- ------- -------- -----------h]h/XPhoton Region Tally 1.
average standard relat FOM stat checks
tally/quantity value deviation uncert (/min) 1 2 3 4 5 6
------------------ ----------- ----------- ------- -------- -----------
total flux (tl) 1.47918E+03 1.57461E+01 0.01065 1.70E+02 X - X X X X
total flux (cd) 1.47936E+03 1.56963E+01 0.01061 1.71E+02 X - X - X X
------------------ ----------- ----------- ------- -------- -----------
Photon Region Tally 2.
average standard relat FOM stat checks
tally/quantity value deviation uncert (/min) 1 2 3 4 5 6
------------------ ----------- ----------- ------- -------- -----------
total flux (tl) 4.57691E+01 2.81778E-01 0.00616 5.07E+02 X X X X X X
total flux (cd) 4.57825E+01 2.80714E-01 0.00613 5.11E+02 X X X X X X
------------------ ----------- ----------- ------- -------- -----------}(hhh jKUubah}(h]h]h]h]h]jjuhjxh!h"hMch j,Uhhubh;)}(hXNote that both detectors have similarly low relative uncertainties
(about 1%) even though the tally values differ by a factor of 30. These
results should be compared to analog results (no biasing at all) and
optimizations of each detector in separate input files, as shown in
:numref:`tab4-22`. The CADIS calculations for each detector (near or far) do
exactly what they were supposed to do---optimize the Monte Carlo
calculation for one tally or the other. The FOMs for the FW-CADIS
calculation were about half of the FOMs for the single-detector CADIS
calculations. Hence, for this two-detector problem, two CADIS
calculations are just as efficient as one FW-CADIS calculation. For
modern well-logging tools with up to a dozen detectors, a single
FW-CADIS would be much more efficient and manageable. Note that the near
detector still needs more time to pass the second (uncertainty fit) and
the fourth (VOV fit) statistical checks. Neither of the single-detector
CADIS calculations passed the fourth statistical check within an hour.h](h/XNote that both detectors have similarly low relative uncertainties
(about 1%) even though the tally values differ by a factor of 30. These
results should be compared to analog results (no biasing at all) and
optimizations of each detector in separate input files, as shown in
}(hXNote that both detectors have similarly low relative uncertainties
(about 1%) even though the tally values differ by a factor of 30. These
results should be compared to analog results (no biasing at all) and
optimizations of each detector in separate input files, as shown in
h jYUhhh!NhNubhp)}(h:numref:`tab4-22`h]jO)}(hjdUh]h/tab4-22}(hhh jfUubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jbUubah}(h]h]h]h]h]refdocj refdomainjpUreftypenumrefrefexplicitrefwarnjtab4-22uhhoh!h"hMsh jYUubh/X. The CADIS calculations for each detector (near or far) do
exactly what they were supposed to do—optimize the Monte Carlo
calculation for one tally or the other. The FOMs for the FW-CADIS
calculation were about half of the FOMs for the single-detector CADIS
calculations. Hence, for this two-detector problem, two CADIS
calculations are just as efficient as one FW-CADIS calculation. For
modern well-logging tools with up to a dozen detectors, a single
FW-CADIS would be much more efficient and manageable. Note that the near
detector still needs more time to pass the second (uncertainty fit) and
the fourth (VOV fit) statistical checks. Neither of the single-detector
CADIS calculations passed the fourth statistical check within an hour.}(hX. The CADIS calculations for each detector (near or far) do
exactly what they were supposed to do---optimize the Monte Carlo
calculation for one tally or the other. The FOMs for the FW-CADIS
calculation were about half of the FOMs for the single-detector CADIS
calculations. Hence, for this two-detector problem, two CADIS
calculations are just as efficient as one FW-CADIS calculation. For
modern well-logging tools with up to a dozen detectors, a single
FW-CADIS would be much more efficient and manageable. Note that the near
detector still needs more time to pass the second (uncertainty fit) and
the fourth (VOV fit) statistical checks. Neither of the single-detector
CADIS calculations passed the fourth statistical check within an hour.h jYUhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMsh j,Uhhubh;)}(h:numref:`fig4-24` shows a mesh tally of total photon flux in the y=0 plane
for all four of the simulations: analog, CADIS for the near detector,
CADIS for the far detector, and the FW-CADIS calculation for both.h](hp)}(h:numref:`fig4-24`h]jO)}(hjUh]h/fig4-24}(hhh jUubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jUubah}(h]h]h]h]h]refdocj refdomainjUreftypenumrefrefexplicitrefwarnjfig4-24uhhoh!h"hMh jUubh/ shows a mesh tally of total photon flux in the y=0 plane
for all four of the simulations: analog, CADIS for the near detector,
CADIS for the far detector, and the FW-CADIS calculation for both.}(h shows a mesh tally of total photon flux in the y=0 plane
for all four of the simulations: analog, CADIS for the near detector,
CADIS for the far detector, and the FW-CADIS calculation for both.h jUhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMh j,Uhhubj)}(hhh](h))}(hFComparison of different CADIS techniques for the litho-density problemh]h/FComparison of different CADIS techniques for the litho-density problem}(hjUh jUubah}(h]h]h]h]h]uhh(h!h"hMh jUubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]jKduhjh jUubj)}(hhh]j8)}(hhh]j=)}(hhh]jL)}(h .. image:: figs/MAVRIC/tab22.pngh]h}(h]h]h]h]h]urifigs/MAVRIC/tab22.pngjY}j[jUsuhjKh jUh!h"hKubah}(h]h]h]h]h]uhj<h jUubah}(h]h]h]h]h]uhj7h jUubah}(h]h]h]h]h]uhjh jUubeh}(h]h]h]h]h]colsKuhjh jUubeh}(h]tab4-22ah]h]tab4-22ah]h]jcenteruhj
h j,Uhhh!NhNubh;)}(h/h]h//}(hjVh jVhhh!NhNubah}(h]h]h]h]h]uhh:h!h"hMh j,Uhhubh)}(h.. _fig4-24:h]h}(h]h]h]h]h]hfig4-24uhh
hMh j,Uhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/4.22.png
:align: center
:width: 800
Mesh tallies showing total photon flux in cm\ :sup:`2`/s (left column) and its relative error (right column) in the y=0 plane.
h]h}(h]h]h]h]h]width800urifigs/MAVRIC/4.22.pngjY}j[j:VsuhjKh j*Vh!h"hMubj)}(h~Mesh tallies showing total photon flux in cm\ :sup:`2`/s (left column) and its relative error (right column) in the y=0 plane.h](h/.Mesh tallies showing total photon flux in cm }(h.Mesh tallies showing total photon flux in cm\ h jh jWhhubjy)}(hread parameters
randomSeed=00003ecd7b4e3e8b
ceLibrary="ce_v7np_endf.xml"
perBatch=2000000 batches=233
photons noNeutrons
end parametersh]h/read parameters
randomSeed=00003ecd7b4e3e8b
ceLibrary="ce_v7np_endf.xml"
perBatch=2000000 batches=233
photons noNeutrons
end parameters}(hhh jXubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMHh jWhhubh;)}(hXThe importance map uses FW-CADIS to construct a map and biased source
that will optimize the photon dose rate in the air outside the cask.
Since photon scatter is typically forward peaked, an S\ :sub:`12`
quadrature and P\ :sub:`5` Legendre scattering expansion are used.h](h/The importance map uses FW-CADIS to construct a map and biased source
that will optimize the photon dose rate in the air outside the cask.
Since photon scatter is typically forward peaked, an S }(hThe importance map uses FW-CADIS to construct a map and biased source
that will optimize the photon dose rate in the air outside the cask.
Since photon scatter is typically forward peaked, an S\ h jXhhh!NhNubj )}(h :sub:`12`h]h/12}(hhh jXubah}(h]h]h]h]h]uhj h jXubh/
quadrature and P }(h
quadrature and P\ h jXhhh!NhNubj )}(h:sub:`5`h]h/5}(hhh jXubah}(h]h]h]h]h]uhj h jXubh/( Legendre scattering expansion are used.}(h( Legendre scattering expansion are used.h jXhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMQh jWhhubjy)}(hXDread importanceMap
adjointSource 1
boundingBox 139.7 -139.7 139.7 -139.7 152.4 -152.4
unit=1 region=7
responseID=5
end adjointSource
respWeighting
gridGeometryID=7
macromaterial
mmTolerance=0.01
end macromaterial
quadrature=12
legendre=5
end importanceMaph]h/XDread importanceMap
adjointSource 1
boundingBox 139.7 -139.7 139.7 -139.7 152.4 -152.4
unit=1 region=7
responseID=5
end adjointSource
respWeighting
gridGeometryID=7
macromaterial
mmTolerance=0.01
end macromaterial
quadrature=12
legendre=5
end importanceMap}(hhh jXubah}(h]h]h]h]h]forcehighlight_args}jjjscaleuhjxh!h"hMVh jWhhubeh}(h]id21ah]h]h]
input fileah]uhh#h jxVhhh!h"hMj:Kubh$)}(hhh](h))}(hOutput fileh]h/Output file}(hjXh jXhhh!NhNubah}(h]h]h]h]h]uhh(h jXhhh!h"hMjubh;)}(hXResults for the mesh tally after 958 minutes (27 forward Denovo, 31
adjoint Denovo, and 900 CE-Monaco) are shown in :numref:`fig4-27`.
Since dose rates inside the package are not of concern, that region was
excluded from the mesh tally. Due to the optimization that focused the
Monte Carlo calculation on dose rates outside the cask, values of the
dose rate inside the cask are underestimated and should not be used.
Also note that voxels along the outer cylindrical edge of the package
could show low dose rates, since the voxel value is an average and only
part of the voxel is actually outside the package. The resolution of the
mesh tally is 2.54 cm.h](h/tResults for the mesh tally after 958 minutes (27 forward Denovo, 31
adjoint Denovo, and 900 CE-Monaco) are shown in }(htResults for the mesh tally after 958 minutes (27 forward Denovo, 31
adjoint Denovo, and 900 CE-Monaco) are shown in h jXhhh!NhNubhp)}(h:numref:`fig4-27`h]jO)}(hjYh]h/fig4-27}(hhh j
Yubah}(h]h](jstd
std-numrefeh]h]h]uhjNh jYubah}(h]h]h]h]h]refdocj refdomainjYreftypenumrefrefexplicitrefwarnjfig4-27uhhoh!h"hMlh jXubh/X .
Since dose rates inside the package are not of concern, that region was
excluded from the mesh tally. Due to the optimization that focused the
Monte Carlo calculation on dose rates outside the cask, values of the
dose rate inside the cask are underestimated and should not be used.
Also note that voxels along the outer cylindrical edge of the package
could show low dose rates, since the voxel value is an average and only
part of the voxel is actually outside the package. The resolution of the
mesh tally is 2.54 cm.}(hX .
Since dose rates inside the package are not of concern, that region was
excluded from the mesh tally. Due to the optimization that focused the
Monte Carlo calculation on dose rates outside the cask, values of the
dose rate inside the cask are underestimated and should not be used.
Also note that voxels along the outer cylindrical edge of the package
could show low dose rates, since the voxel value is an average and only
part of the voxel is actually outside the package. The resolution of the
mesh tally is 2.54 cm.h jXhhh!NhNubeh}(h]h]h]h]h]uhh:h!h"hMlh jXhhubh)}(h.. _fig4-27:h]h}(h]h]h]h]h]hfig4-27uhh
hMwh jXhhh!h"ubj)}(hhh](jL)}(h.. figure:: figs/MAVRIC/4.27.png
:align: center
Dose rates (mrem/hr/Ci) and relative uncertainties from the CE FW-CADIS calculation showing the midplane views of the cask (*z* = 0 above and *y* = 0 below).
h]h}(h]h]h]h]h]urifigs/MAVRIC/4.27.pngjY}j[jJYsuhjKh jhubh;)}(hhh](h/John}(hJohnh jNhubjSbh/C. Wagner, Edward}(hC. Wagner, Edwardh jNhubjSbh/D. Blakeman, and Douglas}(hD. Blakeman, and Douglash jNhubjSbh/
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