CAAScapability.rst 34.4 KB
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.. _CAAScapability:

MAVRIC Appendix A: CAAS Capability
==================================

Introduction
------------

Modeling criticality accident alarm systems (CAAS) presents challenges
since the analysis consists of both a criticality problem and a
deep-penetration shielding problem :cite:`peplow_criticality_2009,peplow_criticality_2010`. Modern codes
are typically optimized to handle one of those types of problems but
usually not both. The two problems also differ in scalethe criticality
problem depends on materials relatively close to the fissionable
materials while the shielding problem can cover a much larger range.
SCALE now contains fully three-dimensional tools to perform both parts
of a CAAS analysis.

CAAS analysis can be performed with SCALE using the KENO-VI criticality
code and the MAVRIC shielding sequence. First, the fission distribution
(in space and energy) is determined by KENO-VI. This distribution is
saved to a file using a user-specified three-dimensional mesh grid and
an energy structure from the cross section library (or a user-defined
energy structure). MAVRIC then uses the fission distribution as the
source for a shielding calculation. MAVRIC is designed to implement
advanced variance reduction methods to calculate dose rates or detector
responses for difficult shielding problems.

For different types of shielding and different combinations of sources
and detector locations, different strategies can be used within
SCALE :cite:`peplow_methods_2012,wetzel_caas_2012`. Due to the way that cross sections for
neutron reactions that create photons are stored in ENDF, some of the
parameters used in the CAAS capability have changed since SCALE 6.1.
Please be sure to understand and follow the new guidance for the correct
accounting of secondary photons from neutron
reactions :cite:`miller_guidance_2013,miller_guide_2013,miller_corrected_2013`.

Methods
-------

The CAAS capability in SCALE is a two-step approach using KENO-VI and
MAVRIC. The first step is the determination of the source distribution,
done with the CSAS6 sequence which uses the KENO-VI functional module.
Along with calculating the system k\ :sub:`eff`, KENO-VI has been modified to
now accumulate the fission distribution over the non-skip generations.
This information is collected on a three-dimensional Cartesian mesh that
overlays the physical geometry model and is saved as a Monaco mesh tally
file. A utility program is used to convert the mesh tally into a Monaco
mesh source.

The mesh source is then used in the second step as the source term in
MAVRIC. The absolute source strength is set by the user based on the
total number of fissions (based on the total power released) during the
criticality excursion. Further neutron multiplication should be
prevented in the MAVRIC transport calculation. Because the fission
neutrons have already been accounted for in the KENO-VI calculation,
failure to suppress neutron multiplication in the MARVIC sequence would
lead to incorrect flux estimates. In addition, if further fissions were
allowed, Monaco would add neutrons to its particle bank faster than they
could be removed (since the system is at or above critical) and the
simulation may never finish.

For the transport part of a CAAS analysis, MAVRIC can be optimized to
calculate one specific detector response at one location using CADIS or
can be optimized to calculate multiple responses/locations with roughly
the same relative uncertainty using FW-CADIS. For calculating mesh
tallies of fluxes or dose rates, MAVRIC also uses FW-CADIS to help
balance the Monaco Monte Carlo calculation such that low flux voxels are
computed with about the same relative uncertainty as high flux voxels.

With this two-step approach, users will have a great deal of flexibility
in modeling CAAS problems. The CSAS6 step and the MAVRIC step could both
use the same geometry and materials definitions or could have different
levels of detail included in each. The fission source distribution from
one CSAS6 calculation could be used in a number of different MAVRIC
building/detector models, with each MAVRIC calculation being optimized
for a given type of detector.

User Input
----------

The user can create either one input file containing both the CSAS6 and
MAVRIC calculations or can create two input filesone for each sequence.
The materials and geometry for these two models could be the same but do
not have to be. For example, the CSAS6 sequence might only contain the
materials and geometry important to the criticality calculation. Note,
however, that the critical source geometry and materials should be
modeled identically in both problems. This allows users greater
flexibility in modeling their specific problems.

KENO-VI input
~~~~~~~~~~~~~

For the criticality problem, the only extra input a user needs to
supply is the keyword cds=yes in the parameter block and a spatial
mesh around all of the fissionable materials of the problem in its own
gridGeometry block. Standard input for KENO-VI is described in the
KENO-VI chapter and CSAS6 chapter. The mesh used for the fission
source distribution is input using the read gridGeometry *id*\ 
block, where *id* is an identification number for that grid. Note that
only one grid can be specified, but that may change in the future. The
cells of the mesh are specified in each dimension separately by either
(1) listing all of the planes bounding the cells (keyword xplanes
followed by an end), (2) using keyword xLinear *n* *a* *b*\  to
specify *n* cells between *a* and *b*, or by (3) specifying the
minimum plane, the maximum plane, and how many cells to make in that
dimension (xmin=, xmax=, numXCells=). The keywords xplanes and
xLinear can be used together and multiple times. Similar keywords
are used for the *y*- and *z*-dimensions. An example CSAS6 input file
that collects the fission distribution information would be as
follows:


.. code:: scale

  =csas6
  CAAS Example
  v7-238n
  read composition
      
  end composition
  read parameters
      
      cds=yes
  end parameters
  read geometry
      
  end geometry
  read gridGeometry 1
      title="Mesh for Collecting Fission Source"
      xLinear 13 0.0 78.0
      yplanes 0 8 16 24 32 34 36 38 40 48 56 64 72 end
      zLinear 10 -2.54 77.46
  end gridGeometry
  end data
  end

The fission source distribution collected by KENO-VI is saved to a
Monaco mesh tally file and copied back to the home area with the name
\ *problemName*.fissionSource.3dmap. This file can be viewed with the
Mesh File Viewer capability of Fulcrum that comes with SCALE. Note that
the finer the mesh spacing is the more generations/histories will have
to be simulated by the criticality calculation in order to reduce the
stochastic uncertainty in each mesh voxel of the distribution.
Regardless of the mesh size, creation of a fission mesh source file will
take more iterations than the number required to find k\ :sub:`eff`. KENO-VI
also saves the value of the system the average number of neutrons per
fission, in a file called \ *problemName*.kenoNuBar.txt. This value is
needed to properly determine the source strength.

Mesh tally to mesh source conversion
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A utility program is used to convert the Monaco mesh tally file into a
Monaco mesh source file. It can be part of the CSAS6 input file. The
user then needs to copy the resulting \*.msm file back to his home area.

.. code:: scale

  =csas6
  
  end

  =mt2msm
  'fissionSource.3dmap'    ! existing Keno fission source mesh tally
  1                        ! which family (for Keno files, there is only 1)
  -1                       ! use the whole family (keep all energy groups)
  1                        ! particle type for *.msm file (1-neutron, 2-photon)
  'fissionSource.msm'      ! name of newly created mesh source map file
  end

  =shell
    copy fissionSource.msm C:\mydocu~1\caasExample
  end

Details on the conversion utility program are contained in :ref:`appendixb` of
the MAVRIC manual.

In SCALE 6.1, the fission source distribution mesh tally produced by
KENO contained data representing the number of fissions in each mesh
cell in each energy group. In SCALE 6.2, the data stored was changed to
be the fissions per unit volume  the fission density. This is more
consistent with other mesh tallies from Monaco which store flux or dose
rates that represent averages over the mesh cells. This change also
allows the Mesh File Viewer to display the KENO fission source
distribution better. The mt2msm utility program also changed from SCALE
6.1 to SCALE 6.2 to account for the change in what is stored in the Keno
mesh tally file. Therefore, **KENO-produced fission source mesh tallies
and the mt2msm utility should not be mixed-and-matched across versions
of SCALE**. Doing so would result in the final Monaco mesh source file
being improperly normalized, which would not represent the KENO fission
source distribution and would give incorrect results in subsequent
MAVRIC calculations. Because there is not a specific version flag in a
mesh tally file or mesh source map file, the user must ensure that they
have used the same version of SCALE for both the CSAS6 and MAVRIC
sequences any time the CAAS capability is used.

MAVRIC input
~~~~~~~~~~~~

The input for the MAVRIC portion of the CAAS problem should include the
materials and geometry of the criticality model, use the fission
distribution as a source, set the source strength, and set any optional
modifiers to the source to change its location or add fission photons.
The cross section library used by the MAVRIC calculation does not need
to have the same group structure as the fission distribution. MAVRIC
will automatically convert the fission source group structure to match
the group structure of its cross section library.

The shielding calculation needs to specify that the source is the
fission distribution file, which is typically fissionSource.msm. The
total source strength can be specified by either the number of fissions
in the criticality accident (fission rate or total number) or by the
number of released neutrons (the fission rate multiplied by :math:`\over{v}` per
fission). The value of :math:`\over{v}` will be read from the file kenoNuBar.txt in the
SCALE temporary directory if it is not given in the source input with
the keyword nu-bar=. The mesh source can also be placed at different
coordinates in the geometry using the origin x=\ *x* y=\ *y* z=\ *z*\ 
keywords, if a different reference frame was used with the criticality
geometry model that created the mesh source. Rotations of mesh sources
are not available at this time. It is also recommended to use filters in
the source block to define the source, such as the mixture= filter to
only allow source sampling from a specific mixture since the mesh source
can be transformed from its original origin or meshes can cover
non-fissionable materials.

For example, using a KENO-VI fission distribution, placing it somewhere
in the MAVRIC model and setting the source strength (in neutrons/s) to
correspond to 10\ :sup:`17` fission/s would look like

.. code:: scale


  =shell
      copy C:\mydocu~1\caasExample\kenoInput.kenoNuBar.txt  kenoNuBar.txt
  end

  =mavric
  
  read sources
      src 1
          meshSourceFile C:\mydocu~1\caasExample\fissionSource.msm"
              origin x=600 y=650 z=400
          fissions=1.0e17
      end src
  end sources

  end data
  end

The source strength in neutrons/s will be calculated by MAVRIC to be the
fission rate multiplied by the value of read from the “kenoNuBar.txt”
file. The neutron strength could have alternatively been specified using
the standard source strength keyword “strength=2.5e17” (for an example
with the average number of neutrons per fission of 2.5).

The Monte Carlo functional module used by MAVRIC, Monaco, is a
fixed-source code. Unless told otherwise, neutrons will multiply in
fissionable materials. Since all of the neutrons were part of the
source, neutron multiplication should not be allowed and MAVRIC should
be run with the keyword “fissionMult=0” in the parameters block. For
systems at or near critical without the “fissionMult=0” keyword, Monaco
simulations may not end since neutrons will be added to the particle
bank at the same rate they leave the system or get killed.

The shielding calculation can be run using standard variance reduction
methods (such as path length stretching, user-defined weight windows
based on geometry regions, and user-defined source biasing) or using the
automated tools which employ approximate discrete-ordinates calculations
to determine the space/energy weight windows as well as a biased source
distribution in space and energy. The automated tools can be used to
optimize the shielding calculation to determine one specific tally using
CADIS or several separate tallies or a mesh tally over a large volume of
the problem space using FW-CADIS. When using these advanced variance
reduction methods, remember to include planes in the discrete‑ordinates
mesh definition that correspond to the planes in the fission
distribution that the source is based on. If they are not included,
MAVRIC will resample the fission source on the discrete-ordinates mesh
it is using for the importance map, possibly smearing or reducing the
original resolution of the fission distribution.

Example problem
---------------

Consider the Jezebel critical plutonium sphere experiment, shown in
:numref:`fig4a1`, taking place inside a simple fictitious building, shown
in :numref:`fig4a2`. The building has two rooms: an experiment room and a
control room. In the control room there is a criticality alarm detector,
and it is positioned furthest from the entry to the experiment room. For
this example, assume that a criticality excursion results in a total of
10\ :sup:`18` fissions. This example will calculate the neutron and
photon doses seen by a detector in the control room, as well as
calculate a dose map for the entire building.

.. _fig4a1:

.. figure:: figs/fig4a1.png
  :align: center
  :width: 60 %

  Cutaway view of Jezebel.

.. _fig4a2:
.. figure:: figs/fig4a2.png
  :align: center
  :width: 60 %

  Simple two-room building.

KENO-VI criticality and fission source distribution
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For the criticality calculation, consider just a bare sphere of
plutonium, with a radius of 6.38493 cm. Atom densities (atoms/b·cm) for
the sphere material are :sup:`239`\ Pu 0.037047; :sup:`240`\ Pu
0.0017512; :sup:`241`\ Pu 0.00011674; and Cu 0.0013752. This can be
easily modeled as a sphere at the origin. For collecting the fission
distribution, a uniform mesh grid can be constructed around the sphere,
extending 7 cm in each direction, with a 1×1×1 cm voxel size. The first
portion of the input files ``mavric.caasA.inp`` and ``mavric.caasB.inp`` looks
like the following:

.. code-block:: scale

  =csas6
  Dose Rates from a Jezebel Accident in a Block Building
  v7-238n
  '-------------------------------------------------------------------------------
  ' Composition Block
  '-------------------------------------------------------------------------------
  read composition
      Pu-239 1 0 0.037047   end
      Pu-240 1 0 0.0017512  end
      Pu-241 1 0 0.00011674 end
      Cu     1 0 0.0013752  end
  end composition

  '-------------------------------------------------------------------------------
  ' Parameters Block
  '-------------------------------------------------------------------------------
  read parameters
      gen=250 npg=200000 nsk=50 htm=no
      cds=yes
  end parameters
  '-------------------------------------------------------------------------------
  ' Geometry Block - SCALE standard geometry package (SGGP)
  '-------------------------------------------------------------------------------
  read geometry
      global unit 2
          sphere 1  6.38493
          media 1 1 1 vol=1090.3277
      boundary 1
  end geometry

  '-------------------------------------------------------------------------------
  ' Grid Block
  '-------------------------------------------------------------------------------
  read gridGeometry 1
      title="Mesh for Collecting Fission Distribution"
      xLinear 14 -7.0 7.0
      yLinear 14 -7.0 7.0
      zLinear 14 -7.0 7.0
  end gridGeometry

  end data
  end

  =mt2msm
  'fissionSource.3dmap'
  1
  -1
  1
  mavric.caas[A/B].fissionSource.msm'
  end

The results of this 26 minute calculation are shown in :numref:`tab4a1`,
and details about the calculated fission distribution are shown in
:numref:`fig4a3` and :numref:`fig4a4`.

.. _tab4a1:

.. table:: Results of the CSAS6 calculation

  +-----------------+----------------------------+-----------------+-------------+
  | **Quantity**    | **Value**                  | **Uncertainty** |             |
  +=================+============================+=================+=============+
  | k\ :sub:`eff`   | best estimate system k-eff | 1.00024         | 0.00014     |
  +-----------------+----------------------------+-----------------+-------------+
  | :math:`\over{v}`| system nu bar              | 3.15671         | 4.77938E-05 |
  +-----------------+----------------------------+-----------------+-------------+

.. _fig4a3:
.. figure:: figs/fig4a3.png
  :align: center
  :width: 60 %

  Fission source spatial distribution for the center horizontal slice.

.. _fig4a4:
.. figure:: figs/fig4a4.png
  :align: center
  :width: 60 %

  Fission source energy distribution for the center voxel.

MAVRIC transport calculations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Two MAVRIC calculations will be done—one that calculates the doses seen
at the detector and one that computes mesh tallies of doses over the
entire building. They will share the same materials, geometry, and
source but will have different tally and variance reduction options.

The two-room building will be a simple model using concrete-block walls,
a concrete floor, and a steel roof, with dimensions shown in
:numref:`fig4a5`. The building exterior dimensions are 1200 cm long,
600 cm wide, and 300 cm high above the ground. The exterior and interior
walls are all made of a double layer of typical concrete blocks (total
of 40 cm thick.) Concrete blocks are typically 39×19×19 cm and weigh
~13.5 kg, since they have a volume fraction of 33.2%. The floor is made
of poured concrete, extending 60 cm into the ground. The roof and the
exterior door (120 cm wide and 210 cm tall) are made of 1/8 in. (0.3175
cm) thick steel. The experiment room on the left connects to the control
room on the right through a maze that prevents radiation streaming.
Assume that the critical experiment was in the center of the experiment
room, 100 cm above the floor. Assume the detector in the control room is
a 30 cm diameter sphere located at position (1145, 55, 285).

.. _fig4a5:
.. figure:: figs/fig4a5.png
  :align: center

  Coordinates of the floor, walls, ceiling, and door of the simple block building model (in cm).

If the MAVRIC transport calculation is not in the same file as the CSAS6 calculation, the MAVRIC input would start by moving the KENO-VI results into the SCALE temporary area:

.. code:: scale

  =shell
      copy %RTNDIR%\caas.kenovi.fissionSource.msm  fissionSource.msm
      copy %RTNDIR%\caas.kenovi.kenoNuBar.txt      kenoNuBar.txt
  end

The materials and geometry blocks of the two MAVRIC input files for each of the two calculations,
``smplprbs/caas.mavricA.inp`` and ``smplprbs/caas.mavricB.inp``, look like the following:

.. code:: scale

  '-------------------------------------------------------------------------------
  ' Composition Block
  '-------------------------------------------------------------------------------
  read composition
      pu-239 1 0 0.037047   end
      pu-240 1 0 0.0017512  end
      pu-241 1 0 0.00011674 end
      cu     1 0 0.0013752  end
      orconcrete 2 1.0     293.0 end
      orconcrete 3 0.33198 293.0 end
      ss304      4 1.0     293.0 end
  end composition

  '-------------------------------------------------------------------------------
  ' Geometry Block - SCALE standard geometry package (SGGP)
  '-------------------------------------------------------------------------------
  read geometry
      global unit 1
          com="jezebel"
          sphere   1  6.38493  origin x=280  y=300  z=100

          com="exterior of the building, roof, floor"
          cuboid   10 1200 0    600 0     300.3175 -60.0
          cuboid   11 1200 0    600 0     300.3175 300.0
          cuboid   12 1200 0    600 0     0.0        -60

          com="air space in building - two rooms and maze"
          cuboid   20 1160 40   560 40    300 0

          com="interior walls to form maze to prevent streaming"
          cuboid   21  560 520  560 120   300 0
          cuboid   22  680 640  480  40   300 0

          com="exterior door"
          cuboid   30 1200 1160       360 240   210 0
          cuboid   31 1200 1199.6825  360 240   210 0

          com="detector sphere"
          sphere  40   15.0  origin x=1145 y=55 z=285

          com="jezebel"
          media  1 1   1   vol=1090.3277

          com="walls, roof, floor"
          media  3 1   10 -20 -11 -12  -30
          media  4 1   11
          media  2 1   12

          com="air space (void) and maze walls"
          media  0 1   20 -21 -22   -40  -11 -12  -1
          media  3 1   21                -11 -12
          media  3 1   22                -11 -12

          com="exterior door"
          media  0 1   30 -31
          media  4 1   31

          com="detector"
          media  0 1   40   vol=14137.167

      boundary 10
  end geometry

The response functions used to compute the doses will be the standard
flux-to-dose rate conversion factors for neutrons and photons. These are
defined in the definitions block. Note that these responses have units
of (rem/hr)/(/cm :sup:`2`/s).

.. code:: scale

  '-------------------------------------------------------------------------------
  ' Definitions Block
  '-------------------------------------------------------------------------------
  read definitions
      response 5
          title="ANSI (1977) neutron flux-to-dose-rate"
          specialDose=9029
      end response
      response 6
          title="ANSI (1977) photon flux-to-dose-rate"
          specialDose=9504
      end response
  end definitions

The source used by each MAVRIC simulation will be based on the fission
distribution mesh source determined by KENO-VI. The strength of the
source can be specified by the total number of fissions that occurred in
the criticality event. Fission photons will be added for :sup:`239`\ Pu.
MAVRIC will determine the total source strength, including the fission
photons, from the value of saved by KENO-VI and the multiplicity data
from the fission photon data file.

.. code:: scale

  '-------------------------------------------------------------------------------
  ' Sources Block
  '-------------------------------------------------------------------------------
  read sources
      src 1
          meshSourceFile=”fissionSource.msm"
          origin x=280  y=300  z=100
          fissions=1.0e18
          mixture=1
      end src
  end sources

Note that further multiplication needs to be turned off in MAVRIC using
the fissionMult=0 keyword in the parameter block as shown below.

For the responses from the tallies, MAVRIC usually calculates dose rates
(rem/hr) using a source strength in particles/s. For this example
problem, instead of a source rate, we used a total number of particles
(by specifying the number of fissions). Hence, the computed fluxes will
have units of particles/cm\ :sup:`2` and the computed responses using
the standard dose responses from the cross section libraries will have
units of rem s/hr. To get a dose in rem, the responses need to be
multiplied by (3600 s/hr)\ :sup:`-1`. This can be done using the MAVRIC
tally multiplier keyword.

Each MAVRIC simulation will need a discrete-ordinates mesh. The planes
in each dimension where there are material changes are listed in
:numref:`tab4a2`. In addition to these planes, the discrete-ordinates mesh
should also subdivide the thick shields in the direction of particle
travel. For example, the walls of the maze should be divided to better
model the radiation attenuation through the walls in the Denovo
calculation. The interior walls of the building will reflect particles,
so the first few centimeters are the most important to capture in the
importance map. Mesh planes should also be added that correspond to the
mesh source after it is placed into the geometry model.

.. _tab4a2:
.. table:: Main planes in the building
  :align: center

  +---------+-------+---------+
  | **x**   | **y** | **z**   |
  +=========+=======+=========+
  | 0       | 0     | -60     |
  +---------+-------+---------+
  | 40      | 40    | 0       |
  +---------+-------+---------+
  | 520     | 120   | 210     |
  +---------+-------+---------+
  | 560     | 240   | 300     |
  +---------+-------+---------+
  | 640     | 360   | 300.318 |
  +---------+-------+---------+
  | 680     | 480   |         |
  +---------+-------+---------+
  | 1160    | 560   |         |
  +---------+-------+---------+
  | 1199.68 | 600   |         |
  +---------+-------+---------+
  | 1200    |       |         |
  +---------+-------+---------+


Detector doses using CADIS
^^^^^^^^^^^^^^^^^^^^^^^^^^

The grid geometry for this calculation should also include planes that bound the adjoint source,
which is the detector area (these values are shown in brackets [] below). The definitions block in
``smplprbs/caas.mavricA.inp`` also includes the location of the center of the detector, which is used in the adjoint source description.

.. code:: scale

   location 1
        position 1145 55 285
    end location

    gridGeometry 1
        title="mesh for discrete ordinates 57 x 47 x 31 = 83049"
        xplanes 0     10 20 30 35
                40    120 160 240
                      270 272 274 276 278 280 282 284 286 288 290
                      360 440
                520   525 530 550 555
                560   600
                640   645 650 670 675
                680   760 840 920 1000 1080
                      [1130 1140 1150]
                1160  1165 1170 1180 1190
                1199.6825
                1200  end
        yplanes 0     10 20 30 35
                40    [50 60] 70
                120   125 130 140 200
                240   280 290 292 294 296 298 300 302 304 306 308 310
                      320
                360   440 460 470 475
                480
                560   565 570 580 590
                600   end
        zplanes -60   -30 -20 -10 -5
                0     45
                      90 92 94 96 98 100 102 104 106 108 110
                      140 175
                210   255  [280 290]
                300
                300.3175   end
    end gridGeometry

The tallies are region tallies over the detector region (the 10th media
card in unit 1) using the appropriate response function for the particle
type of the tally. The volume of the detector sphere needs to be listed
in the geometry block so that the fluxes and tallies will be correctly
computed. The importance map uses standard CADIS to bias the particles
towards the detectors, optimizing the calculation of the total dose (by
listing both response functions together, the total response will be
used in the adjoint source).

.. code:: scale

  '-------------------------------------------------------------------------------
  ' Tallies Block
  '-------------------------------------------------------------------------------
  read tallies
      regionTally 1
          title="Doses seen by the detector"
          neutron
          unit=1 region=10
          responseID=5
          multiplier=2.777778e-4
      end regionTally
      regionTally 2
          title="Doses seen by the detector"
          photon
          unit=1 region=10
          responseID=6
          multiplier=2.777778e-4
      end regionTally
  end tallies

  '-------------------------------------------------------------------------------
  ' Parameters Block - 3 min batch
  '-------------------------------------------------------------------------------
  read parameters
      randomSeed=3263827
      perBatch=654000  batches=40
      fissionMult=0
  end parameters

  '-------------------------------------------------------------------------------
  ' Importance Map Block
  '-------------------------------------------------------------------------------
  read importanceMap
      gridGeometryID=1
      adjointSource 1
          locationID=1
          responseIDs 5 6 end
      end adjointSource
  end importanceMap

The results of this example problem are shown in :numref:`tab4a3`.
Calculation times were 12 minutes for Denovo and 135 minutes for Monaco.
Note that the uncertainty for the photon dose is much higher than the
neutron dose uncertainty. This is because the simulation was optimized
for the calculation of total dose, and the photon component of the total
dose is less than 2%. Had a separate calculation been done that used an
adjoint source of just the photon response, the photon dose rate
uncertainty would have been much smaller but at the expense of the
neutron dose rate uncertainty. A single calculation could have also been
performed using two adjoint sources, one using the neutron dose response
and one using the photon dose response, and forward weighting to help
calculate each component of dose with more uniform relative
uncertainties.

.. _tab4a3:
.. table:: Doses seen by the detector
  :align: center

  +----------+-----------+----------+
  | ** **    | **Value** | **Rel.** |
  +==========+===========+==========+
  | **Dose** | **(rem)** | **Unc.** |
  +----------+-----------+----------+
  | neutron  | 1539      | 0.78%    |
  +----------+-----------+----------+
  | photon   | 30.0      | 8.00%    |
  +----------+-----------+----------+


Dose map using FW-CADIS
^^^^^^^^^^^^^^^^^^^^^^^

The grid geometry for this calculation does not need extra planes around the detector. The grid geometry in
``smplprbs/caas.mavricB.inp`` looks like the following:

.. code:: scale

  gridGeometry 1
          title="mesh for discrete ordinates 46x36x23 = 38088"
          xplanes 0     10 20 30 35
                  40    120 160 240
                        270 272 274 276 278 280 282 284 286 288 290
                        360 440
                  520   525 530 550 555
                  560   600
                  640   645 650 670 675
                  680   760 840 920 1000 1080
                  1160  1165 1170 1180 1190
                  1199.6825
                  1200  end
          yplanes 0     10 20 30 35
                  40
                  120   125 130 140 200
                  240   280 290 292 294 296 298 300 302 304 306 308 310
                        320
                  360   440 460 470 475
                  480
                  560   565 570 580 590
                  600   end
          zplanes -60   -30 -20 -10 -5
                  0     45
                        90 92 94 96 98 100 102 104 106 108 110
                        140 175
                  210   255
                  300   300.3175   end
  end gridGeometry

A second grid geometry also needs to be added to the definitions block for the mesh tally to use.

.. code:: scale

    gridGeometry 2
        title="mesh for uniform mesh tally - 40x40x30 cm voxels"
        xLinear 30 0.0 1200.0
        yLinear 15 0.0  600.0
        zLinear 10 0.0  300.0
    end gridGeometry

The mesh tallies for each particle type are listed, along with the appropriate response function. The importance map uses FW-CADIS to better spread the particles out over the entire geometry, optimized for the calculation of total dose in the void regions.

.. code:: scale

  '-------------------------------------------------------------------------------
  ' Tallies Block
  '-------------------------------------------------------------------------------
  read tallies
      meshTally 1
          title="Neutron doses mapped over the entire building"
          neutron
          gridGeometryID=2
          responseID=5
          noGroupFluxes
          multiplier=2.777778e-4
      end meshTally
      meshTally 2
          title="Photon doses mapped over the entire building"
          photon
          gridGeometryID=2
          responseID=6
          noGroupFluxes
          multiplier=2.777778e-4
      end meshTally
  end tallies

  '-------------------------------------------------------------------------------
  ' Parameters Block - 3 min batch
  '-------------------------------------------------------------------------------
  read parameters
      randomSeed=3263827
      perBatch=669000  batches=40
      fissionMult=0
  end parameters

  '-------------------------------------------------------------------------------
  ' Importance Map Block
  '-------------------------------------------------------------------------------
  read importanceMap
      gridGeometryID=1
      adjointSource 1
          boundingBox 1200 0  600 0  300.3175 -60.0
          responseIDs 5 6 end
          mixture=0
      end adjointSource
      respWeighting
  end importanceMap


This calculation used 5 minutes for the forward Denovo S\ :sub:`N`
calculation, 6 minutes for the adjoint Denovo, and 120 minutes for the
Monaco Monte Carlo. The resulting mesh tally is shown in
:numref:`fig4a6`. The uncertainties for each voxel are shown in
:numref:`fig4a7`. Note that the dose in the voxel containing the
detector (not shown in the figures) is 1.552×10\ :sup:`3` rem with a
relative uncertainty of 3.8%, closely matching the value calculated
with the first MAVRIC simulation.

Similar to the detector doses above, a single calculation could have
also been performed for the dose maps using two adjoint sources, one
using the neutron dose response and one using the photon dose response,
and forward weighting to help calculate each component of dose with more
uniform relative uncertainties.

.. _fig4a6:
.. figure:: figs/4a6.png
  :align: center

  Dose (rem) results for the z=100 cm plane (containing the source).

.. _fig4a7:
.. figure:: figs/fig4a7.png
  :align: center

  Relative uncertainties in the dose, most less than 1%, for the z=100 cm plane.

Summary
-------

SCALE now has the capability to do detailed simulations of criticality accident alarm systems. The advanced variance reduction capabilities of the MAVRIC radiation transport sequence allow for the full three-dimensional analysis of CAAS problems in reasonable amounts of computer time. This enables the use of more realistic source definitions, such as a detailed spatial/energy dependent fission source distribution determined by the KENO-VI criticality code, and the critical assembly itself can be included in the transport model.







.. bibliography:: bibs/41a.bib