Monaco.rst 208 KB
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.. _Monaco:


Monaco: A Fixed-Source Monte Carlo Transport Code for Shielding Applications
============================================================================

*D. E. Peplow and C. Celik*


Monaco is a general-purpose, fixed-source, Monte Carlo shielding code
for the SCALE package. It is a functional module that uses either AMPX
cross sections or continuous energy libraries to calculate neutron and
photon fluxes and responses to specific geometry regions, to point
detectors and to mesh tallies. Basic multigroup transport methods are
inherited from Monaco’s predecessor, MORSE. Continuous energy physics
has been incorporated into the code with a new physics package that uses
the same CE data as CE-KENO-VI, with extensions for simulating photons.
Variance reduction capabilities include source biasing and weight
windows, either by geometry region or by using a mesh-based importance
map. User input includes the cross section file unit number; the
geometry description using the SCALE General Geometry Package; source
description as a function of position, energy, and direction; tally
descriptions (fluxes in which regions, at what point detectors, or over
what mesh grids); and response functions (functions of energy). Output
consists of tables detailing the region and point detector fluxes (and
their responses), as well as files for mesh tallies.

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


Monaco is a neutron/photon, fixed-source Monte Carlo shielding code for
the SCALE code package. Monaco uses the SCALE General Geometry Package
(SGGP)---the same geometry description as KENO-VI. Monaco has many
options available to the user for specifying source distributions, many
tally options, and many variance reduction capabilities. Monaco was
originally based on the MORSE Monte Carlo code but has been extensively
modified to modernize the coding, increase the number of capabilities in
terms of sources and tallies, and allow for either multigroup or
continuous energy (CE) transport through the use of the new SCALE CE
Modular Physics Package (SCEMPP).

Monaco was developed to address a number of long-term goals for the
Monte Carlo shielding capabilities in SCALE. The principal goals for
this project included (1) unification of geometric descriptions between
the SCALE shielding and criticality Monte Carlo codes,
(2) implementation of a mesh-based importance map and mesh-based biased
source distribution so that automated variance reduction could be used,
and (3) establishment of a code using modern programming practices from
which to continue future development. The addition of a
continuous-energy transport capability is a significant change as well.

Monaco is the key component of the MAVRIC sequence, which also uses
Denovo to create the mesh-based importance map and mesh-based biased
source distribution for general 3-D automated variance reduction. See
the MAVRIC chapter for more information.

Monaco Capabilities
-------------------

Monaco has a wide range of source descriptions and tallies for
performing general radiation transport calculations. Note that Monaco
can work with either the AMPX-based multigroup libraries or the newer
AMPX-based CE libraries. Note that for CE calculations, tallies still
employ a multigroup energy structure to store and report results.

Source Descriptions
~~~~~~~~~~~~~~~~~~~

Multiple sources can be defined for a Monaco calculation. Sampling of
the different sources can be biased by the user. Each source is
specified by its spatial distribution, its energy distribution, its
directional distribution, and its strength. Distributions defined by the
user can also be biased and can be used multiple times by different
sources. The Monaco tallies assume that the sources all have units of
particles/second. If the source strengths are given in other units, the
user will have to incorporate the proper conversion to the tally results
and remember to interpret the results accordingly.

Distributions
^^^^^^^^^^^^^

Two types of basic distributions are used by Monaco – binned histograms
and a set of value/function pairs. The binned histogram type is defined
by :math:`n + 1` bin boundaries and *n* values, representing the
integrated amount in each bin. For the true distribution\ :math:`f(x)`,
the bin boundaries
:math:`\left\lbrack x_{0},\ x_{1},\ \ldots,\ x_{n} \right\rbrack` and
the integrated amounts
:math:`F_{i} = \ \int_{x_{i - 1}}^{x_{i}}{f\left( x \right)\text{dx}}`
are given. The distribution will be normalized by Monaco after reading.
The user can optionally bias a binned histogram distribution by
supplying one of the following: the biased sampling distribution
amounts,
:math:`G_{i} = \ \int_{x_{i - 1}}^{x_{i}}{g\left( x \right)\text{dx}}`;
the importance of each bin, :math:`I_{i}`; or the suggested weight for
each bin, :math:`w_{i}`.

Based on what type of input is given, Monaco will compute a properly
normalized probability distribution function for sampling. If the
importances are given, the sampling distribution is computed as

.. math::
  :label: Monaco-1

  G_{i} = \frac{I_{i}F_{i}}{\sum_{i}^{}{I_{i}F_{i}}}

If suggested weights are given, then the sampling distribution is
computed as

.. math::
  :label: Monaco-2

  G_{i} = \frac{\frac{F_{i}}{w_{i}}}{\sum_{i}^{}\frac{F_{i}}{w_{i}}}

for bins with non-zero weight. The sampling distribution for bins with a
suggested weight of zero are set to :math:`G_{i} = \ 0`. When sampled,
particles are assigned a weight of :math:`\frac{F_{i}}{G_{i}}`.

The second type of distribution that a user can define is for a series
of point values of a function. For a set of :math:`n + 1` point pairs,
:math:`\left( x_{i},\ f_{i} \right)` for
:math:`i \in \left\lbrack 0\ldots n \right\rbrack`, defining :math:`n`
intervals, a distribution can be made by linearly interpolating between
adjacent point pairs. This type of distribution can also be biased by
supplying one of the following: the biased sampling distribution
function value :math:`g_{i}` at each point, the importance of each
point, :math:`I_{i}`; or the suggested weight for each point,
:math:`w_{i}`. Similar to above, if importances or weights are given,
Monaco computes the biased distribution for sampling. For the
value/function point pairs type of distribution, the weight assigned to
the sampled particle is a continuous function.

Some commonly used distributions are built into Monaco and can be used
by simple keywords. Monaco can produce a graph of any distribution so
that the user can verify that the input was entered correctly.

Spatial energy and directional attributes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Each Monaco source is described by three separable components: spatial,
energy and directional.

The spatial component of a source in Monaco is simple but very flexible.
First, the general shape of the source region is defined in global
coordinates. The basic solid shapes and their allowed degenerate cases
are listed in :numref:`Monaco-tab1`. The user can reference any of the defined
distributions to describe the source distribution in any coordinate
(*x*, *y*, and *z* for cuboids, *r* and *z* for cylinders and *r* for
spheres) to use for sampling or leave the source distribution as uniform
over each dimension for the solid shape. The source region can be
limited by the underlying SGGP geometry variables of unit, media, and
mixture. This way, source volumes (or planes, lines, or points) can be
defined that are independent or dependent on the model geometry. A
cylinder or cylindrical shell region can be oriented with its axis in
any direction.

.. _Monaco-tab1:
.. table:: Available source shapes and their allowed degenerate cases

  +-----------------------------------+-----------------------------------+
  | **Shape**                         | **Allowable degenerate cases**    |
  +===================================+===================================+
  | cuboid                            | rectangular plane, line, point    |
  +-----------------------------------+-----------------------------------+
  | cylinder                          | circular plane, line, point       |
  +-----------------------------------+-----------------------------------+
  | cylindrical shell                 | cylinder, planar annulus,         |
  |                                   | circular plane, cylindrical       |
  |                                   | surface, line, ring, point        |
  +-----------------------------------+-----------------------------------+
  | sphere                            | point                             |
  +-----------------------------------+-----------------------------------+
  | spherical shell                   | sphere, spherical surface, point  |
  +-----------------------------------+-----------------------------------+

Monaco samples the source position using either the given distributions
or uniformly over the basic solid shape and then uses rejection if any
of the optional SGGP geometry limiters have been specified. For sources
that are confined to a particular unit, media, or mixture, users should
make sure the basic solid shape tightly bounds the desired region for
efficient sampling.

For the energy component of each source, either type of distribution
described above can be used. Biasing can be used in the energy component
of the source as well. The Watt spectrum is a built-in distribution
which uses the Froehner and Spencer :cite:`froehner_method_1981` method for sampling. If the
defined energy distribution has point(s) that are out of the problem’s
energy range for a CE problem, these points will be rejected in the
source energy sampling and an error message will be generated. The
warnings will be suppressed if the number of rejected source points
exceeds a pre-defined threshold (1000).

Distributions can be used to define the directional component of the
source. A function of the cosine of the polar angle, with respect to
some reference direction in global coordinates, can be used by Monaco.
If no directional distribution is specified, the default is an isotropic
distribution (one directional bin from *µ*\ = −1 to *µ*\ =1). The
default reference direction is the positive *z*-axis (<0,0,1>).

Monaco mesh source map files
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

An alternative to specifying the separate spatial and energy
distributions, a Monaco mesh source file can be used. A mesh source
consists of a 3D Cartesian mesh that overlay the geometry. Each mesh
cell has some probability of emitting a source particle, and within each
mesh cell, a different energy distribution can be sampled. Position
within each mesh cell is sampled uniformly, and the emission direction
is sampled from the standard directional distribution. Monaco mesh
source files are typically produced by the MAVRIC sequence or by other
Monaco calculations (see the mesh source saver option in the source
input). For a source constructed from the separable spatial and energy
distributions, Monaco can create a mesh source file which can then be
visualized using the Mesh File Viewer. This is a convenient way to
ensure that the source being used is what was intended.

Tallies
~~~~~~~

Monaco offers three tally types: point detectors, region tallies, and
mesh tallies. Each is useful in determining quantities of interest in
the simulation. Any number of each can be used, up to the limit of
machine memory. The tallies will compute flux for each group, the total
neutron and total photon fluxes, and any number of dose-like responses.
A typical dose-like response, *R*, is the integral over energy of the
product of a response function, :math:`f\left( E \right)`, and the flux,
:math:`\phi\left( E \right)`.


 .. math::
  :label: Monaco-3

  R = \int_{}^{}{f\left(E \right)\phi \left( E \right)\ } dE


In multigroup calculations, the total response would be expressed as the
sum over all groups :math:`R = \sum_{}^{}{f_{g}\phi_{g}}`. For CE
calculations, tallies can be segmented into energy and time bins which
can be thought of as “groups”. All three of the tally types can be
scaled with a constant – for example, to account for units conversions.

Tally statistics
^^^^^^^^^^^^^^^^

The three Monaco tallies are really just collections of simple and
extended tallies for each group, each total, and each group contribution
to a response or total response. The simple tally works in the following
way: a history score :math:`h_{i}` is zeroed out at the start of history
:math:`i`. During the course of the history, when an event occurs during
substep :math:`j`, a score consisting of some contribution
:math:`c_{\text{ij}}` weighted by the current particle weight
:math:`w_{\text{ij}}` is calculated and added to :math:`h_{i}`. At the
end of the history, the history score is the total weighted score for
each substep :math:`j` in the history.


 .. math::
  :label: Monaco-4

  h_{i} = \sum_{j}^{}w_{\text{ij}}c_{\text{ij}}


Note that the values for the contribution :math:`c_{\text{ij}}` and when
it is added to the accumulator are determined by the tally type. At the
end of the each history, the history score is added to two accumulators
(power sums) - the first accumulator is for finding the tally average,
:math:`S_{1}`, and the second accumulator is for finding the uncertainty
in the tally average, :math:`S_{2}`.


 .. math::
   :label: Monaco-5

   S_{1} = \ \sum_{i}^{}h_{i}^{\ }

 .. math::
   :label: Monaco-6

   S_{2} = \ \sum_{i}^{}h_{i}^{2}


At the end of all :math:`N` histories, the second sample central moment
is found from the power sums


 .. math::
   :label: Monaco-7

    m_{2} = \frac{S_{2}}{N} - \ \frac{S_{1}^{2}}{N^{2}}


and then the tally average is computed as
:math:`\overline{x} = \frac{S_{1}}{N}` and the uncertainty in the tally
average is :math:`u = \sqrt{\frac{m_{2}}{N}}`.

The extended tally uses four accumulators – the first and second are the
same as the simple tally – with the third and fourth accumulators used
for finding the variance of the variance (VOV). These extra
accumulators, :math:`S_{3}` and :math:`S_{4}`, are calculated as


 .. math::
   :label: Monaco-8

    S_{3} = \ \sum_{i}^{}h_{i}^{3}

 .. math::
   :label: Monaco-9

    S_{4} = \ \sum_{i}^{}h_{i}^{4}


At the end of all :math:`N` histories, the tally average
:math:`\overline{x}\ `\ and uncertainty in the tally average :math:`u`
are found in the same way as a simple tally. For the VOV calculation,
the third and fourth sample central moments are found as

At the end of all :math:`N` histories, the tally average
:math:`\overline{x}\ `\ and uncertainty in the tally average :math:`u`
are found in the same way as a simple tally. For the VOV calculation,
the third and fourth sample central moments are found as


 .. math::
   :label: Monaco-10

   m_{3} = \frac{S_{3}}{N} - \frac{3S_{1}S_{2}}{N^{2}} + \frac{2S_{1}^{3}}{N^{3}}

.. math::
  :label: Monaco-11

  m_{4} = \frac{S_{4}}{N} - \frac{4S_{1}S_{3}}{N^{2}} + \ \frac{6S_{1}^{2}S_{2}}{N^{3}} - \ \frac{3S_{1}^{4}}{N^{4}}


and then the VOV :cite:`pederson_confidence_1997` and figure-of-merit (FOM) are found using


 .. math::
   :label: Monaco-12

   \mathrm{\text{VOV}} = \frac{m_{4} - \ m_{2}^{2}}{Nm_{2}^{2}}

 .. math::
   :label: Monaco-13

   \mathrm{\text{FOM}} = \ \frac{1}{\left( \frac{u}{\overline{x}} \right)^{2} \ T}

where *T* is the calculation time (in minutes).

Extended tallies are used for the total neutron flux, total photon flux
and any responses for the Monaco tallies. Simple tallies are used for
each group’s flux and each group’s contribution to a response.

Detailed, group-wise results for each tally are saved to separate files
at the end of each batch of particles. Users can view these files (in
the SCALE temporary directory) as the Monaco simulation progresses.
Summaries of the extended tallies appear in the final Monaco output
file.

Statistical tests
^^^^^^^^^^^^^^^^^

Statistical tests are performed on the extended tallies at the end of
each batch. Results for each batch are stored in files and the results
for the final batch are shown in the main output tally summary. The six
tests are:

+-------------+-------------+-------------+-------------+------------------+
|             | **Quantity**| **Test**    | **Goal**    | **Within**       |
|             |             |             |             |                  |
+=============+=============+=============+=============+==================+
| 1.          | mean        | relative    | = 0.00      | ±0.10            |
|             |             | slope of    |             |                  |
|             |             | linear fit  |             |                  |
+-------------+-------------+-------------+-------------+------------------+
| 2.          | standard    | exponent of | = -0.50     | .. math::        |
|             | deviation   | power fit   |             |    R^{2} > 0.99  |
+-------------+-------------+-------------+-------------+------------------+
| 3.          | relative    | final value | < 0.05      |                  |
|             | uncertainty |             |             |                  |
+-------------+-------------+-------------+-------------+------------------+
| 4.          | relative    | exponent of | = -1.00     | .. math::        |
|             | VOV         | power fit   |             |  R^{2} > 0.95    |
+-------------+-------------+-------------+-------------+------------------+
| 5.          | relative    | final value | < 0.10      |                  |
|             | VOV         |             |             |                  |
+-------------+-------------+-------------+-------------+------------------+
| 6.          | figure-of-m | relative    | = 0.00      | ±0.10            |
|             | erit        | slope of    |             |                  |
|             |             | linear fit  |             |                  |
+-------------+-------------+-------------+-------------+------------------+


For the tests that are fit to a function with respect to batch (1, 2, 4,
and 6), only the last half of the simulation is used. The basis for
these tests is that in a well-behaved Monte Carlo, the mean should not
increase or decrease as a function of the number of histories
(:math:`N`), the standard deviation should decrease with
:math:`\frac{1}{\sqrt{N}}`, the variance of the variance should decrease
with :math:`\frac{1}{N}` and the figure-of-merit should neither

increase or decrease as a function of the number of histories
(proportional to time). For tests 2 and 4, the coefficient of
determination, :math:`R^{2}`, from a forced fit to a function with the
right exponent is used as the tally test.

Point detector tallies
^^^^^^^^^^^^^^^^^^^^^^

Point detectors are a form of variance reduction in computing the flux
or response at a specific point. At the source emission site and at
every interaction in the particle’s history, an estimate is made of the
probability of the particle striking the position of the point detector.
For each point detector, Monaco tallies the uncollided and total flux
for each energy group, the total for all neutron groups, and the total
for all photon groups. Any number of optional dose-like responses can be
calculated as well.

Multigroup
..........

After a source particle of group *g* is started, the distance *R*
between the source position and the detector position is calculated.
Along the line connecting the source and detector positions, the sum of
the distance *s\ j* through each region *j* multiplied by the total
cross section :math:`\Sigma_{j}^{g}`\ for that region is also
calculated. The contribution *c\ g* to the uncollided flux estimator is
then made to the tally for group *g*.

.. math::
  :label: Monaco-14

  c_{g} = \frac{1}{4\pi R^{2}}\mathrm{\exp}\left( - \sum_{j}^{}{s_{j}\Sigma_{j}^{g}} \right)

Continuous Energy
.................

After a source particle with energy *E* is started, the distance *R*
between the source position and the detector position is calculated. For
each bin :math:`g` of the tally energy structure, a specific energy
:math:`E_{g}` is sampled uniformly within the bin. Along the line
connecting the source and detector positions, the sum of the distance
*s\ j* through each region *j* multiplied by the total cross section
:math:`\Sigma_{j}\left( E_{g} \right)` for that region. The contribution
*c\ g* to the uncollided flux estimator is then made to the tally for
group *g*. total cross section :math:`\Sigma_{j}\left( E \right)` :


.. math::
  :label: Monaco-15

  c_{g} = \frac{1}{4\pi R^{2}}\mathrm{\exp}\left( - \sum_{j}^{}{s_{j}\Sigma_{j}\left( E \right)} \right)


Only source particles contribute to the uncollided flux tally. At each
interaction point during the life of the particle, similar contributions
are made to each of the tallies. For each group *g′* that the particle
could scatter into and reach the detector location, a contribution is
made that also includes the probability to scatter from the current
direction towards the detector and having the energy change from group
*g* to group *g′.*

This type of tally is costly, since ray-tracing through the geometry
from the current particle position to the detector location is required
many times over the particle history. Point detectors should be located
in regions made of void material, so that contributions from
interactions arbitrarily close to the point detector cannot overwhelm
the total estimated flux (as
:math:`\frac{1}{4\pi R^{2} \rightarrow \infty}`).

Care must be taken in using point detectors in deep penetration problems
to ensure that the entire phase space that could contribute has been
well sampled—so that the point detector is not underestimating the flux
by leaving out areas far from the source but close to the point detector
position. One way to check this is by examining how the tally average
and uncertainty change with each batch of particles used in the
simulation. Large fluctuations in either quantity could indicate that
the phase space is not being sampled well.

Region tallies
^^^^^^^^^^^^^^

Region tallies are used for calculating the flux and/or responses over
one of the regions listed in the SGGP geometry. Both the track-length
estimate of the flux and the collision density estimate of the flux are
calculated—and for each, the region tally contains simple tallies for
finding flux in each group, the total neutron flux, and the total photon
flux. For each of the optional response functions, the region tally also
contains simple tallies for each group and the total response.

For the track-length estimate of flux, each time a particle of energy
:math:`E` moves through the region of interest, a contribution of
:math:`l` (the length of the step in the region) is made to the history
score for the simple tally for flux for tally group \ *g*. The same
contribution is made for the history score for the simple tally for
total particle flux, neutron or photon, depending on the particle type.

If any optional response functions were requested with the tally, then
the contribution of :math:`\text{lf}\left( E \right)`\ is made for the
response group, where :math:`f\left( E \right)` is the response function
value for energy :math:`E`. The history score for the total response
function is also incremented using :math:`\text{lf}\left( E \right)`.

At the end of all of the histories, the averages and uncertainties of
all of the simple tallies for fluxes are found for every group and each
total. These results then represent the average track-length over the
region. To determine flux, these results are divided by the volume of
the region. If the volume :math:`V` of the region was not given in the
geometry input nor calculated by Monaco, then the tally results will be
just the average track lengths and their uncertainties. A reminder
message is written to the tally detail file if the volume of the region
was not set.

For the collision density estimate of the flux, each time a particle of
energy :math:`E` has a collision in the region of interest, a
contribution of :math:`\frac{1}{\Sigma}` (the reciprocal of the total
macroscopic cross section) is made to the history scores for the simple
tally for flux for tally energy group *g* and for the total particle
flux. At the end of the simulation, the averages and uncertainties of
all of the simple tallies for every group flux and total flux are found
and then divided by the region volume, if available.

Similar to the point detector tallies, region tallies produce a file
listing the tally average and uncertainty at the end of each batch of
source particles (a \*.chart file). This file can be plotted using the
simple 2-D plotter (ChartPlot) to observe the tally convergence
behavior.

Mesh tallies
^^^^^^^^^^^^

For a D Cartesian mesh or a cylindrical mesh (independent of the SGGP
geometry), Monaco can calculate the track-length estimate of the flux.
Since the number of cells (voxels) in a mesh can become quite large, the
mesh tallies are not updated at the end of each history but are instead
updated at the end of each batch of particles. This prevents the mesh
tally accumulation from taking too much time but means that the estimate
of the statistical uncertainty is slightly low.

Like the other tallies, mesh tallies can calculate optional response
functions.

Since a mesh tally consists of many actual tallies, the statistical
tests are a bit more complex than for the region and point detector
tallies. Several statistical quantities and tests are used in Monaco
similar to those in several recent studies :cite:`kiedrowski_statistical_2011,kiedrowski_evaluating_2011` which
look at a distribution of relative variances over the mesh tally. In
Monaco, the basis of the statistical tests center on the distribution of
relative uncertainties and its mean, :math:`\overline{r}`, of the voxels
(:math:`V`) with score.


.. math::
  :label: Monaco-16

  \overline{r} = \frac{1}{V}\sum_{}^{}R_{i}


where :math:`R_{i}` is the relative uncertainty of the flux or dose in
voxel :math:`i`. If every voxel has been sampled well and its relative
uncertainty :math:`R_{i} \propto \frac{1}{\sqrt{N}}`, then the mean
relative uncertainty of the voxels should also behave as
:math:`\frac{1}{\sqrt{N}}`. The variance of the mean relative
uncertainty can be calculated and a figure of merit (FOM) for the mesh
tally can be constructed using


.. math::
  :label: Monaco-17

  FOM = \frac{1}{{\overline{r}}^{2}T}


with the time\ :math:`\text{\ T}` in minutes. The four tests measure
over the simulation: 1) if :math:`\zeta`, the fraction of voxels with
non-zero score, is constant; 2) if the mean relative uncertainty is
decreasing as :math:`\frac{1}{\sqrt{N}}` (as measured by the coefficient
of determination, :math:`R^{2}`, of a fit to a curve with power of
-0.5); 3) if the variance of the mean relative uncertainty is decreasing
with :math:`\frac{1}{N}`; and 4) if the FOM is constant.

+----+------------------------------------------------------------+------------------------------+----------+---------------------------+
|    | Quantity                                                   | Test                         | Goal     | Within                    |
+====+============================================================+==============================+==========+===========================+
| 1. | :math:`\zeta`, fraction with score                         | relative slope of linear fit | = 0.00   | ±0.10                     |
+----+------------------------------------------------------------+------------------------------+----------+---------------------------+
| 2. | :math:`\overline{r}`, mean relative uncertainty            | exponent of power fit        | = -0.50  | .. math:: R^{2} > 0.99    |
+----+------------------------------------------------------------+------------------------------+----------+---------------------------+
| 3. | variance of :math:`\overline{r}`                           | exponent of power fit        | = -1.00  | .. math:: R^{2} > 0.95    |
+----+------------------------------------------------------------+------------------------------+----------+---------------------------+
| 4. | figure-of-merit                                            | exponent of power fit        | = 0.00   | ±0.10                     |
+----+------------------------------------------------------------+------------------------------+----------+---------------------------+

For non-uniform meshes (especially cylindrical), these tests may not be
the best measure of performance since different size voxels will have a
wider variety of relative uncertainties. The user is also cautioned that
if there are individual voxels within the mesh tally that have relative
uncertainties that are not decreasing as :math:`\frac{1}{\sqrt{N}}`,
then the mesh tally statistical tests will not be meaningful. It is
ultimately up to the user to decide if the mesh tally is performing well
(is the goal of the mesh tally just to calculate dose, not flux?; are
all spatial areas of the mesh tally equally important?; are all
magnitudes of the flux or response values equally important?; etc.)

Mesh tallies can be viewed with the Mesh File Viewer, a Java utility
that can be run from GeeWiz (on PC systems) or can be run separately (on
any system). The Mesh File Viewer will show the flux for each group, the
total flux for each type of particle and the optional responses.
Uncertainties and relative uncertainties can also be shown for mesh
tallies using the Mesh File Viewer. For more information on the Mesh
File Viewer, see its on-line documentation.

Continuous Energy Transport
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using multigroup data in Monte Carlo transport calculations is generally
sufficient for most problems (both shielding and criticality). Many of
the reaction cross sections vary slowly with energy, so energy “groups”
can be made with one set of properties for the group. Multigroup
treatments can further simplify radiation transport by combining the
different types of reactions that can occur into a simple scattering
matrix – particles then have certain probabilities to scatter from their
current energy group to another energy group. If the user is not
interested in knowing which specific type of interaction happened at
each collision, this simplification can increase calculation efficiency.

One major drawback of the multigroup approach is in representing discrete gammas,
such as the decay radiation from common isotopic sources.  Consider a simple shielding
simulation using cobalt-60.  This isotope gives off two high-energy gamma rays when it decays
(1173230 eV with intensity 99.85% and 1332490 eV with intensity 99.9826%).  In the SCALE multigroup
calculations, a cobalt-60 source spectrum is represented by a broad pdf, controlled by the group structure.
This is shown in :numref:`fig8-1`. for the fine 47-group structure and the broad 19-group structure.

.. _fig8-1:

.. figure:: figs/Monaco/Picture1.png
  :width: 400
  :align: center

  The multigroup representation of a cobalt-60 source.

Note that in both group structures, 1.33 MeV is a group boundary, so the
1332490 eV line is represented by group that covers higher energies. The
cross section for that group is lower than the cross section for the
specific line, so multigroup transport calculations will tend to
overestimate the number of photons penetrating a shield, which will
overestimate dose rates.

Using CE and the two multigroup libraries, the total cross sections for the cobalt lines are listed in :numref:`tab8-2`.
:numref:`fig8-2`. shows the total cross section of photons in tungsten, in both CE and the two SCALE multigroup structures.
On the whole, the multigroup data represents the CE data well.  :numref:`fig8-3`. shows the same cross section information
near the two cobalt lines, which shows how the multigroup cross sections average over quite large energy ranges.

.. _tab8-2:
.. table:: Total macroscopic cross section in tungsten (/cm).
  :align: center

  +----------+------------+------------+
  |          | 1173230 eV | 1332490 eV |
  +==========+============+============+
  | SCALE CE | 1.03353    | 0.94864    |
  +----------+------------+------------+
  | SCALE 47 | 1.09066    | 0.92743    |
  +----------+------------+------------+
  | SCALE 19 | 1.05167    | 0.89289    |
  +----------+------------+------------+

The small differences in cross section can make large differences in the
transport. Consider just 5 cm of tungsten. Using the cross sections in
:numref:`tab8-2`, the attenuation (:math:`e^{- \mu x}`) of either line can
vary by 30%.

In addition to source representation problems, multigroup transport is
not adequate for applications where line spectra are measured. Because
of the group structure, tally results will be averaged out within a
group. With the fixed boundaries, specific lines in the tallies will not
be able to be seen. For examples, in the 19-group library, there is no
group around the 511 keV annihilation gammas – they are averaged in with
other photons from 400 to 600 keV. No multigroup structure could contain
thin groups around every line of interest.

.. _fig8-2:
.. figure:: figs/Monaco/8-2.png
  :width: 500
  :align: center

  Photon total cross section in tungsten.  The energies of the cobalt-60 are displayed as lines at 1173230 and 1332490 eV.

.. _fig8-3:
.. figure:: figs/Monaco/8-3.png
  :width: 500
  :align: center

  Photon total cross section in tungsten, near the cobalt lines.  The energies of the cobalt-60 are displayed as lines at 1173230 and 1332490 eV.

A sample problem involving a cobalt source and a slab of tungsten will
compare the use of continuous-energy transport to multigroup transport,
to demonstrate the large difference in results for single-line sources.
For distributions, differences between multigroup and continuous-energy
may not be very significant.

Monaco Input Files
------------------

The input file for Monaco consists of two lines of text (“=monaco”
command line and one for the problem title) and then several blocks,
with each block starting with “read xxxx” and ending with “end xxxx”.
There are three blocks that are required and seven blocks that are
optional. The cross section and geometry blocks must be listed first and
in the specified order. Other blocks may be listed in any order.

Blocks (must be in this order):

-  Cross Sections – (required) lists the cross-section file and the mixing table information

-  Geometry – (required) SCALE general geometry description

-  Array – optional addition to the above geometry description

-  Volume – optional calculation or listing of region volumes

-  Plot – create 2D slices of the SGGP geometry

Other Blocks (any order, following the blocks listed above):

-  Definitions – defines locations, response functions, grid geometries, cylindrical mesh geometries, energy bin boundaries, time bin boundaries and various distributions used by other blocks

-  Source – (required) description of multiple sources; with the spatial, energy, and directional distributions and particle type
      for each

-  Tallies – description of what to calculate: point detector tallies,
      region tallies, or mesh tallies

-  Parameters – how to perform the simulation (random number seed, how
      many histories, etc.)

-  Biasing – data for reducing the variance of the simulation

The physical model blocks (Geometry, Array, Volume and Plot) follow the
standard SCALE format. See the other SCALE references as noted in the
following sections for details.

For the other six blocks, scalar variables are set by “keyword=value”,
fixed length arrays are set with “keyword value\ :sub:`1` ...
value\ :sub:`N`\ ”, variable length arrays are set with “keyword
value\ :sub:`1` ... value\ :sub:`N` end”, and some text and filenames
are read in as quoted strings. Single keywords to set options are also
used in some instances. The indention, comment lines, and upper/lower
case shown in this document are not required—they are used in the
examples only for clarity. Except for strings in quotes (like
filenames), SCALE is not case sensitive.

After all of the blocks are listed, a single line with “end data” should
be listed. A final “end” should also be listed, to signify the end of
all Monaco input. See :numref:`tab8-3` for an overview of the Monaco input
file structure.

Cross sections block
~~~~~~~~~~~~~~~~~~~~

Monaco does its own mixing, so it needs a mixing table. For each element
of each mixture, an identifier and a number density must be supplied.
These can be found in the output of whatever sequence was used to make
the cross-section file, such as CSAS-MG. Two coupled neutron/photon
multigroup libraries were created specifically for shielding problems
from ENDF/B-VII.0 data—the v7-200n47g fine-group and the v7-27n19g
coarse-group libraries. CE libraries made from ENDF/BVII.0 are also
available in SCALE.

.. _tab8-3:
.. list-table:: Overall input format for Monaco
  :align: center

  * - ``Input File``
    - ``Comment``
  * - .. code:: scale

        =monaco
        Some title for this problem
        read crossSections
           ...
        end crossSections
        read geometry
           ...
        end geometry
        read array
           ...
        end array
        read volume
           ...
        end volume
        read plot
           ...
        end plot
        read definitions
           ...
        end definitions
        read sources
           ...
        end sources
        read tallies
           ...
        end tallies
        read parameters
           ...
        end parameters
        read biasing
           ...
        end biasing
        end data
        end
    - .. code:: scale

        name of sequence
        title
        List of isotopes/mixtures
            [required block]

        SCALE SGGP geometry
            [required block]

        SCALE SGGP arrays
            [optional block]

        SCALE SGGP volume calc
            [optional block]

        SGGP Plots
            [optional block]

        Definitions
            [possibly required]

        Sources definition
            [required block]

        Tally specifications
            [optional block]

        Monte Carlo parameters
            [optional block]

        Biasing information
            [optional block]

        end of all blocks
        end of Monaco input

For example, if CSAS-MG was used to produce an AMPX file using the
following input,

.. code:: scale

  =csas-mg
  Demonstration problem, three mixtures
  v7-200n47g
  read composition
      uo2   1 0.2 293.0 92234 0.0055 92235 3.5 92238 96.4945 end
      ss304 2 1.0 293.0 end
      h2o   4 1.0 293.0 end
  end composition
  end

in addition to creating an AMPX file, the output would include a tables similar to

.. code:: scale

  m i x i n g   t a b l e    (THREAD = 00 )
  entry   mixture   isotope   number density   new identifier   explicit temperature
      1       1        92234     2.73451E-07             92234             293.0
      2       1        92235     1.73272E-04             92235             293.0
      3       1        92238     4.71674E-03             92238             293.0
      4       1         8016     9.78057E-03              8016             293.0

  m i x i n g   t a b l e    (THREAD = 00 )
  entry   mixture   isotope   number density   new identifier   explicit temperature
      1       2         6000     3.18488E-04              6000             293.0
      2       2        14028     1.57010E-03             14028             293.0
      3       2        14029     7.97625E-05             14029             293.0
      4       2        14030     5.26416E-05             14030             293.0
      5       2        15031     6.94688E-05             15031             293.0
      6       2        24050     7.59178E-04             24050             293.0
      7       2        24052     1.46400E-02             24052             293.0
      8       2        24053     1.66006E-03             24053             293.0
      9       2        24054     4.13224E-04             24054             293.0
     10       2        25055     1.74072E-03             25055             293.0
     11       2        26054     3.42190E-03             26054             293.0
     12       2        26056     5.37166E-02             26056             293.0
     13       2        26057     1.24055E-03             26057             293.0
     14       2        26058     1.65094E-04             26058             293.0
     15       2        28058     5.26873E-03             28058             293.0
     16       2        28060     2.02951E-03             28060             293.0
     17       2        28061     8.82212E-05             28061             293.0
     18       2        28062     2.81288E-04             28062             293.0
     19       2        28064     7.16357E-05             28064             293.0

   m i x i n g   t a b l e    (THREAD = 00 )
   entry   mixture   isotope   number density   new identifier   explicit temperature
      1       4         1001     6.67531E-02              1001             293.0
      2       4         8016     3.33765E-02              8016             293.0

which can be used to construct the Monaco cross-section block mixing table.

.. highlight:: scale

::

  read crossSections
      ampxFileUnit=4
      mixture 1
          element    92234 2.73451E-07
          element    92235 1.73272E-04
          element    92238 4.71674E-03
          element     8016 9.78057E-03
      end mixture
      mixture 2
          element     6000 3.18488E-04
          element    14028 1.57010E-03
          element    14029 7.97625E-05
          element    14030 5.26416E-05
          element    15031 6.94688E-05
          element    24050 7.59178E-04
          element    24052 1.46400E-02
          element    24053 1.66006E-03
          element    24054 4.13224E-04
          element    25055 1.74072E-03
          element    26054 3.42190E-03
          element    26056 5.37166E-02
          element    26057 1.24055E-03
          element    26058 1.65094E-04
          element    28058 5.26873E-03
          element    28060 2.02951E-03
          element    28061 8.82212E-05
          element    28062 2.81288E-04
          element    28064 7.16357E-05
      end mixture
      mixture 4
          element     1001 6.67531E-02
          element     8016 3.33765E-02
      end mixture
  end crossSections

For a CE calculation, instead of the keyword “ampxFileUnit=” (which
refers to a given AMPX library), the keyword “ceLibrary=” should be used
with a CE library name, enclosed in quotes. Also for CE, a default
temperature can be set before any mixtures are defined using the
“ceTempDefault=” temperature (in Kelvins). With each mixture, a specific
temperature can be set using “temperature.”

Other keywords that can be used in the cross-section block for
multigroup problems include flags to turn on printing of different
aspects of the cross-section mixing process (“printTotals”,
“printScatters”, “printAngleProb”, “printFissionChi”, “printExtra”, and
“printLegendre”). The keyword “fullyCoupled” can be used to specify all
groups to be treated as primary groups. These keywords do not work in CE
problems since the point wise data contain an enormous number of points.

Users are encouraged to use Monaco by running the MAVRIC sequence, which
creates the cross-section mixing table automatically, for both
multigroup and CE calculations.

Geometry block
~~~~~~~~~~~~~~

The geometry input uses the standard SGGP, similar to KENO-VI. Input
instructions can be found in *Geometry Data* in the KENO-VI chapter of
the SCALE manual.

Shielding calculations (Monaco, MAVRIC, SAS4) differ from their
criticality cousins (KENO V.a, KENO-VI) in a very special way—sources
and detectors can be located outside of the materials where the
transport takes place. To accommodate this fact in Monaco and MAVRIC,
make sure that a void region (a media record using mixture 0) surrounds
the source area and any point detectors, if they are not located in a
region of the actual geometry.

For example, if the objective is to calculate the effectiveness of a
simple slab shield, the model geometry would consist of just one slab of
material. The source would be on one side of the slab, and a detector
would be on the other side of the slab. In Monaco (and the MAVRIC
sequence), the input should list at least two regions: (1) the slab
itself and (2) a void region outside of the slab containing both the
source and detector positions.

Monaco tracks particles through the SGGP geometry as well as other
geometries used for mesh tallies or mesh importance maps. Because Monaco
must track through all of these geometries at the same time, users
should not use the reflective boundary capability in the SGGP geometry.

The graphical user interfaces GeeWiz and Keno3D can be used on Windows
platforms to develop and view the geometry.

Array, volume, and plot blocks
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Geometry array input uses the standard SGGP, similar to KENO-VI. Input
instructions can be found in KENO-VI chapter on *Array Data* of the
SCALE manual.

Volumes of various geometry regions are used to calculate fluxes for
those regions. Volumes can be input as part of the geometry input block
above, or calculated by the SGGP using one of two different methods. See
KENO-VI chapter on *Volume Data* for instructions.

The “read plot” block allows users to create a 2-D character or color
plots of slices through a specified portion of the 3-D geometrical
representation of the problem. These images can be saved as \*.png
files. For more information, see the KENO-VI chapter on *Plot Data*.

Definitions block
~~~~~~~~~~~~~~~~~

The definitions block defines different types of data (locations,
detector response functions, grid geometries, cylindrical geometries,
distributions, energy bin boundaries and time bin boundaries) that are
used by some of the other blocks in Monaco. Individual data can be
listed in any order. Identification numbers must be positive integers
and unique within that type of data. Each type of data begins with a
keyword and ends with an “end” and that same keyword. All of the
different data types can have an optional title using the keyword
“title=”.

::

  read definitions
      location 43

      end location
      response 45

      end response
      distribution 1

      end distribution
      response 12

      end response
  end definitions

Locations
^^^^^^^^^

Locations (“location”) require an identification number and the physical
position in global coordinates using the “position” keyword (a fixed
length array). A position is specified by listing its *x*, *y*, and
*z* coordinates.

::

    location  1
       title="Radial detector - close to surface"
        position 162.0 0.0 0.0
    end location
    location  2  position 0.0 0.0 295.6   end location
    location  3
        title=”Corner detector”
        position 162.0 0.0 295.6
    end location
    location 105 position   0.0 0.0 385.6   end location
    location 106 position 252.0 0.0 385.6   end location

Response functions
^^^^^^^^^^^^^^^^^^

Response functions (“response”) require an identification number
and information on how to build an energy dependent response function.
There are three basic types of responses: 1) the general user-defined
response, 2) a response based on cross-section data, and 3) a response
based on a specific flux-to-dose conversion factor. For multigroup
calculations, a fourth type of a response simply listing multigroup
values is also available. Responses must be defined as either a neutron
response or a photon response.

  Type 1.
    A general user-defined response function can be either a binned
    histogram function (*n*\ +1 energies and *n* values) or a set of
    value/function pairs that will be linearly interpolated (*n*\ +1
    energies and *n*\ +1 values). The energies (in eV) are set using the
    “bounds … end” keyword. The response values are entered with the “values
    … end” keyword. The energies can be entered from low energy to high
    energy order or the traditional high energy to low energy order but must
    be monotonic. The values array of the response is interpreted to
    correspond to the order of the bounds array. These two examples

    ::

      response 11
          title="user-defined response, histogram"
          neutron
          bounds 1e7   8e6   6e6   4e6   2e6   1e5 end
          values    1.0   0.8   0.6   0.4   0.2    end
      end response
      response 12
          title="user-defined response, value/function pairs"
          photon
          bounds  1e5 2e6 4e6 6e6 8e6 1e7 end
          values 0.01 0.2 0.4 0.6 0.8 1.0 end
      end response

    are shown in :numref:`fig8-4` and :numref:`fig8-5`.

    .. _fig8-4:
    .. figure:: figs/Monaco/8-4.png
      :align: center
      :width: 400

      Histogram-type response.

    .. _fig8-5:
    .. figure:: figs/Monaco/8-5.png
      :align: center
      :width: 400

      Value/function pair response.

  Type 2.
    Data from the cross-section library can also be used to define a
    response, for example in finding reaction rates. For the cross section
    (with units of barns) for a single isotope, the user specifies a
    material/ZAID/MT combination. The keyword “macro” can be used to
    multiply the cross section by the atom density of the ZAID in the
    material (which converts the units of the response from barns to /cm).
    Users can also specify just the material and MT numbers, to produce the
    macroscopic cross section of reaction MT for the entire material (with
    units of /cm). A partial list of common MT numbers is shown in Table
    F23.3.2 (the full list is in XSECLIB M04, Appendix B). To match some
    other sequences in SCALE, users can also use text strings to specify the
    ZAID and MT by using keywords “nuclide=” (for example, nuclide=U-235)
    and “reaction=” (for example reaction=fission). If the user requested a
    microscopic cross section response for a reaction in a CE problem, the
    response will be generated for the nuclide from the AMPX CE libraries
    even if the nuclide itself is not included in any of the material
    definitions in the problem. Available reaction lists depend on the
    nuclide and the list will be printed as a warning message in the output
    if a non-existing reaction is requested.

    ::

      read composition
          uo2 7 1.0 293.0 end
      end composition

      read definitions
          response 41
              title=”get the microscopic (b) for 235”
              neutron
              material=7 ZAID=92235 MT=18
          end response
          response 43
              title=”get the macroscopic (/cm) for 235”
              neutron
              material=7 ZAID=92235 MT=18
              macro
          end response
          response 45
              title=”get the macroscopic (/cm) for UO_2 (234, 235, 238)”
              neutron
              material=7 MT=18
          end response
      end definitions

    For the examples above, response 41 is shown in :numref:`fig8-6`. and
    :numref:`fig8-7`. for both MULTIGROUP and CE.

    .. list-table:: Common MT (reaction) numbers for responses
      :name: tab8-4
      :align: center

      * - .. image:: figs/Monaco/tab8-4.png

    .. _fig8-6:
    .. figure:: figs/Monaco/8-6.png
      :align: center
      :width: 400

      Multigroup :sup:`235`\ U total fission cross section.

    .. _fig8-7:
    .. figure:: figs/Monaco/8-7.png
      :align: center
      :width: 400

      CE :sup:`235`\ U total fission cross section.

Type 3.
  Flux-to-dose conversion factors are a little different in
  multigroup and continuous-energy implementations. The AMPX multigroup
  shielding libraries contain neutron and photon dose responses from
  several sources. These have been processed by the AMPX system (the
  jergens module). To form the multigroup values for the libraries, the
  original data was extrapolated to cover the entire energy range of the
  shielding libraries and was then collapsed into the group structures
  using a weighting spectrum. These dose responses can be accessed through
  Monaco/MAVRIC by defining a response object that uses the keyword
  “specialDose=” and then providing the MT number of the particular
  response. The dose responses available in the shielding libraries in are
  shown in :numref:`tab8-5`. Note that the coupled responses in SCALE 6.1 are
  no longer used by Monaco, since responses are now defined to be either a
  neutron response or a photon response. When using the “specialDose=”
  keyword, the “neutron” or “photon” designation is ignored, since the
  particle type is inherent with the MT number.

  ::

    read definitions
        response 1
            specialDose=9031
        end response
    end definitions

  .. list-table:: Flux-to-Dose conversion factor MT numbers
    :name: tab8-5
    :align: center

    * - .. image:: figs/Monaco/tab8-5.png

  The standard flux-to-dose conversion factors have not been made part of
  the continuous-energy libraries. Routines have been added to the Monaco
  code base to generate data points to allow users to define responses
  based on the original references. Note that the responses in these
  references were defined over different energy ranges, as shown in
  :numref:`tab8-6`.

  .. list-table:: Energy ranges of the original Flux-to-Dose responses
    :align: center
    :name: tab8-6
    :width: 70 %

    * - .. image:: figs/Monaco/tab8-6.png

  The keyword “doseData=” can be used to create a response using the
  original, point-wise data (except for Claiborne-Trubey where the
  original data is a histogram). Data points are also extrapolated to
  cover the energy range of 10\ :sup:`-5` to 2×10\ :sup:`7` eV for
  neutrons and up to 20 MeV for photons. (The optional keyword
  “noExtrapolation” can be used to get just the original data without the
  extrapolations.) The final response is formed by interpolating (lin-lin)
  between these points. For multigroup problems, these keywords will
  collapse the original data (with or without extrapolation) into a
  multigroup structure but without the weighting function used to create
  the dose factors in the multigroup libraries. This will not match the
  multigroup responses in the those libraries.

  ::

    read definitions
        response 1
            doseData=9031
        end response
        response 1
            doseData=9031  noExtrapolation
        end response
    end definitions

  As an example of the various forms of a flux-to-dose conversion factor,
  the ANSI 1991 values (MT=9031 and 9505) are shown in
  :numref:`fig8-8` through :numref:`fig8-11`.

  .. _fig8-8:
  .. figure:: figs/Monaco/8-8.png
    :align: center
    :width: 600

    ANSI 1991 neutron CE (left is log-log, right is linear-linear)

  .. _fig8-9:
  .. figure:: figs/Monaco/8-9.png
    :align: center
    :width: 600

    ANSI 1991 neutron MULTIGROUP (left is log-log, right is linear-linear)

  .. _fig8-10:
  .. figure:: figs/Monaco/8-10.png
    :align: center
    :width: 600

    ANSI 1991 photon CE (left is log-log, right is linear-linear)

  .. _fig8-11:
  .. figure:: figs/Monaco/8-11.png
    :align: center
    :width: 600

    ANSI 1991 photon MULTIGROUP (left is log-log, right is linear-linear)

  The use of the “specialDose=” and “doseData=” keywords is summarized in
  :numref:`tab8-7`. Users should understand that the only way to get the ‘true’
  response described in the original references is to use the “doseData=”
  and “noExtrapolation” keywords. The traditional approach in SCALE has
  been to extrapolate the original data over the entire energy range of
  the problem, yielding higher dose rates than the ‘true’ response would.

  .. list-table:: Use of the “specialDose=” and “doseData=” keywords.
    :align: center
    :name: tab8-7

    * - .. image:: figs/Monaco/tab8-7.png

Type 4.
  For multigroup calculations, since the energy structure is
  already known, a response can be defined by listing just the values for
  each group using the keyword “values … end”. The array length of this
  type of response should match the number of energy groups for that
  particle type in the cross-section library. Values should be entered in
  the standard multigroup order – from high energy to low energy. The
  shortcut keyword “unity” places a value of 1.0 as the response for each
  group.

  ::

    response 19
        title="Total Photon Dose at Each Detector Point Location (ANSI 9504)"
        photon
        values                         1.16200E-05  8.74457E-06  7.45967E-06
             6.35058E-06  5.39949E-06  4.60165E-06  3.95227E-06  3.45885E-06
             3.01309E-06  2.62001E-06  2.19445E-06  1.82696E-06  1.51490E-06
             1.15954E-06  8.70450E-07  6.21874E-07  3.70808E-07  2.68778E-07
             5.93272E-07  end
    end response
    response 4
         title=”total photon flux above 1 MeV, photons/(/cm2/sec)”
         photon
         values 11r1.0  8r0.0 end
    end response
    response 99
         title=”put a 1 in every group”
         neutron
         unity
    end response

  The different response types all share some optional keywords. The
  keyword “makeChart” can be used to produce a \*.chart file (called
  ‘\ *outputName*.resp\ *id*.chart’) so that the response can be plotted
  with the ChartPlot 2D plotter. To create files for every response, use
  the keyword “makeCharts” inside the definitions block but outside any
  particular response definition. The keyword “multiplier=” can be used
  with any type of response, which is useful for things such as units
  conversions. Multiple uses of the “multiplier=” keyword within one
  response definition will apply the product of all multipliers to that
  response. Using the keyword “multiplier=” in the definitions block but
  outside any particular response will apply that multiplier to all
  responses. Keywords “eHigh=” and “eLow=” can be used to only keep the
  response values in a range between eHigh and eLow (both in eV). The
  keyword “lessOutput” can be used to suppress response data echoing in
  the output file and minimize output file size particularly for CE
  responses that can have fine point-wise data. It will cause to print
  only the first five and the last five points of the data if the number
  of bins is greater than twenty for binned histogram and value/function
  pairs type of responses.

  The original flux-to-dose conversion factor references that were
  incorporated into Monaco are:

   - ANSI/ANS-6.1.1-1977 (N666) “American National Standard Neutron and
     Gamma-Ray Flux-to-Dose-Rate Factors,” Prepared by the American Nuclear
     Society Standards Committee Working Group ANS-6.1.1, Published by the
     American Nuclear Society, 555 North Kensington Avenue LaGrange Park,
     Illinois 60525, Approved March 17, 1977 by the American National
     Standards Institute, Inc.

   - ANSI/ANS·6.1.1-1991, “American National Standard for Neutron and
     Gamma-Ray Fluence-to-Dose Factors,” Prepared by the American Nuclear
     Society Standards Committee Working Group ANS-6.1.1, Published by the
     American Nuclear Society, 555 North Kensington Avenue LaGrange Park,
     Illinois 60525 USA, Approved August 26, 1991 by the American National
     Standards Institute, Inc.

   - H. C. Claiborne and D. K. Trubey, “Dose Rates in a Slab Phantom from
     Monoenergetic Gamma Rays,” *Nuclear Applications & Technology*, Vol. 8,
     May 1970.

   - B. J. Henderson, “Conversion of Neutron or Gamma Ray Flux to Absorbed
     Dose Rate,” ORNL Report No. XDC-59-8-179, August 14, 1959.

   - International Commission of Radiation Units and Measurements, *ICRU
     Report 44: Tissue Substitutes in Radiation Dosimetry and Measurement*,
     Bethesda, MD, 1989.

   - International Commission of Radiation Units and Measurements, *ICRU
     Report 57: Conversion Coefficients for use in Radiological Protection
     Against External Radiation*, Bethesda, MD, August 1, 1998.

Grid geometries
^^^^^^^^^^^^^^^

Grid geometries (“gridGeometry”) require an identification number and
then a description of a 3‑D rectangular mesh by specifying the bounding
planes of the cells in each of the *x*, *y*, and *z* dimensions. The
keyword “xplanes … end” can be used to list plane values (in any order).
The keyword “xLinear *n* *a* *b*\ ” can be used to specify *n* cells
between *a* and *b*. The keywords “xplanes” and “xLinear” can be used
together and multiple times – they will simply add planes to any already
defined for that dimension. Any duplicate planes will be removed.
Similar keywords are used for the *y*- and *z*-dimensions.

::

    gridGeometry 3
        title="Boring uniform grid"
        xLinear 10 -100 100
        yLinear 10 -100 100
        zLinear 10 -100 100
    end gridGeometry
    gridGeometry 2
        xplanes -100.0 -90.0 -99.0 -95.0 end
        xLinear  9 -90.0  0.0
        xLinear 18   0.0 90.0
        xplanes 95.0 100.0 99.0  end
        yLinear 20  100.0 -100.0
        zLinear 40  100.0 -100.0
    end gridGeometry

When using multiple instances of the keyword \*Linear and \*planes for a
given dimension, duplicates should be removed from the final list. In
some cases, double precision math will leave two planes that are nearly
identical but not removed (for example: 6.0 and 5.9999999). To prevent
this, a default tolerance is set to remove planes that are within
10\ :sup:`-6` cm of each other. The user is free to change this by using
the keyword “tolerance=” and specifying something else. Note that the
tolerance can be reset to a different value in between each use of
\*Linear or \*planes.

The keyword “make3dmap” for a particular grid geometry definition will
create a file called ‘\ *outputName*.grid\ *id*.3dmap’ which can be
visualized using the Java Mesh File Viewer. Using the keyword
“make3dmaps” in the definitions block but outside any particular
gridGeometry definition will create a geometry file for each
gridGeometry defined.

Cylindrical mesh geometries
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Cylindrical geometries (“cylGeometry”) require an identification number
and then a description of a 3‑D cylindrical mesh by specifying the
bounding planes of the cells in each of the *r*, *θ*, and
*z* dimensions. The keywords “radii … end”, “thetas … end”, and “zplanes
… end” can be used to list the plane values in any order. The keywords
“radiusLinear *n* *a* *b*\ ”, “thetaLinear *n* *a* *b*\ ”, and “zLinear
*n* *a* *b*\ ” can be used to specify *n* cells between *a* and *b*.
Note that the keywords “thetas” and “thetaLinear” expect values between
0 and 2π. For entering values between 0 and 360°, use the keywords
“degrees” and “degreeLinear” instead. The keywords for each dimension
can be used together and multiple times – they will simply add planes to
any already defined for that dimension. Any duplicate planes will be
removed.

Cylindrical meshes are oriented along the positive z-axis by default. To
change this, the user can specify the axis of the cylinder using the
keyword “zaxis *u v w*\ ” and specify the perpendicular direction where
*θ* =0 using “xaxis *u v w*\ ”. To change the base position of the
cylinder, use the keyword “position *x y z*\ ”. Some examples of
cylindrical mesh geometries include:

::

    cylGeometry 12
        radiusLinear 20 100.0 168.0
        radiusLinear 10 168.0 368.0
        degreeLinear 12 0 360
        zLinear 25 255.2 -255.2
        zPlanes  -45.0 -40. -35.0 end
    end cylGeometry
    cylGeometry 13
        title="degenerate: only one angular bin"
        radiusLinear 10 168.0 368.0
        thetaLinear  1 0.0 6.2831853
        zLinear 25 255.2 -255.2
    end cylGeometry
    cylGeometry 14
        title="degenerate: emulate surface tally over partial angle range"
        radiusLinear 1 367.5 368.5
        degreeLinear 1 45 135
        zLinear 25 255.2 -255.2
        zaxis 0 0 1
        xaxis 0 -1 0
     end cylGeometry

Similar to the grid geometries, the user can use the keyword
“tolerance=” to specify how close duplicate planes can be when being
considered for removal. The keyword “makeCylMap” for a particular
cylindrical geometry definition will create a file called
‘\ *outputName*.cyl\ *id*.3dmap’ which can be visualized using the Java
Mesh File Viewer. Using the keyword “makeCylMaps” in the definitions
block but outside any particular gridGeometry definition will create a
geometry file for each gridGeometry defined. The Mesh File Viewer is
written for rectilinear geometries and will not display circles. The
only view that works in the Mesh File Viewer for cylindrical meshes is
the *x*-*z* view, which will correctly show an *r*-*z* slice. The slider
(marked “\ *y*\ ”) will control which *θ* value to display (from 0 to
2π).

Cylindrical meshes can only be used for tallies. They cannot be used for
making mesh sources or for any importance calculations in MAVRIC.

Distributions
^^^^^^^^^^^^^

Distributions (“distribution”) require an identification number and
several other keywords depending on the type of distribution. For a
binned histogram distribution over *n* intervals, the keyword “abscissa
… end” is used to list the :math:`n + 1` bin boundaries and the keyword
“truePDF … end” is used to list the :math:`n` values of the pdf
integrated over those bins. For a pdf defined using a series of
evaluated points over :math:`n` intervals, use the keywords “abscissa …
end” and “truePDF … end” listing the :math:`n + 1` values for each. The
“truePDF” values should be the value of the pdf evaluated at the
corresponding point in the abscissa array. The abscissa array should
either be in increasing order or decreasing order – monotonic either way
– with the truePDF array ordered accordingly.

For either the binned histogram or the value/function point pairs
distributions, biasing can also be specified for a given distribution
using the “biasedPDF … end” keyword, the “weight … end” keyword, or the
“importance ... end” keyword, with a length that matches the truePDF
array. Weights specify the suggested sampling weights for particles and
importances specify the suggested importance. For biasing, the user only
needs to specify just one of “biasedPDF”, “weight” or “importance”. The
other arrays will be computed by Monaco.

For discrete distributions (such as gamma line sources), use the keyword
“discrete … end” to list the discrete abscissa values and use the
keyword “truePDF … end” to list the probabilities. The “biasedPDF …
end”, “trueCDF … end”, and “biasedCDF … end” keywords can also be used.
Each array should have the same length – the number of discrete lines.

To visualize a distribution, add the keyword “runSampleTest” and a
\*.chart file will be produced showing the true pdf, the pdf used for
sampling (the biased pdf) and the results of a sampling test using
10\ :sup:`6` samples. The file will be named using the output name of
the SCALE job and the distribution identification number
‘\ *outputName*.dist\ *id*.chart’ and can be viewed with the ChartPlot
2D Interactive Plotter. To perform a sampling test and create a \*.chart
file for all of the distributions in the definitions block, use the
keyword “runSampleTests” inside the definitions block but outside any
particular distribution.

Some example distribution inputs are listed below and shown in
:numref:`fig8-12`.

::

      distribution 11
         title="a binned histogram"
         abscissa -5 -4 -3 -2 -1 0 1 2 3 4 5 end
         truePDF   1  2  3  4  5 4 3 2 2 2   end
      end distribution
      distribution 12
         title="value/function pairs"
         abscissa   -5 -4 -3 -2 -1 0 1 2 3 4 5  end
         truePDF     0  1  2  3  4 5 4 3 2 2 2  end
      end distribution
      distribution 21
         title="a binned histogram with biasing"
         abscissa -5 -4 -3 -2 -1 0 1 2 3 4 5 end
         truePDF   1  2  3  4  5 4 3 2 2 2   end
         biasedPDF 3  2  1  1  1 1 1 2 2 2   end
      end distribution
      distribution 22
         title="value/function pairs with importances"
         abscissa   -5 -4 -3 -2 -1 0 1 2 3 4 5  end
         truePDF     0  1  2  3  4 5 4 3 2 2 2  end
         importance  4  3  2  1  1 1 1 1 2 2 2  end  
      end distribution
      distribution 31
         title="a binned histogram using CDF's"
         abscissa -5 -4 -3 -2 -1  0  1  2  3  4 5 end
         trueCDF   1  3  6 10 15 19 22 24 26 28   end
      end distribution
      distribution 32
         title="a binned histogram with biasing using CDF's"
         abscissa -5 -4 -3 -2 -1  0  1  2  3  4 5 end
         trueCDF   1  3  6 10 15 19 22 24 26 28   end
         biasedPDF 3  5  6  7  8  9 10 12 14 16   end
      end distribution

Other notes on distributions:

  1) Binned histogram distributions can also be specified using cdf’s
     (keywords “trueCDF” and “biasedCDF”).

  2) For distributions that will be used for source energy sampling, use
     abscissa values of eV.

  3) For multigroup calculations using histograms, the keywords
     “neutronGroups” or “photonGroups” can be used instead of specifying
     the abscissa values. In this case, be sure to list the binned pdf
     values in order from the highest energy group to the lowest energy
     group.

  4) For CE calculations, instead of specifying abscissa values, the bin
     boundaries of an energyBounds object (see next section) can be
     specified using “energyBoundsID=”.

.. _fig8-12:
.. figure:: figs/Monaco/8-12.png
  :align: center
  :width: 90 %

  Sampling tests for the distribution examples.

Several special (built-in) distributions are available in Monaco. To use
one of these, specify the keyword “special=” with a distribution name in
quotes and the keyword “parameters … end” (if required) for that type of
distribution. These special distributions are summarized in Table 8.2.8.

The Watt spectrum has the form

.. math::
  :label: Monaco-18

  p(E) = ce^{-E/a} \text{sinh}(\sqrt{bE})

with the parameters *a* and *b* (with *c* as a normalization constant).
For spontaneous fission of :sup:`252`\ Cf, values typically used are
*a*\ =1.025 MeV and *b*\ =2.926/MeV. For thermal fission of
:sup:`235`\ U, the parameters are *a*\ =1.028 MeV and *b*\ =2.249/MeV.
For induced fission, the parameters *a* and *b* are, in general,
functions of incident neutron energy. See Table 8.2.9 for an example.
The Watt spectrum distribution will be displayed in the \*.chart plot as
a histogram distribution using the cross-section energy structure
neutron groups but when sampled in Monaco, the continuous Froehner and
Spencer\ :sup:`1` method is used to select an energy of source particles
using a Watt spectrum distribution.

with the parameters *a* and *b* (with *c* as a normalization constant).
For spontaneous fission of :sup:`252`\ Cf, values typically used are
*a*\ =1.025 MeV and *b*\ =2.926/MeV. For thermal fission of
:sup:`235`\ U, the parameters are *a*\ =1.028 MeV and *b*\ =2.249/MeV.
For induced fission, the parameters *a* and *b* are, in general,
functions of incident neutron energy. See Table 8.2.9 for an example.
The Watt spectrum distribution will be displayed in the \*.chart plot as
a histogram distribution using the cross-section energy structure
neutron groups but when sampled in Monaco, the continuous Froehner and
Spencer\ :sup:`1` method is used to select an energy of source particles
using a Watt spectrum distribution.

.. _tab8-8:
.. table:: Special (built-in) distributions
  :align: center

  +-----------------------+-----------------------+-----------------------+
  | **Distribution**      | **Parameters**        | **Description**       |
  +=======================+=======================+=======================+
  | "wattSpectrum"        | *a* *b n*             | Watt spectrum         |
  |                       |                       | distribution. Units   |
  |                       |                       | are: *a* in MeV, *b*  |
  |                       |                       | in /MeV. Optional     |
  |                       |                       | parameter *n*         |
  |                       |                       | specifies how many    |
  |                       |                       | subintervals in each  |
  |                       |                       | neutron group to use  |
  |                       |                       | in integrating the    |
  |                       |                       | pdf (default 100) for |
  |                       |                       | the histogram         |
  |                       |                       | representation in the |
  |                       |                       | sampling test and     |
  |                       |                       | mesh source           |
  |                       |                       | representation.       |
  +-----------------------+-----------------------+-----------------------+
  | "fissionNeutrons"     | *m ZAID*              | Spectrum of fission   |
  |                       |                       | neutrons from the     |
  |                       |                       | MULTIGROUP            |
  |                       |                       | cross-section library |
  |                       |                       | for material *m* and  |
  |                       |                       | nuclide *ZAID*.       |
  +-----------------------+-----------------------+-----------------------+
  | "fissionPhotons"      | *ZAID*                | Spectrum of fission   |
  |                       |                       | photons from nuclide  |
  |                       |                       | *ZAID*.               |
  +-----------------------+-----------------------+-----------------------+
  | "origensBinaryConcent | *c s*                 | Spectrum from an      |
  | rationFile"           |                       | ORIGEN-S binary       |
  |                       |                       | concentration file    |
  |                       |                       | case number *c*,      |
  |                       |                       | spectra type *s*.     |
  |                       |                       | For the spectra type  |
  |                       |                       | *s*, values are:  1 – |
  |                       |                       | total neutron, 2 –    |
  |                       |                       | spontaneous fission,  |
  |                       |                       | 3 – (α,n), and 4 –    |
  |                       |                       | delayed neutrons, 5 – |
  |                       |                       | photons.  The         |
  |                       |                       | ORIGEN-S filename     |
  |                       |                       | should be supplied    |
  |                       |                       | with the keyword      |
  |                       |                       | filename= “…” and the |
  |                       |                       | path/filename in      |
  |                       |                       | quotes.               |
  +-----------------------+-----------------------+-----------------------+
  | "cosine"              | *n*                   | Cosine function from  |
  |                       |                       | –π /2 to π/2.         |
  |                       |                       | Optional parameter    |
  |                       |                       | *n* (default 100) is  |
  |                       |                       | the number of         |
  |                       |                       | value/function pairs  |
  |                       |                       | to show in the        |
  |                       |                       | sampling test.        |
  +-----------------------+-----------------------+-----------------------+
  | "pwrNeutronAxialProfi | none                  | Typical neutron PWR   |
  | le"                   |                       | axial profile.        |
  +-----------------------+-----------------------+-----------------------+
  | "pwrGammaAxialProfile"| none                  | Typical gamma PWR     |
  |                       |                       | axial profile.        |
  +-----------------------+-----------------------+-----------------------+
  | "pwrNeutronAxialProfi | none                  | Typical neutron PWR   |
  | leReverse"            |                       | axial profile,        |
  |                       |                       | reversed top to       |
  |                       |                       | bottom.               |
  +-----------------------+-----------------------+-----------------------+
  | "pwrGammaAxialProfile | none                  | Typical gamma PWR     |
  | Reverse"              |                       | axial profile,        |
  |                       |                       | reversed top to       |
  |                       |                       | bottom.               |
  +-----------------------+-----------------------+-----------------------+
  | “exponential”         | *a n*                 | Exponential function  |
  |                       |                       | *e\ ax* from -1 to 1. |
  |                       |                       | Optional parameter    |
  |                       |                       | *n* (default 100) is  |
  |                       |                       | the number of         |
  |                       |                       | value/function pairs  |
  |                       |                       | to show in the        |
  |                       |                       | sampling test.        |
  +-----------------------+-----------------------+-----------------------+
  |“origensDiscreteGammas"| *z a m*               | Discrete gammas from  |
  |                       |                       | the ORIGEN mpdkxgam   |
  |                       |                       | database for isotope  |
  |                       |                       | of atomic number *z*, |
  |                       |                       | mass *a* and          |
  |                       |                       | metastable state *m*. |
  |                       |                       | (default is m=0)      |
  +-----------------------+-----------------------+-----------------------+


For the ORIGEN-S binary concentration sources, the ORIGEN input file
should be specified using the filename=“…” with the path/filename in
quotes. Note that the ORIGEN calculation has to be set to save the
neutron or photon data will be used as a Monaco distribution. This can
be done by specifying the number of photon or neutron groups on the 3$
(library integer constants) array and specifying the energy bin
boundaries on the 83\* and 84\* (group structure) arrays. In Monaco, to
show all of the cases in the binary concentration file, ask for case 0.
To show what data is available for a particular case, ask for that case
number and spectra type 0.

Other notes on special distributions: 1) Fission neutron distributions
use MT=1018 for the specified ZAID of the specified isotope from the
cross-section library. 2) Fission photon distributions are not read from
the cross-section file but are instead read from a separate file
containing only ENDF/B-VII.0 fission photon data. 3) The neutron and
photon axial profile distributions come from the SCALE 5.1 SAS4 manual,
Table S4.4.5. 4) Fission neutron distributions are not allowed in the CE
problems, users are advised to use “wattSpectum” in order to get a
similar distribution.


.. list-table:: Watt spectrum parameters for neutron induced fission of :sup:`233`\U (From ENDF/B-VII.0)
  :align: center
  :name: tab8-9

  * - .. image:: figs/Monaco/tab8-9.png
         :width: 300

Some example special distribution inputs are listed below and shown in
:numref:`fig8-13`.

::

      distribution 11
          special="wattSpectrum"
          parameters 1.0 3.0 end
      end distribution
      distribution 12
          special="fissionNeutrons"
          parameters 1 92235 end
      end distribution
      distribution 21
          special="fissionPhotons"
          parameters 94239 end
      end distribution
      distribution 22
          special="origensBinaryConcentrationFile"
          filename="c:\\path\somefile.f71"
          parameters 9 5 end
      end distribution
      distribution 31
          special="origensBinaryConcentrationFile"
          filename="c:\\path\somefile.f71"
          parameters 9 1 end
      end distribution
      distribution 32
          special="cosine"
          parameters 100 end
      end distribution
      distribution 41
          special="pwrNeutronAxialProfile"
      end distribution
      distribution 42
          special="exponential"
          parameters 1.0 100 end
      end distribution

.. _fig8-13:
.. figure:: figs/Monaco/8-13.png
  :align: center

  Sampling tests for the special (built-in) distribution examples.

Energy boundaries
^^^^^^^^^^^^^^^^^

Energy boundaries (“energyBounds”) require an identification number and
a specification of a set of bin boundaries in energy (eV). Energy bounds
objects are typically used in CE calculations for specifying and energy
grid for tallies. The keyword “bounds … end” can be used to list energy
values (in eV, in any order). The keyword “linear *n* *a* *b*\ ” can be
used to specify *n* bins between *a* and *b*. Likewise, the keyword
“logarithmic *n a b*\ ” can be used for :math:`n` bins logarithmically
spaced between *a* and *b*. The keywords “bounds”, “linear” and
“logarithmic” can be used together and multiple times – they will simply
add energy boundaries to any already defined. Any duplicate planes will
be removed using the absolute tolerance, specified with the keyword
“tolerance=”. To specify one of the more common SCALE energy structures
(handy for doing tallies one a standard structure in CE calculations),
one of the following shortcut keywords can be used: “252n”, “238n”,
“200n”, “56n”, “47p”, “44n”, “27n”, or “19p”.

These keywords will cause to load the energy structures from the MG
cross-section libraries aliased in the “FileNameAliases.txt” with names
of “xn252”, “xn238”, “xn200”, “xn56”, “xg47”, “xn44”, “xn27”, and “xg19”
relatively. If required energy structure is for neutrons and there is no
alias for MG cross-section library or the library is missing, MG JEFF
reaction data library will be searched as “n{NG}.reaction.data” to load
the energy structure. These can be used in combination with the other
keywords to use existing structures supplemented with extra boundaries.

::

    energyBounds 1
        title="bounds command, check for duplicates"
        bounds 1 4 2 3 5 end
        bounds 7 6 10 5 9 8 7 end
    end energyBounds
    energyBounds 3
        title="logarithmic command"
        logarithmic  21  1.0 10000000.0
    end energyBounds
    energyBounds 11
        title="SCALE 19 group photon structure with extras"
        19p
        linear 10 6.0e6 7.0e6
    end energyBounds

An energyBounds object can also be used to set the energy bin boundaries
for a response (type1) instead of using the “bounds … end” keyword. This
is done by using with the keyword “energyBoundsID=” and referencing a
defined energyBounds object. Likewise for distributions, instead of
specifying the “abscissa … end” keyword and listing abscissa values, an
energyBounds object can be used. This allows the user to define a set of
energy bin boundaries once and re-use them across multiple responses and
definitions. When using the “energyBoundsID=” keyword, the data values
should be entered in the standard multigroup order – from high energy to
low energy. For a stand-alone multigroup Monaco calculation, do not use
ID numbers of 1 or 2 for energyBounds objects – these ID numbers are
reserved.

Time boundaries
^^^^^^^^^^^^^^^

Time boundaries (“timeBounds”) are similar to energy bin boundaries but
take values in seconds. These objects are only used in tallies in CE
calculations.

::

    timeBounds 2
        title="linear command"
        linear 10 0.0 10.0e-3
    end timeBounds
    timeBounds 7
        title="logarithmic command"
        logarithmic  6  1.0e-6 1.0
    end timeBounds

Sources block
~~~~~~~~~~~~~

The sources block specifies what sources to use. Multiple sources are
allowed and each is sampled according to its strength, relative to the
total strength of all sources. Each source description must be contained
with a “src *id*\ ” and an “end src” (where the *id* is the source
identification number). The sources block must contain at least one
source.

For each user-defined source, the user can specify the spatial
distribution, the energy distribution and the directional distribution
separately. Many options for each distribution are available and
defaults are used for most if the user does not specify anything. The
source strength is set using the keyword “strength=” and the type of
source is set using the keyword “neutron” or “photon”. The “strength=”
keyword is required for each source.

When using more than one source, the user can set the true strength of
each using the keyword “strength=” and can also specify how often to
sample each source using the keyword “biasedStrength=”. The true
strengths of the sources will be combined to form the true source
distribution PDF. The biased strengths of sources will be combined to
form a PDF from which to sample. The weights of the source particles
will be properly weighted to account for the biased sampling strengths.
For example, consider two sources of strengths 10\ :sup:`9` and
9×10\ :sup:`9` /sec that should be sampled in a ratio of 4:1. The biased
sampling strengths are then set to 4 and 1. Monaco will sample the first
source 80% of the time and the particles will be born with a weight of
0.125. The second source will be sampled 20% of the time and its
particles will be born with weights of 4.5.

Spatial distribution
^^^^^^^^^^^^^^^^^^^^

+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| Keyword        | Parameters                                                                                      | Possible degenerate cases                             |
+================+=================================================================================================+=======================================================+
| cuboid         | :math:`x_{max}` :math:`x_{min}` :math:`y_{max}` :math:`y_{min}` :math:`z_{max}` :math:`z_{min}` | rectangular plane, line, point                        |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| xCylinder      | *r* :math:`x_{max}` :math:`x_{min}`                                                             | circular plane, line, point                           |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| yCylinder      | *r* :math:`y_{max}` :math:`y_{min}`                                                             | circular plane, line, point                           |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| zCylinder      | *r* :math:`z_{max}` :math:`z_{min}`                                                             | circular plane, line, point                           |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| xShellCylinder | *r1* *r2* :math:`x_{max}` :math:`x_{min}`                                                       | cyl., planar annulus, cyl. surface, line, ring, point |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| yShellCylinder | *r1* *r2* :math:`y_{max}` :math:`y_{min}`                                                       | cyl., planar annulus, cyl. surface, line, ring, point |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| zShellCylinder | *r1* *r2* :math:`z_{max}` :math:`z_{min}`                                                       | cyl., planar annulus, cyl. surface, line, ring, point |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| sphere         | *r*                                                                                             | point                                                 |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+
| shellSphere    | *r1* *r2*                                                                                       | sphere, spherical surface, point                      |
+----------------+-------------------------------------------------------------------------------------------------+-------------------------------------------------------+


Note that other than the shell-type solids, the parameters are the same
as the SGGP geometry specification of those solids. The SGGP keyword
“origin” (followed by at least one of “x=”, “y=”, and/or“z=”) is
available for all of the different source solid bodies. For the cylinder
based solid bodies, the direction of the axis of the cylinder can be set
by using the keyword “cylinderAxis *u* *v* *w*\ ”, where *u*, *v*, and
*w* are the direction cosines with respect to the global *x*-, *y*-, and
*z*-directions.

The source can be limited to only be from the parts of the solid body
that are inside a specific unit (“unit=”), inside a specific region
(“region=”) within the specified unit, or made of a certain material
(“mixture=”). A mixture and a unit/region cannot both be specified since
that would either be redundant or mutually exclusive.

If no source spatial information is provided by the user, the default is
a point source located at the origin (in global coordinates). Like SGGP
input, the geometry keywords used for the bounding shape are fixed
lengths arrays and do not have an “end” terminator. They must be
followed by the correct number of parameters.

The spatial distribution in each dimension of the cuboid shape is
specified by using the keywords “xDistributionID=”, “yDistributionID=”,
or “zDistributionID=” and pointing to a distribution defined in the
definitions block. For the cylindrical shapes, “rDistributionID=” and
“zDistributionID=” can be used. For spherical shapes, only the
“rDistributionID=” can be specified. Distributions defined using
abscissa values that are different than the length of the simple
geometry bounding shape can still be used if the keyword “xScaleDist”
(or “y”, “z”, or “r”) is used. This linearly scales the distribution
abscissa values to the length of the simple geometry bounding shape.
Note that for cylindrical sources, since the axis can point in any
direction, the z distribution is interpreted as the length along the
axis, with the base position as z=0.

Energy distribution
^^^^^^^^^^^^^^^^^^^

“eDistributionID=” and pointing to one of the distributions defined in
the definitions block. Energies will be sampled from the distribution in
a continuous manner. For MULTIGROUP calculations, that energy will then
be mapped onto the group structure of the cross-section library being
used by Monaco. Each source should have an energy distribution that has
abscissa values in units of eV. If no energy distribution is given, 1
MeV (translated to the current group structure if a multigroup problem)
will be used.

To use the total of an energy distribution as the source strength, use
the keyword “useNormConst” without either “strength=” or “fissions=”.
This will set the strength to be equal to the normalization constant of
the distribution – the total of the distribution before it was
normalized into a pdf. An optional “multiplier=” keyword can be used to
increase or decrease that strength. For example, consider a case using
the neutron spectrum information from a case of an ORIGEN-S binary
concentration file that used a basis of an entire core. If the Monaco
source was just one of the 200 assemblies, then the “multiplier=”
keyword can be set to 0.005 so that the source strength is scaled
appropriately.

Directional distribution
^^^^^^^^^^^^^^^^^^^^^^^^

The directional distribution of the source is specified by using the
keyword “dDistributionID=” and pointing to one of the distributions
defined in the definitions block. The distribution will be used to
sample the cosine of the polar angle, :math:`\mu`, from the reference
direction. The reference direction, where :math:`\mu = 1`, is set with
the keyword “direction *u* *v* *w*\ ”, where *u*, *v*, and *w* are the
direction cosines with respect to the global *x*-, *y*-, and
*z*-directions. The default value for the reference direction is the
positive *z*-axis (<0,0,1>). The keyword “dScaleDist” can be used to
linearly scale the distribution abscissa values to the range of
:math:`\mu \in \left\lbrack - 1,1 \right\rbrack`. If no directional
distribution is specified with the keyword “dDistributionID=”, then an
isotropic directional distribution will be used.

Using a Monaco mesh source map file
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The user can alternatively specify an existing Monaco mesh source map
file—a binary file created by a previous MAVRIC or Monaco calculation.
The mesh source map must be a binary file using the Monaco mesh source
map format (a \*.msm file). This option is specified with the
“meshSourceFile=” keyword and the file name (and full path if necessary)
in quotes.

::

  read sources
      src 1
          meshSourceFile=”c:\mydocu~1\previouslyMadeSource.msm”
      end src
  end sources

If the “meshSourceFile=” keyword is used, all energy distribution
keywords and most spatial distribution keywords will be ignored. Source
keywords that can be used with a mesh source include “strength=” to
override the source strength in the mesh source; “biasedStrength=” to
set the sampling strength; “origin”, “x=”, “y=”, and “z=” to place the
origin of the mesh source file at a particular place in the current
global coordinate system; and the keywords for describing the
directional distribution – “dDistributionID=”, “direction *u* *v* *w*\ ”
and “dScaleDist”.

Mesh sources are sampled using the following algorithm: First, a
direction is sampled. Second, a voxel is sampled and a position is
picked uniformly within the voxel. If that position does not match the
optional limiters (unit, region, material specified in the mesh source),
a new position is chosen within the voxel until a match is made. If a
position cannot be found within the voxel after 10000 tries, Monaco will
stop. (This can occur if the mesh voxel contained just a sliver of
source volume when generated. For this case, the keyword
“allowResampling” can be used to select a new voxel instead of stopping.
In general, this keyword should not be used.)

Creating a mesh source
^^^^^^^^^^^^^^^^^^^^^^

To create a mesh source out of the source definition, use the
“meshSourceSaver” subblock inside the sources block. It is quite handy
to visualize the sources and ensure they are what were intended. You
must specify which one of the defined grid geometries to use (keyword
“gridGeometryID=”) and a filename for the resulting mesh source file
(keyword “filename=” with the filename in quotes
“\ *path*\\\ *name*.msm”). For more than one source, each will be stored
separately and the filename will include the source id number.

::

  read sources
      src 1


      end src
      src 5


      end src
      meshSourceSaver
          gridGeometryID=7
          filename="meshSource.msm"
          subcells=3
      end meshSourceSaver
  end sources

To create the mesh source, Monaco determines if the defined source
exists within each cell. This is done by dividing each mesh cell into
*n×n×n* subcells (from the keyword subCells=\ *n* with a default of
*n*\ =2) and testing each subcell center. For every subcell center that
is a valid source position (within the spatial solid and meets the
optional unit, region, or mixture requirements), an amount of source
proportional to the subcell volume is assigned to the mesh cell. The
keyword subCells= can be used to better refine how much source is
computed for the mesh cells at the boundary of a curved source region.
Of course, more subcell testing takes more time. If a given source is
degenerate in any dimension (point, line, or plane), that information
will be stored in the resulting mesh source so that particles will not
be sampled over the entire corresponding voxel but will have closer to
the original spatial distribution. Likewise, if the original source had
restrictions based on unit, region or mixture, those restrictions will
be stored as part of the resulting mesh source.

The above process may miss small sources or degenerate sources
(surfaces, lines, points) that do not lay on the tested subcell centers.
If none of the mesh cells contain any source after the subcell method,
then random sampling of the source is used. A number of source positions
are sampled from the source (set by the “sourceTrials=” keyword, default
of 1000000) and then placed into the proper mesh cell. If this method is
used, the resulting mesh source file should be visualized to ensure that
the statistical nature of the source trials method does not unduly
influence the overall mesh source. To skip the subcell method and go
directly to the source trials method, use “subCells=0”.

The keyword “makeTotal” will make a single mesh source file which is the
composite of all of the individual sources. Geometric degeneracies or
restrictions to only sample particles from a specified unit, region or
material will only be kept if they are the same for all of the sources.
For this reason, users may not wish to use a mesh source using the
“makeTotal” keyword for transport but rather use it to verify that all
of the sources have been input properly.

The keyword “reduce” can be used to only save the smallest rectangular
portion of the mesh surrounding the voxels with non-zero source amounts.
This can result in much smaller file sizes for sources that are small
compared to the extents of the grid geometry.

Monaco mesh source files (\*.msm) can be viewed with the Mesh File
Viewer. Plots can be made showing the source values for each group (or
total). The viewer can also show the geometry regions or material
mixtures as well. Using the viewer is an easy way to confirm that the
source definition was entered correctly. Note that the \*.msm files
actually only store the biased sampling distribution and the initial
weights (to speed up the sampling process). So, in the viewer the “true”
source is computed as the product of the sampled distribution and the
weights. If groups with real source are set to zero importance, the
viewer cannot recreate the original true source. The true source shown
by the viewer is the amount of true source only in groups that have
non-zero importance.

Mesh source advanced features
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Two advanced features exist in the meshSourceSaver subblock – mainly
used by the MAVRIC sequence when the importance map calculations use a
different cross-section library than the final Monaco calculation.

The keyword “sampleFromMesh” can be used to tell Monaco to sample from
the created mesh file(s) instead of the standard source definition. This
can be useful in determining if the mesh source is fine enough to
accurately represent the original source definition. If the “makeTotal”
keyword was used, then Monaco will sample from the total mesh source
file.

The keyword “meshBiasFile=” can be optionally be used when
“sampleFromMesh” is on. This tells Monaco to sample from the mesh source
file(s) version of the source definition that has been modified using
just the importance information from the named mesh source file. For
example, using a 27-group biased mesh source for a Watt spectrum source
may not represent the high energy tail very well. In this case, it would
be better to do a 200-group Monaco calculation but still use the
importance information from 27-group mesh source file using
“sampleFromMesh” and “meshBiasFile=”.

Tallies block
~~~~~~~~~~~~~

The tallies block tells Monaco what to compute: fluxes at certain points
in space (point detectors), fluxes in certain geometry regions, or
fluxes in each voxel of a mesh grid. The computed fluxes can also be
integrated with response functions to compute dose, reaction rate or