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<li class="toctree-l1"><a class="reference internal" href="Keno.html">Keno: A Monte Carlo Criticality Program</a></li>
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<li class="toctree-l1"><a class="reference internal" href="KenoC.html">Keno Appendix C: Sample problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="Monaco.html">Monaco: A Fixed-Source Monte Carlo Transport Code for Shielding Applications</a></li>
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<p class="caption"><span class="caption-text">Radiation Shielding</span></p>
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<li class="toctree-l1"><a class="reference internal" href="MAVRIC.html">MAVRIC: Monaco with Automated Variance Reduction using Importance Calculations</a></li>
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<li class="toctree-l1"><a class="reference internal" href="appendixb.html">MAVRIC Appendix B: MAVRIC Utilities</a></li>
<li class="toctree-l1"><a class="reference internal" href="appendixc.html">MAVRIC Appendix C: Advanced Features</a></li>
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  <div class="section" id="csas5-control-module-for-enhanced-criticality-safety-analysis-sequences-with-keno-v-a">
<span id="csas5"></span><h1>CSAS5:  Control Module For Enhanced Criticality Safety Analysis Sequences With KENO V.a<a class="headerlink" href="#csas5-control-module-for-enhanced-criticality-safety-analysis-sequences-with-keno-v-a" title="Permalink to this headline"></a></h1>
<p><em>L. M. Petrie, K. B. Bekar, S. Goluoglu,</em><sup>*</sup> <em>D. F. Hollenbach,</em><sup>*</sup> <em>N. F. Landers</em></p>
<p>The <strong>C</strong>riticality <strong>S</strong>afety <strong>A</strong>nalysis <strong>S</strong>equences with
KENO V.a (CSAS5) provides reliable and efficient means of performing
<em>k</em><sub>eff</sub> calculations for systems that are routinely encountered in
engineering practice. In the multigroup calculation mode, CSAS5 uses
XSProc to process the cross sections for temperature corrections and
problem-dependent resonance self-shielding and calculates the <em>k</em><sub>eff</sub>
of a three-dimensional (3-D) system model. If the continuous energy
calculation mode is selected no resonance processing is needed and the
continuous energy cross sections are used directly in KENO V.a, with
temperature corrections provided as the cross sections are loaded. The
geometric modeling capabilities available in KENO V.a coupled with the
automated cross-section processing within the control sequences allow
complex, 3-D systems to be easily analyzed. A search capability is
achieved by repeatedly activating the control module MODIFY, to alter
either the system dimensions or densities, and the functional module
KENO V.a to calculate the <em>k</em><sub>eff</sub> for the modified dimensions or
densities.</p>
<p>*Formerly with Oak Ridge National Laboratory.</p>
<div class="section" id="acknowledgments">
<h2>Acknowledgments<a class="headerlink" href="#acknowledgments" title="Permalink to this headline"></a></h2>
<p>CSAS5 and its related Criticality Safety Analysis Sequences are based on the old CSAS2 control
module (no longer in SCALE) and the KENO V.a functional module described in the KENO V.a chapter.
Therefore, special acknowledgment is made to J. A. Bucholz, R. M. Westfall, and J. R. Knight who developed CSAS2.
G. E. Whitesides is acknowledged for his contributions through early versions of KENO.
Appreciation is expressed to C. V. Parks and S. M. Bowman for their guidance in developing CSAS5.</p>
<p>Special appreciation is expressed to S. J. Poarch and S. Y. Walker for their efforts in formatting this document.</p>
</div>
<div class="section" id="introduction">
<span id="csas5-intro"></span><h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
<p>Criticality Safety Analysis Sequence with KENO V.a (CSAS5) provides
reliable and efficient means of performing <em>k</em><sub>eff</sub> calculations for
systems that are routinely encountered in engineering practice,
especially in the calculation of <em>k</em><sub>eff</sub> of three-dimensional (3-D)
system models. CSAS5 implements XSProc to process material input and
provide a temperature and resonance-corrected cross-section library
based on the physical characteristics of the problem being analyzed. If
a continuous energy cross-section library is specified, no resonance
processing is needed and the continuous energy cross sections are used
directly in KENO V.a, with temperature corrections provided as the cross
sections are loaded. A search capability is available to find a desired
values of <em>k</em><sub>eff</sub> as a function of dimensions or densities. The two
basic search options offered are (1) an optimum search seeking a maximum
or minimum value of <em>k</em><sub>eff</sub> and (2) a critical search seeking a fixed
value of <em>k</em><sub>eff</sub>.</p>
<p>All the control sequences in the CSAS5 control module are listed in
<a class="reference internal" href="#tab2-1"><span class="std std-numref">Table 4</span></a> with the modules they invoke. The first four sequences are
subsets of the CSAS5 sequence.</p>
<span id="tab2-1"></span><table class="docutils align-center" id="id8">
<caption><span class="caption-number">Table 4 </span><span class="caption-text">CSAS5 sequences for criticality safety</span><a class="headerlink" href="#id8" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 19%" />
<col style="width: 36%" />
<col style="width: 27%" />
<col style="width: 10%" />
<col style="width: 8%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Control sequence</p></th>
<th class="head"><p>Function</p></th>
<th class="head"><p>Functional modules
executed by the
control sequence
for multigroup libraries</p></th>
<th class="head"></th>
<th class="head"></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>CSAS5</p></td>
<td><p><span class="math notranslate nohighlight">\(k_{eff}\)</span> (3-D)</p></td>
<td><p>XSProc</p></td>
<td><p>KENO V.a</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>CSAS5S</p></td>
<td><p><span class="math notranslate nohighlight">\(k_{eff}\)</span> (3-D) search</p></td>
<td><p>XSProc</p></td>
<td><p>KENO V.a</p></td>
<td><p>MODIFY</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="sequence-capabilities">
<h2>Sequence Capabilities<a class="headerlink" href="#sequence-capabilities" title="Permalink to this headline"></a></h2>
<p>In order to minimize human error, the SCALE data handling is automated
as much as possible. CSAS5 and many other SCALE sequences apply a
standardized procedure to provide appropriate number densities and
cross sections for the calculation. XSProc is responsible for reading
the standard composition data and other engineering-type specifications,
including volume fraction or percent theoretical density, temperature,
and isotopic distribution as well as the unit cell data. XSProc then
generates number densities and related information, prepares geometry
data for resonance self-shielding and flux-weighting cell calculations,
if needed, and (if needed) provides problem-dependent multigroup
cross-section processing. Sequences that execute KENO V.a include a
KENO V.a Data Processor to read and check the KENO V.a data. Sequences
that execute a search use a Search Data Processor to read and check the
search data. When the data checking has been completed, the control
sequence executes XSProc to prepare a resonance-corrected microscopic
cross-section library in the AMPX working library format if a multigroup
library has been selected.</p>
<p>For each unit cell specified as being cell-weighted, XSProc performs the
necessary calculations and produces a cell-weighted microscopic
cross-section library. KENO V.a may be executed to calculate the
<em>k</em><sub>eff</sub> or neutron multiplication factor using the cross-section
library that was prepared by the control sequence. MODIFY may be invoked
to perform a search <a class="bibtex reference internal" href="#lorek-improved-1979" id="id1">[LDPW79]</a> by repeatedly altering the unit cell
(multigroup mode only) and KENO V.a data prior to executing the next
pass through the calculation. Cross sections are updated at the
beginning of each search pass with the modified data. If unit cell data
is altered as part of the search, i.e., pitch or material search, the
cross-sections are correctly processed with the updated data.</p>
<p>The search capability is implemented by the control module MODIFY. It
performs operations according to the specified search data to determine
(1) the maximum or minimum value of <span class="math notranslate nohighlight">\(k_{eff}\)</span> as a function of pitch,
dimensions or densities or (2) the pitch, dimensions, or densities
corresponding to a specified value of <span class="math notranslate nohighlight">\(k_{eff}\)</span>. An iterative procedure
is used, making use of all previous information to modify the dimensions
or densities to achieve the desired result. The procedures for
conducting optimum and critical searches are summarized in the following
sections.</p>
<div class="section" id="optimum-minimum-maximum-search">
<h3>Optimum (minimum/maximum) search<a class="headerlink" href="#optimum-minimum-maximum-search" title="Permalink to this headline"></a></h3>
<p>Because only an initial value of <span class="math notranslate nohighlight">\(k_{eff}\)</span> and a set of boundary
constraints are available, four initial points are generated spanning
the range defined by the constraints. The search package identifies the
type of cubic equation [i.e., a cubic with no local extrema (type A) or
a cubic with two local extrema (type B)] and utilizes this knowledge in
determining the pitch, dimensions, or material densities corresponding
to the maximum (or minimum) value of <span class="math notranslate nohighlight">\(k_{eff}\)</span>. The optimum search
procedure is summarized as follows:</p>
<blockquote>
<div><ol class="arabic simple">
<li><p>Calculate <span class="math notranslate nohighlight">\(k_{eff}\)</span> for the specified problem.</p></li>
<li><p>Calculate <span class="math notranslate nohighlight">\(k_{eff}\)</span> for the minimum constraint.</p></li>
<li><p>Calculate <span class="math notranslate nohighlight">\(k_{eff}\)</span> for the maximum constraint.</p></li>
<li><p>Calculate <span class="math notranslate nohighlight">\(k_{eff}\)</span> for a fourth point that lies approximately
equidistant between the initial guess and the constraint that is
farthest from it.</p></li>
<li><p>Utilize a weighted least-squares fit to a cubic polynomial on the
data points.</p></li>
<li><p>Determine the type of cubic. For a type A cubic, go to step 11.</p></li>
<li><p>Take the first derivative of the least-squares cubic.</p></li>
<li><p>Solve the quadratic for its roots.</p></li>
<li><p>Take the second derivative of the least-squares cubic to determine
which root is the maximum (or minimum), and if it falls within
the constraints, use this root as the next guess. Otherwise,
convergence has been defined as occurring at the constraint with
the maximum (or minimum) <span class="math notranslate nohighlight">\(k_{eff}\)</span>.</p></li>
<li><p>Calculate the <span class="math notranslate nohighlight">\(k_{eff}\)</span> corresponding to the next guess. Go to
step 5. Repeat this procedure until convergence is achieved.</p></li>
<li><p>If the cubic equation is a type A cubic, the optimum lies on one of
the boundaries. If the fit shows that the cubic is actually a
type B cubic, go to step 7 and continue.</p></li>
</ol>
</div></blockquote>
<p>Convergence is defined as occurring when a <em>k</em><sub>eff</sub> has been calculated
for a point on the curve where the value of the curve is within epsilon
of the maximum (or minimum) of the curve. Additionally, the calculated
<em>k</em><sub>eff</sub> must be within two standard deviations of the value of the
curve at that point. The search is terminated when convergence is
achieved, when the code determines there is no local maximum within the
constraints, or the maximum number of search iterations is reached.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>At the beginning of each search pass, the cross sections are
updated using the updated values of pitch, dimensions, or material
densities. Also, the unit or material being modified can be directly
tied to a unit cell, so that unit cell is updated during the search.
Therefore, the final result should be consistent with the results
obtained by running a non-search problem using the data from the last
pass.</p>
</div>
</div>
<div class="section" id="critical-search">
<h3>Critical search<a class="headerlink" href="#critical-search" title="Permalink to this headline"></a></h3>
<p>The critical search option searches for the pitch, dimensions, or
material densities corresponding to a specified value of <em>k</em><sub>eff</sub>. If
the calculated value of <em>k</em><sub>eff</sub> is within the specified search
tolerance (EPS) of the desired <em>k</em><sub>eff</sub>, the search is considered to be
complete. The critical search procedure is summarized as follows:</p>
<blockquote>
<div><p>1. Calculate <em>k</em><sub>eff</sub> for the specified problem. If it is within EPS of
the specified <em>k</em><sub>eff</sub>, convergence has been achieved.</p>
<p>2. Calculate <em>k</em><sub>eff</sub> for one of the constraints. If the specified
<em>k</em><sub>eff</sub> of the system does not fall between the initial value and
the <em>k</em><sub>eff</sub> of the constraint, calculate the <em>k</em><sub>eff</sub> of the other
constraint. If the calculated <em>k</em><sub>eff</sub> is within EPS of the specified
<em>k</em><sub>eff</sub>, convergence has been achieved.</p>
<p>3. Calculate <em>k</em><sub>eff</sub> for a point chosen from a linear fit of the two
existing points closest to the specified <em>k</em><sub>eff</sub>.</p>
<p>4. Repeat step 3 until convergence has been achieved, the program
determines that the specified value lies outside the constraints, or
the maximum number of search iterations is reached. Convergence has
been achieved when the calculated **k*<sub>eff</sub> is within EPS of the
specified <em>k</em><sub>eff</sub>.</p>
<p>5. If convergence is achieved, calculate <em>k</em><sub>eff</sub> for a point determined
from fitting the previous points to a cubic and solving the cubic for
the point closest to the desired <em>k</em><sub>eff</sub>. If all roots lie outside
the constraints, the problem is terminated and an appropriate message
is written. If the maximum number of iterations is reached without
the problem converging, the problem is terminated and an appropriate
message is written.</p>
</div></blockquote>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>At the beginning of each search pass, the cross sections are
updated using the updated values of pitch, dimensions, or material
densities. Also, the unit or material being modified can be directly
tied to a unit cell, so that unit cell is updated during the search.
Therefore, the final result should be consistent with the results
obtained by running a non-search problem using the data from the last
pass.</p>
</div>
</div>
<div class="section" id="multigroup-csas5-limitations">
<h3>Multigroup CSAS5 limitations<a class="headerlink" href="#multigroup-csas5-limitations" title="Permalink to this headline"></a></h3>
<p>The CSAS5 control module was developed to use simple input data and
prepare problem-dependent cross sections for use in calculating the
effective neutron multiplication factor of a 3-D system using KENO V.a.
An attempt was made to make the system as general as possible within the
constraints of the standardized methods chosen to be used in SCALE.
Standardized methods of data input were adopted to allow easy data entry
and for quality assurance purposes. Some of the limitations of the CSAS5
multigroup sequences are a result of using preprocessed multigroup
cross sections. Inherent limitations in multigroup CSAS5 calculations
are as follows:</p>
<blockquote>
<div><p>1. Two-dimensional (2-D) effects such as fuel rods in assemblies where
some positions are filled with control rod guide tubes, burnable
poison rods and/or fuel rods of different enrichments. The
cross sections are processed as if the rods are in an infinite
lattice of identical rods. If the user inputs a Dancoff factor for
the cell (such as one computed by MCDancoff), XSProc can produce an
infinite lattice cell, which reproduces that Dancoff. This can
mitigate some two dimensional lattice effects</p>
</div></blockquote>
</div>
<div class="section" id="continuous-energy-csas5-limitations">
<h3>Continuous energy CSAS5 limitations<a class="headerlink" href="#continuous-energy-csas5-limitations" title="Permalink to this headline"></a></h3>
<p>When continuous energy KENO calculations are desired, none of the
resonance processing capabilities of XSProc are applicable or needed.
The continuous energy cross sections are directly used in KENO. An
existing multigroup input file can easily be converted to a continuous
energy input file by simply specifying the continuous energy library. In
this case, all cell data is ignored. However, the following limitations
exist:</p>
<blockquote>
<div><ol class="arabic simple">
<li><p>If CELLMIX is defined in the cell data, the problem will not run in
the continuous energy mode. CELLMIX implies new mixture cross
sections are generated using XSDRNPM-calculated cell fluxes and
therefore is not applicable in the continuous energy mode.</p></li>
<li><p>Only VACUUM, MIRROR, PERIODIC, and WHITE boundary conditions are
allowed. Other albedos, e.g., WATER, CARBON, POLY, etc. are for
multigroup only.</p></li>
<li><p>Problems with DOUBLEHET cell data are not allowed as they inherently
utilize CELLMIX feature.</p></li>
</ol>
</div></blockquote>
</div>
</div>
<div class="section" id="input-data-guide">
<h2>Input Data Guide<a class="headerlink" href="#input-data-guide" title="Permalink to this headline"></a></h2>
<p>This section describes the input data required for CSAS5. Several
subsets of the CSAS5 sequences listed in <a class="reference internal" href="#tab2-1"><span class="std std-numref">Table 4</span></a> are available to
achieve several different levels of processing.</p>
<p>The input data for these CSAS5 sequences are composed of three broad
categories of data. The first is XSProc, including Standard Composition
Specification Data and Unit Cell Geometry Specification. This first
category specifies the cross-section library and defines the composition
of each mixture and optionally unit cell geometry that may be used to
process the cross sections. This data block is necessary for all CSAS5
sequences. The second category of data, the KENO V.a input data, is used
to specify the geometric and boundary conditions that represent the
physical 3-D configuration of a KENO V.a problem. Both data blocks are
necessary for CSAS5 and CSAS5S. The last category of data is the search
data and is required only for CSAS5S.</p>
<p>All data are entered in free form, allowing alphanumeric data,
floating-point data, and integer data to be entered in an unstructured
manner. Up to 252 columns of data entry per line are allowed. Data can
usually start or end in any column with a few exceptions. As an example,
the word END beginning in column 1 and followed by two blank spaces or a
new line will end the problem and any data following will be ignored.
Each data entry must be followed by one or more blanks to terminate the
data entry. For numeric data, either a comma or a blank can be used to
terminate each data entry. Integers may be entered for floating-point
values. For example, 10 will be interpreted as 10.0. Imbedded blanks are
not allowed within a data entry unless an E precedes a single blank as
in an unsigned exponent in a floating-point number. For example, 1.0E 4
would be correctly interpreted as 1.0 × 10<sup>4</sup>.</p>
<p>The word “END” is a special data item. An “END” may have a name or label
associated with it (e.g., “END DATA”). The name or label associated with
an “END” is separated from the “END” by a single blank and is a maximum
of 12 characters long. <em>At least two blanks or a new line MUST follow
every labeled and unlabeled “END.” It is the user’s responsibility to
ensure compliance with this restriction. Failure to observe this
restriction can result in the use of incorrect or incomplete data
without the benefit of warning or error messages.</em></p>
<p>Multiple entries of the same data value can be achieved by specifying
the number of times the data value is to be entered, followed by either
R, *, or $, followed by the data value to be repeated. Imbedded blanks
are not allowed between the number of repeats and the repeat flag. For
example, 5R12, 5*12, 5$12, or 5R 12, etc., will enter five successive
12s in the input data. Multiple zeros can be specified as nZ where n is
the number of zeroes to be entered.</p>
<p>The purpose of this section is to define the input data in discrete
subsections relating to a particular type of data. Tables of the input
data are included in each subsection, and the entries are described in
more detail in the appropriate sections.</p>
<p>Resonance-corrected cross sections are generated using the appropriate
boundary conditions for the unit cell description (i.e., void for the
outer surface of a single unit, white for the outer surface of an
infinite array of cylinders). As many unit cells as needed may be
specified in a problem. A unit cell is cell-weighted by using the
keyword “CELLMIX=” followed by a unique user specified mixture number in
the unit cell data.</p>
<p>To check the input data without actually processing the cross sections,
the words “PARM=CHECK” or “PARM=CHK” should be entered, as shown below.</p>
<blockquote>
<div><div class="line-block">
<div class="line">=CSAS5 PARM=CHK</div>
<div class="line">or</div>
<div class="line">#CSAS5 PARM=CHK</div>
</div>
</div></blockquote>
<p>This will cause the input data for CSAS5 to be checked and appropriate
error messages to be printed. If plots are specified in the data, they
will be printed. This feature allows the user to debug and verify the
input data while using a minimum of computer time.</p>
<div class="section" id="xsproc-data">
<h3>XSProc data<a class="headerlink" href="#xsproc-data" title="Permalink to this headline"></a></h3>
<p>The XSProc reads the standard composition specification data and the
unit cell geometry specifications. It then produces the mixing table and
unit cell information necessary for processing the cross sections if
needed. The XSProc section of this manual provides a detailed
description of the input data and processing options.</p>
</div>
<div class="section" id="keno-v-a-data">
<h3>KENO V.a data<a class="headerlink" href="#keno-v-a-data" title="Permalink to this headline"></a></h3>
<p>If the problem utilizes a sequence that contains KENO V.a as a
functional module, the input to KENO V.a comes after the XSProc input.
<a class="reference internal" href="#tab2-2"><span class="std std-numref">Table 5</span></a> contains the outline for the KENO V.a input and the SEARCH
input, which is required for a search case (i.e., CSAS5S). The KENO V.a
input is divided into 13 data blocks and CSAS5S includes an additional
block of search data. A brief outline of commonly used data blocks is
shown in <a class="reference internal" href="#tab2-2"><span class="std std-numref">Table 5</span></a>. Note that parameter data must precede all other
KENO data blocks. Information on all KENO V.a input is provided in the
KENO chapter of this document and will not be repeated here.</p>
<span id="tab2-2"></span><table class="docutils align-center" id="id9">
<caption><span class="caption-number">Table 5 </span><span class="caption-text">Outline of KENO data</span><a class="headerlink" href="#id9" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Type of
data</strong></p></td>
<td><p><strong>Starting
flag</strong></p></td>
<td><p><strong>Comments</strong></p></td>
<td><p><strong>Termination
flag</strong></p></td>
</tr>
<tr class="row-even"><td><p>Parameters*</p></td>
<td><p>READ PARAMETER</p></td>
<td><p>Enter
desired
parameter
data</p></td>
<td><p>END PARAMETER</p></td>
</tr>
<tr class="row-odd"><td><p>Geometry</p></td>
<td><p>READ GEOMETRY</p></td>
<td><p>Enter
desired
geometry
data</p></td>
<td><p>END GEOMETRY</p></td>
</tr>
<tr class="row-even"><td><p>Array data</p></td>
<td><p>READ ARRAY</p></td>
<td><p>Enter
desired
array data</p></td>
<td><p>END ARRAY</p></td>
</tr>
<tr class="row-odd"><td><p>Boundary
conditions</p></td>
<td><p>READ BOUNDS</p></td>
<td><p>Enter
desired
boundary
conditions</p></td>
<td><p>END BOUNDS</p></td>
</tr>
<tr class="row-even"><td><p>Energy group
boundaries</p></td>
<td><p>READ ENERGY</p></td>
<td><p>Enter
desired
neutron
energy group
boundaries</p></td>
<td><p>END ENERGY</p></td>
</tr>
<tr class="row-odd"><td><p>Start data
or initial
source</p></td>
<td><p>READ START</p></td>
<td><p>Enter
desired
start data</p></td>
<td><p>END START</p></td>
</tr>
<tr class="row-even"><td><p>Plot data</p></td>
<td><p>READ PLOT</p></td>
<td><p>Enter
desired plot
data</p></td>
<td><p>END PLOT</p></td>
</tr>
<tr class="row-odd"><td><p>Grid
geometry
data</p></td>
<td><p>READ GRID</p></td>
<td><p>Enter
desired mesh
data</p></td>
<td><p>END GRID</p></td>
</tr>
<tr class="row-even"><td><p>Reaction</p></td>
<td><p>READ REACTION</p></td>
<td><p>Enter desire
reaction
tallies (CE
mode only)</p></td>
<td><p>END REACTION</p></td>
</tr>
<tr class="row-odd"><td><p>KENO V.a
data
terminus</p></td>
<td><p>END DATA</p></td>
<td><div class="line-block">
<div class="line">Enter to
signal the
end of all</div>
<div class="line">KENO V.a
data</div>
</div>
</td>
<td></td>
</tr>
<tr class="row-even"><td><p>Search data</p></td>
<td><p>READ SEARCH</p></td>
<td><p>Enter for
CSAS5</p></td>
<td><p>END SEARCH</p></td>
</tr>
<tr class="row-odd"><td><p>*Must precede
all other data
blocks in this
table.</p></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="search-data">
<h3>Search data<a class="headerlink" href="#search-data" title="Permalink to this headline"></a></h3>
<p>Search data must be entered for CSAS5S. The search data enable the code
to perform a search according to the instructions specified by the user.
The code begins reading search data when it encounters the words READ
SEARCH and continues reading search data until it encounters the words
END SEARCH. Search data consist of the search type specification and
auxiliary search commands.</p>
<div class="section" id="search-type-specification">
<h4>Search type specification<a class="headerlink" href="#search-type-specification" title="Permalink to this headline"></a></h4>
<p>These data are used to define the type of search and to set the
parameters that provide limits for the search. The search type
specification data consist of (a) a search descriptor, (b) the search
type, and (c) optional search parameters as described below.</p>
<p>SEARCH DESCRIPTOR is used to define the search mode.</p>
<blockquote>
<div><p>Use OPTIMUM if the maximum value of <em>k</em><sub>eff</sub> is to be determined.</p>
<p>Use CRITICAL if a specified value of <em>k</em><sub>eff</sub> is to be obtained.</p>
<p>Use MINIMUM if the minimum value of <em>k</em><sub>eff</sub> is to be determined.</p>
</div></blockquote>
<p>SEARCH TYPE is used to specify the variable that is to be changed during the search procedure.</p>
<blockquote>
<div><p>Use PITCH to alter the center-to-center spacing between the units at
the lowest array level. By default only the spacing in the X and
Y directions will be altered. Use DIMENSION to alter the dimensions
of one or more geometry regions in one or more units. Use
CONCENTRATION to alter the concentration of one or more standard
compositions in one or more mixtures.</p>
</div></blockquote>
<p>The combination of the search descriptor and the search type defines the
search method. Each search type has a set of predefined defaults and the
ability to change the default settings and expand the scope of the
search. Only one SEARCH DESCRIPTOR and one SEARCH TYPE are allowed in a
problem.</p>
<p>An OPTIMUM PITCH search determines the pitch that gives the maximum
value of <em>k</em><sub>eff</sub>.* By default the X spacing will be altered for slab
arrays, the X and Y spacing will be altered for arrays of cylinders, and
the X, Y, and Z spacing will be altered for spherical arrays. Auxiliary
search commands can be used to instruct the code to change any of these
defaults.</p>
<p>An OPTIMUM DIMENSION search determines the maximum value of <em>k</em><sub>eff</sub> by
altering the dimensions of one or more geometry regions in one or more
units in accordance with the specified auxiliary search commands. Only
the dimensions specified in the search commands will be modified. The
relative variations in dimensions are determined by the search constants
specified for each dimension.</p>
<p>An OPTIMUM CONCENTRATION search determines the maximum value of <em>k</em><sub>eff</sub>
by altering the concentration of standard compositions in mixtures in
accordance with specified search commands. Only the standard
compositions in the materials specified are altered. The relative
variations in concentrations are determined by the search constants
specified for each composition.</p>
<p>A CRITICAL PITCH search alters the spacing between units in the same
manner as an optimum pitch search to achieve the specified value of
<em>k</em><sub>eff</sub>. By default the X spacing will be altered for slab arrays, the
X and Y spacing will be altered for arrays of cylinders, and the X, Y,
and Z spacing will be altered for spherical arrays. Auxiliary search
commands can be used to instruct the code to change any of these
defaults.</p>
<p>A CRITICAL DIMENSION search alters the dimensions of one or more
geometry regions in accordance with the specified auxiliary search
commands to achieve the specified value of <em>k</em><sub>eff</sub>.* Only the dimensions
specified in the search commands will be modified. The relative
variations in dimensions are determined by the search constants
specified for each dimension.</p>
<p>A CRITICAL CONCENTRATION search alters the concentration of standard
compositions in mixtures in accordance with the specified auxiliary
search commands to achieve the specified value of <em>k</em><sub>eff</sub>. Only the
standard compositions in the materials specified are altered. The
relative variations in concentrations are determined by the search
constants specified for each composition.</p>
<p>A MINIMUM PITCH search determines the pitch that gives the minimum value
of <em>k</em><sub>eff</sub>. By default the X spacing will be altered for slab arrays,
the X and Y spacing will be altered for arrays of cylinders, and the X,
Y, and Z spacing will be altered for spherical arrays. Auxiliary search
commands can be used to instruct the code to change any of these
defaults.</p>
<p>A MINIMUM DIMENSION search determines the minimum value of <em>k</em><sub>eff</sub> by
altering the dimensions of one or more geometry regions in one or more
units in accordance with the specified auxiliary search commands. Only
the dimensions specified in the search commands will be modified. The
relative variations in dimensions are determined by the search constants
specified for each dimension.</p>
<p>A MINIMUM CONCENTRATION search determines the minimum value of <em>k</em><sub>eff</sub>
by altering the concentration of standard compositions in mixtures in
accordance with specified search commands. Only the standard
compositions in the materials specified are altered. The relative
variations in concentrations are determined by the search constants
specified for each composition.</p>
<p>OPTIONAL SEARCH PARAMETERS are entered after the SEARCH DESCRIPTOR AND
SEARCH TYPE and are used to alter the default values of the optional
search parameters. Only one set of optional search parameters can be
entered for a problem. The optional search parameters are listed below.</p>
<dl class="simple">
<dt>PAS=nn</dt><dd><p>is used to set the maximum number of times the search will
calculate <em>k</em><sub>eff</sub>.* The first pass calculates the <em>k</em><sub>eff</sub> corresponding
to the initial geometry dimensions. The second pass calculates the
<em>k</em><sub>eff</sub> corresponding to one of the constraints, and the third pass
often corresponds to the other constraint. After the third pass, the
search dimensions or concentrations are changed based on a fit to a
quadratic or cubic equation. The default value of nn is 10.</p>
</dd>
<dt>NPM=nn</dt><dd><p>is used to set the number of search parameters. The default value
of nn is 1 and should not be overridden.</p>
</dd>
<dt>EPS=ff</dt><dd><p>is used to set the search convergence tolerance (the amount by
which <em>k</em><sub>eff</sub> is allowed to vary from the desired <em>k</em><sub>eff</sub>)<em>.</em> An
optimum or minimum search is terminated when the calculated <em>k</em><sub>eff</sub> is
within EPS of the optimum or minimum value as indicated by the
mathematical fit to the calculated points. A critical search is
terminated when the calculated <em>k</em><sub>eff</sub> is within EPS of the specified
<em>k</em><sub>eff</sub>. The default value of ff is 0.005.</p>
</dd>
<dt>KEF=ff</dt><dd><p>is used only for a CRITICAL search. The default value of ff is
1.000.</p>
</dd>
<dt>MINPITCH=ff</dt><dd><p>is allowed ONLY for a PITCH search. It is used to specify
the minimum allowed pitch (center-to-center spacing in the X; X,Y; or
X,Y,Z directions depending on array type) between the units in an array.
The search will terminate if the pitch becomes smaller than the
specified minimum pitch. The default value of ff is the pitch at which
the region immediately inside the outer most region of the unit touches
the same region in an adjacent unit. It is much easier to specify the
minimum allowed pitch than to calculate the appropriate value of the
minimum constraint.</p>
</dd>
<dt>MAXPITCH=ff</dt><dd><p>is allowed ONLY for a PITCH search. It is used to specify
the maximum allowed pitch (center-to-center spacing in the X; X, Y; or
X, Y, Z directions depending on array type) between units in an array.
The search will terminate if the specified pitch is exceeded. The
default value of ff is the pitch corresponding to −5 times the parameter
that corresponds to the minimum pitch. It is much easier to specify a
maximum allowed pitch than to calculate the appropriate value of the
maximum constraint.</p>
</dd>
<dt>MORE</dt><dd><p>is used to terminate the optional search parameters and initiate
the auxiliary search commands. Do not enter MORE unless auxiliary search
commands are to be entered. This command may only be entered once,
immediately prior to the auxiliary search commands.</p>
</dd>
</dl>
<span id="tab2-3"></span><table class="docutils align-center" id="id10">
<caption><span class="caption-number">Table 6 </span><span class="caption-text">Outline of search type specification</span><a class="headerlink" href="#id10" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Entry</strong></p>
<p><strong>No.</strong></p>
</td>
<td><p><strong>Type of
data</strong></p></td>
<td><p><strong>Data entry</strong></p></td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-even"><td><p>1</p></td>
<td><p>Search
descriptor</p></td>
<td><p>OPTIMUM</p></td>
<td><p>Initiates a
search for the
maximum value
of <em>keff</em>.</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td><p>CRITICAL</p></td>
<td><p>Initiates a
search for a
specified value
of <em>keff</em>.</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td><p>MINIMUM</p></td>
<td><p>Initiates a
search for the
minimum value
of <em>keff</em>.</p></td>
</tr>
<tr class="row-odd"><td><p>2</p></td>
<td><p>Search type</p></td>
<td><p>PITCH</p></td>
<td><p>Vary the pitch
of an array.</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td><p>DIMENSION</p></td>
<td><p>Vary one or
more dimensions
in one or more
regions of one
or more units.</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td><p>CONCENTRATION</p></td>
<td><p>Vary the
concentration
of one or more
standard
compositions in
one or more
mixtures.</p></td>
</tr>
<tr class="row-even"><td><p>3</p></td>
<td><p>Optional search
parameters</p></td>
<td></td>
<td><p>Optional search
parameters
allow changing
default values.
Any or all may
be entered in
any order.</p></td>
</tr>
<tr class="row-odd"><td><p>3a</p></td>
<td><p>No. of search
passes</p></td>
<td><p>PAS=</p></td>
<td><p>Enter the
keyword PAS=
followed by the
desired number
of search
passes.
Default=10.</p></td>
</tr>
<tr class="row-even"><td><p>3b</p></td>
<td><p>No. of search
parameters</p></td>
<td><p>NPM=</p></td>
<td><p>Enter the
keyword NPM=
followed by the
number of
search
parameters.
Present
capability is
limited to 1.</p></td>
</tr>
<tr class="row-odd"><td><p>3c</p></td>
<td><p>Search
convergence
tolerance</p></td>
<td><p>EPS=</p></td>
<td><p>Enter the
keyword EPS=
followed by the
desired
convergence
tolerance.
Default=0.005.</p></td>
</tr>
<tr class="row-even"><td><p>3d</p></td>
<td><p>Desired value
of <em>keff</em></p></td>
<td><p>KEF=</p></td>
<td><p>Enter the
keyword KEF=
followed by the
desired value
of <em>keff</em>.
The default
value is 1.000.</p>
<p>DO NOT ENTER
FOR OPTIMUM OR
MINIMUM
SEARCHES.</p>
</td>
</tr>
<tr class="row-odd"><td><p>3e</p></td>
<td><p>Maximum allowed
pitch</p></td>
<td><p>MAXPITCH=</p></td>
<td><p>Enter the
keyword
MAXPITCH=
followed by the
maximum allowed
pitch for a
search whose
search type,
entry 2 above,
is PITCH. The
default value
is the pitch
corresponding
to −5.0 times
the parameter
at the minimum
possible pitch.</p></td>
</tr>
<tr class="row-even"><td><p>3f</p></td>
<td><p>Minimum allowed
pitch</p></td>
<td><p>MINPITCH=</p></td>
<td><p>Enter the
keyword
MINPITCH=
followed by the
minimum allowed
pitch for a
search whose
search type,
entry 2 above,
is PITCH. The
default value
is the minimum
possible pitch
(i.e., the
pitch at which
the shapes in
the array
touch).</p></td>
</tr>
<tr class="row-odd"><td><p>4</p></td>
<td><p>Additional
search data</p></td>
<td><p>MORE</p></td>
<td><p>Enter the
delimiter MORE.
This delimiter
ends the
optional search
commands and
initiates the
auxiliary
search commands
found in
Table 2.1.4.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="auxiliary-search-commands-and-constraints">
<h4>Auxiliary search commands and constraints<a class="headerlink" href="#auxiliary-search-commands-and-constraints" title="Permalink to this headline"></a></h4>
<p>Auxiliary search commands are entered <strong>only</strong> if MORE, item 4, of the
search type specification data is entered (see :numref`tab2-3`). Individual
search commands are used to specify search constraints and to
communicate to the search program. Searches can alter geometric
dimensions (PITCH or DIMENSION Search) or alter standard composition
number densities (CONCENTRATION Search).</p>
<p>A PITCH or DIMENSION search may require the user to specify the units
that will be altered, the regions that will be altered within those
units, and the faces or surfaces of those regions that will be altered.
For a PITCH search, the program automatically assigns the units in the
arrays to a unit cell if possible. If multiple units are contained in
the array, each unit could be assigned a unit cell if the data in the
unit cells match the geometry data of the units in the array. This data
may be overridden in the MORE section of the search data. For a
DIMENSION search, if the user wishes to tie a unit to unit cell this
must be explicitly done in the MORE section of the search data. Several
examples of search problems are provided in <a class="reference internal" href="#csas5-intro"><span class="std std-ref">Introduction</span></a>.</p>
<p>A CONCENTRATION search requires the user to specify the mixture,
standard composition name, and the search constant for the component
being altered. For a CONCENTRATION search, the program automatically
assigns the material being changed to a unit cell. This data may be
overridden in the MORE section of the search data. Several examples of
search problems are provided in <a class="reference internal" href="#csas5-intro"><span class="std std-ref">Introduction</span></a>.</p>
<p>The data comprising the auxiliary search commands are listed in
<a class="reference internal" href="#tab2-4"><span class="std std-numref">Table 7</span></a>. All data except items 1a, 1b, and 1c are keyworded (i.e.,
the data are entered by specifying a keyword, followed by a value).
An explanation of each individual search command follows the table.</p>
<dl>
<dt>1 Command Definition</dt><dd><p>A command definition tells the code what action is to be taken.  A new search command is
initiated whenever an item 1a through 1c is encountered.  The code will vary the geometry
according to subsequent commands.</p>
</dd>
<dt>1a. ALTER CHANGE MODIFY</dt><dd><p>Alter geometry regions. These words specify that modifications will be made to the geometry
according to subsequent commands.</p>
</dd>
<dt>1b. MAINTAIN</dt><dd><p>Maintain the thickness.  The thickness of the specified geometry region(s) will be maintained
when the interior regions grow or shrink (i.e., the specified region will grow or shrink in
conjunction with the interior region in such a way as to maintain the original distance between the two regions).
This means that the original thickness of the region is preserved.  For instance, the inner radius of a pipe
can be altered and the wall thickness can be preserved by applying the MAINTAIN command to the region defining
the outer radius of the pipe.</p>
</dd>
<dt>1c. KEEP HOLD</dt><dd><p>Keep the original specification.  This command causes the specified geometry region(s)
to be reset to their original input value for every search pass.  Therefore they go
through the entire search process unchanged.</p>
</dd>
<dt>2 PAR=</dt><dd><p>Parameter number.  The search parameter number is not functional.  The default number is 1 and should not be overridden.</p>
</dd>
<dt>3 +CON=</dt><dd><p>Maximum constraint.  Enter the maximum value you wish to allow the search parameter to obtain.
The maximum constraint must be larger than the minimum constraint.  For a DIMENSION or PITCH
search the default value of the maximum constraint is 1011.  For a CONCENTRATION search the default
value of the maximum constraint is as follows:</p>
<blockquote>
<div><p>+CON= min(−1/FACTOR ), if any FACTOR &lt; 0</p>
<p>+CON= −5*(−CON ), if all FACTOR &gt; 0</p>
</div></blockquote>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>For a PITCH search, the maximum constraint is redefined and is calculated from the data entered for MAXPITCH.
+CON should not be entered if a value was entered for MAXPITCH.  If constraints, +CON= and/or −CON= are
not entered as data, the code computes the minimum constraint corresponding to the pins touching,
and the maximum constraint is then negative five times the magnitude of the minimum constraint.</p>
</div>
<dl>
<dt>4 −CON=</dt><dd><p>Minimum constraint.  Enter the minimum value you wish to allow the search parameter to obtain.
The minimum constraint must be smaller than the maximum constraint but need not be a negative number.
The default value of the minimum constraint for a dimension search is −1011.
The default value of the minimum constraint for a pitch search is redefined to correspond to the pins
in the lattice touching.  For a CONCENTRATION search the default value of the minimum constraint is as follows:</p>
<blockquote>
<div><p>−CON= −5(+CON ), if all FACTOR &lt; 0</p>
<p>−CON= max(−1/FACTOR ), if any FACTOR &gt; 0</p>
</div></blockquote>
</dd>
<dt>5 CELL=</dt><dd><p>Unit Cell Number.  This is the unit cell to which the unit or mixture will be tied.
It needs to follow either the UNIT= or MIX= keyword data.  Tying a unit cell to a unit or mixture
ensures the unit cell data gets changed as the geometry or mixture data gets changed thus ensuring the
cross sections are properly processed.</p>
</dd>
<dt>6 UNIT=</dt><dd><p>Geometry unit number.  This is the geometry unit to which the previously entered command definition
(item 1a, 1b, or 1c) is applied.  Items 7, 8, and 9 specify the region(s) within the unit and the surfaces of
the region(s) to be altered.</p>
</dd>
<dt>7 REGION=</dt><dd><p>First region to be altered.  This is used to specify the first or only region in the unit (specified by item 6)
that is to be altered according to the search command (item 1a, 1b, or 1c).  The region(s) are altered according
to the search constants (items 9a, 9b, 9c, and/or 9d).</p>
</dd>
<dt>8 TO</dt><dd><p>Last region to be altered.  This item is entered to specify the last region to be altered,
starting with the region specified by REG=.  For example, assume unit 3 contains eight regions and you
wish to make changes to regions 4, 5, 6, 7, and 8.  These regions are identified by entering the following data.
UNIT=3  REG=4 TO 8.</p>
</dd>
</dl>
<p>Geometric search constants.  A search constant is the proportionality factor utilized to alter a geometry region.
A search constant must be entered for each surface of a region that is to be altered.
A nonzero search constant will cause the region dimension for that surface to be changed.
A search constant of 0.0 will cause the region dimension to remain unchanged.
The default value of the search constant is 0.0.</p>
<dl class="simple">
<dt>9 ALL=</dt><dd><p>Search constant for all surfaces.  All of the surfaces in a region are altered simultaneously by using this search command.</p>
</dd>
<dt>9a. +X=</dt><dd><p>Search constant for +X face.  This parameter is used to specify the value of the search constant for the +X face of a cuboid.</p>
</dd>
<dt>9a. -X=</dt><dd><p>Search constant for −X face.  This parameter is used to specify the value of the search constant for the −X face of a cuboid.</p>
</dd>
<dt>9a. +Y=</dt><dd><p>Search constant for +Y face.  This parameter is used to specify the value of the search constant for the +Y face of a cuboid.</p>
</dd>
<dt>9a. -Y=</dt><dd><p>Search constant for −Y face.  This parameter is used to specify the value of the search constant for the −Y face of a cuboid.</p>
</dd>
<dt>9a. +Z=</dt><dd><p>Search constant for +Z face.  This parameter is used to specify the value of the search constant for the +Z face of a cuboid.</p>
</dd>
<dt>9a. -Z=</dt><dd><p>Search constant for −Z face.  This parameter is used to specify the value of the search constant for the −Z face of a cuboid.</p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>If it is desirable to change all the faces of a cuboid except the −Z face by some amount
(search constant of 1.0), items 9a and 9b can be used together as follows:  ALL=1.0 −Z=0.0.
This is the same as entering +X=1.0 −X=1.0 +Y=1.0 −Y=1.0 +Z=1.0.  If both Z faces are to remain unchanged,
items 8a and 8b can be entered as:  ALL=1.0 +Z=0.0 −Z=0.0 or as +X=1.0 −X=1.0 +Y=1.0 −Y=1.0.</p>
</div>
<dl class="simple">
<dt>9b. RADIUS=</dt><dd><p>Search constant for radius.  This parameter is used to specify the value of the search constant for the radius of a
sphere, hemisphere, cylinder, or hemicylinder.</p>
</dd>
<dt>9c. +HEIGHT=</dt><dd><p>Search constant for +height.  This parameter is used to specify the value of the search constant for the
+height of a cylinder or hemicylinder.</p>
</dd>
<dt>9c. -HEIGHT=</dt><dd><p>Search constant for −height.  This parameter is used to specify the value of the search constant for the −height of
a cylinder or hemicylinder.</p>
</dd>
<dt>9d. CHORD=</dt><dd><p>Search constant for chord.  This parameter is used to specify the value of the search constant for the
chord of a hemisphere or hemicylinder.</p>
</dd>
<dt>10 MIX=</dt><dd><p>Search constant for mixture.  This parameter is the mixture number containing the standard composition that
is to be changed during the search.</p>
</dd>
<dt>11 SCNAME=</dt><dd><p>Search constant for the standard composition name.  This parameter is the standard composition name associated with
the material that is to be changed during the search.  Only compositions listed in the
<em>Standard Composition Library</em> section of the Standard Composition Library chapter are allowed (SECTIONREFERENCE).
Standard compositions beginning with SOLN cannot be altered directly.</p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>If the standard composition name specified in the Material Information Data
begins with SOLN and the Concentration Search Data specifies SCNAME=UO2(NO3)2, the amount of UO2(NO3)2
in the solution is altered but the amount of H2O and nitric acid is not altered during the search.
The resulting mixture, when the search is finished, may no longer meet the criteria associated with the SOLN
specification.</p>
</div>
<dl class="simple">
<dt>12 FACTOR=</dt><dd><p>Concentration search factor used to specify the value of the search constant used in the concentration search.
It is a proportionality factor used to alter the specified mixture standard composition.  A search constant must
be entered for each standard composition that is altered.  A non-zero search constant will cause the concentration
of the associated standard composition to be altered.  The default value of the search constant is 1.0.
A set of concentration search data consists of the mixture to be altered, the standard composition to be
altered in the mixture, and the search factor.  Keywords are used to enter the data.  Each set of data consists of
items 10, 11, and 12.  The keywords used in this data may be entered using terse notation.</p>
</dd>
</dl>
<span id="tab2-4"></span><table class="docutils align-center" id="id11">
<caption><span class="caption-number">Table 7 </span><span class="caption-text">Outline of auxiliary search commands and constraints</span><a class="headerlink" href="#id11" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Entry</strong></p>
<p><strong>no.</strong></p>
</td>
<td><p><strong>Keyword</strong></p>
<p><strong>name</strong></p>
</td>
<td><p><strong>Type of
data</strong></p></td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-even"><td><p>GENERIC SEARCH
DATA — May be
used with all
Search Types —</p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>1a</p></td>
<td><p>ALTER</p>
<p>CHANGE MODIFY</p>
</td>
<td><p>Begin a new
search command</p></td>
<td><p>These words are
used to specify
that
modifications
will be made to
the geometry or
concentration
according to
subsequent
commands
(entries 3
through 12 as
required to
specify the
desired
changes).</p></td>
</tr>
<tr class="row-even"><td><p>1b</p></td>
<td><p>MAINTAIN</p></td>
<td><p>Begin a new
search command</p></td>
<td><p>The spacing
(thickness) of
the specified
geometry
regions will be
maintained when
the interior
regions grow or
shrink.</p></td>
</tr>
<tr class="row-odd"><td><p>1c</p></td>
<td><p>KEEP</p>
<p>HOLD</p>
</td>
<td><p>Begin a new
search command</p></td>
<td><p>This command
resets the
specified
geometry to the
original input
specifications.</p></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>PAR=</p></td>
<td><p>Parameter
number</p></td>
<td><p>Enter the
parameter
number that the
current command
(ALTER,
MAINTAIN, KEEP)
applies to.
Default=1 and
should not be
changed.</p></td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>+CON=</p></td>
<td><p>Maximum
constraint</p></td>
<td><p>Enter the
maximum
constraint for
the current
parameter.
Default =
+10E10.</p></td>
</tr>
<tr class="row-even"><td><p>4</p></td>
<td><p>−CON=</p></td>
<td><p>Minimum
constraint</p></td>
<td><p>Enter the
minimum
constraint for
the current
parameter.
Default =
−10E10.</p></td>
</tr>
<tr class="row-odd"><td><p>5</p></td>
<td><p>CELL=</p></td>
<td><p>Unit Cell
Associated with
search data</p></td>
<td><p>Default values
are assigned
for PITCH and
CONCENTRATION
searches.
Associated Unit
Cells must be
entered for a
DIMENSION
search if
desired.</p></td>
</tr>
<tr class="row-even"><td><p>PITCH &amp;
DIMENSION
SEARCH DATA —
Defines
Geometric
Changes —</p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>6</p></td>
<td><p>UNIT=</p></td>
<td><p>Unit to which
the current
command applies</p></td>
<td><p>Enter the unit
in which
regions are to
be altered.</p></td>
</tr>
<tr class="row-even"><td><p>7</p></td>
<td><p>REGION=</p></td>
<td><p>First region to
be altered in
the unit</p></td>
<td><p>Enter the first
or only region
in the unit
that the search
constants
(entry 9a, b, c
and/or d) apply
to. Default is
the first
region.</p></td>
</tr>
<tr class="row-odd"><td><p>8</p></td>
<td><p>TO</p></td>
<td><p>Last region to
be altered in
the unit</p></td>
<td><p>Enter the last
region in the
unit to which
the search
constants apply
(entry 9a, b, c
and/or d).</p>
<blockquote>
<div><p>Default is
the first
region.</p>
</div></blockquote>
</td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><strong>NOTE:</strong>
Entry 7 must be
entered in
order to alter
a single region
in a unit.
Entries 7 and 8
must both be
entered in
order to alter
more than one
region in a
unit.</p></td>
</tr>
</tbody>
</table>
<table class="docutils align-default">
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p>Table 2.1.4.
Outline of
auxiliary
search commands
and constraints
(continued)</p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p><strong>Entry</strong></p>
<p><strong>no.</strong></p>
</td>
<td><p><strong>Keyword</strong></p>
<p><strong>name</strong></p>
</td>
<td><p><strong>Type of
data</strong></p></td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-odd"><td><p>9</p></td>
<td><p>ALL=</p></td>
<td><p>Search constant
for all
surfaces
(faces) of the
region(s)</p></td>
<td><p>Enter a value
for the search
constants for
the specified
regions.
This value will
be applied to
all surfaces of
the region(s).</p></td>
</tr>
<tr class="row-even"><td><p>9a</p></td>
<td><p>+X=</p></td>
<td><p>Search constant
for +X face of
cuboid</p></td>
<td><p>Enter a value
for the search
constant for
the +X face
of a cuboid.</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>−X=</p></td>
<td><p>Search constant
for −X face of
cuboid</p></td>
<td><p>Enter a value
for the search
constant for
the −X face
of a cuboid.</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>+Y=</p></td>
<td><p>Search constant
for +Y face of
cuboid</p></td>
<td><p>Enter a value
for the search
constant for
the +Y face
of a cuboid.</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>−Y=</p></td>
<td><p>Search constant
for −Y face of
cuboid</p></td>
<td><p>Enter a value
for the search
constant for
the −Y face
of a cuboid.</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>+Z=</p></td>
<td><p>Search constant
for +Z face of
cuboid</p></td>
<td><p>Enter a value
for the search
constant for
the +Z face
of a cuboid.</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>−Z=</p></td>
<td><p>Search constant
for −Z face of
cuboid</p></td>
<td><p>Enter a value
for the search
constant for
the −Z face
of a cuboid.</p></td>
</tr>
<tr class="row-even"><td><p>9b</p></td>
<td><p>RADIUS=</p></td>
<td><p>Search constant
for radius</p></td>
<td><p>Enter a value
for the search
constant for
the radius
of a sphere or
a cylinder.</p></td>
</tr>
<tr class="row-odd"><td><p>9c</p></td>
<td><p>+HEIGHT=</p></td>
<td><p>Search constant
for +height</p></td>
<td><p>Enter a value
for the search
constant for
the +height
of a cylinder.</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>−HEIGHT=</p></td>
<td><p>Search constant
for −height</p></td>
<td><p>Enter a value
for the search
constant for
the −height
of a cylinder.</p></td>
</tr>
<tr class="row-odd"><td><p>9d</p></td>
<td><p>CHORD=</p></td>
<td><p>Search constant
for chord</p></td>
<td><p>Enter a value
for the search
constant for
the chord face
of a hemisphere
or
hemicylinder.</p></td>
</tr>
<tr class="row-even"><td><p>CONCENTRATION
SEARCH DATA —
Defines
concentration
changes —</p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>10</p></td>
<td><p>MIX=</p></td>
<td><p>Search constant
for mixture</p></td>
<td><p>Enter the
mixture number
containing the
standard
composition to
be changed.</p></td>
</tr>
<tr class="row-even"><td><p>11</p></td>
<td><p>SCNAME=</p></td>
<td><p>Search constant
for Standard
Composition</p></td>
<td><p>Enter the
standard
composition
name whose
density is to
be changed.</p></td>
</tr>
<tr class="row-odd"><td><p>12</p></td>
<td><p>FACTOR=</p></td>
<td><p>Search
proportionality
constant</p></td>
<td><p>Enter the value
of the search
constant for
the
concentration
search.</p></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="section" id="example-problems">
<h2>Example problems<a class="headerlink" href="#example-problems" title="Permalink to this headline"></a></h2>
<p>This section contains example problems to demonstrate some of the options available in CSAS5 and its
associated sequences.  A brief problem description and the associated input data for multigroup mode of
calculation are included for each problem.  The same sample problems may be executed in the continuous
energy mode by changing the library name from “v7-238” to “ce_v7”.  The sample problems can also be
executed with the multigroup or continuous energy libraries based on ENDF/B-VII.1. The complete list
of libraries distributed with SCALE is provided in the Nuclear Data Libraries (SECTIONREFERENCE) section of the SCALE manual.
Note that sample problems 3, 7, and 8 do not run in the continuous energy mode because they use CELLMIX or
DOUBLEHET cell type.  See Appendix A (CSAS5App) for additional and historical examples.</p>
<div class="section" id="sample-problem-1-keff-calculation">
<h3>Sample problem 1: <em>k</em><sub>eff</sub> calculation<a class="headerlink" href="#sample-problem-1-keff-calculation" title="Permalink to this headline"></a></h3>
<p>The purpose of this problem is to calculate the k-effective of a
system. This problem is the same as the KENO V.a sample problem 12 in
Appendix B (SECTIONREFERENCE) except the cross-section library and KENO V.a mixing table
are prepared by CSAS. The problem represents a critical experiment
consisting of a composite array <a class="bibtex reference internal" href="KenoC.html#thomas-critical-1973" id="id2">[Tho73]</a><a class="bibtex reference internal" href="KenoC.html#thomas-critical-1964" id="id3">[Tho64]</a> of four
highly-enriched (93.2%) uranium metal cylinders having a density of
18.76 g/cc and four 5.0677-L Plexiglas containers filled with uranyl
nitrate solution. The uranium metal cylinders have a radius of
5.748 cm and a height of 10.765 cm. The uranyl nitrate solution has a
specific gravity of 1.555 and contains 415 g of uranium per liter. The
ID of the Plexiglas bottle is 19.05 cm and the inside height is
17.78 cm. The Plexiglas is 0.635 cm thick. The center-to-center
spacing between the metal units is 13.18 cm in the Y direction and
13.45 cm in the Z direction. The center-to-center spacing between the
solution units is 21.75 cm in the Y direction and 20.48 cm in the
Z direction. The spacing between the Y-Z plane that passes through the centers of the metal units and the
Y-Z plane that passes through the centers of the solution units is
17.465 cm in the X direction.</p>
<p>The metal units in this experiment are designated in Table II of Ref. 2
as cylinder index 11 and reflector index 1. A photograph of the
experiment, Fig. 9 in Ref. 3, is given in <a class="reference internal" href="#fig2-1-1"><span class="std std-numref">Fig. 11</span></a>.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5   parm=(centrm)</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">1</span>  <span class="err">set</span> <span class="err">up</span> <span class="m">4</span><span class="err">aqueous</span> <span class="m">4</span> <span class="err">metal</span> <span class="err">in</span> <span class="err">csas</span><span class="m">5</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">composition</span>
  <span class="err">uranium</span>        <span class="m">1</span> <span class="m">0</span><span class="err">.</span><span class="m">985</span> <span class="m">300</span><span class="err">.</span>  <span class="m">92235</span> <span class="m">93</span><span class="err">.</span><span class="m">2</span> <span class="m">92238</span> <span class="m">5</span><span class="err">.</span><span class="m">6</span> <span class="m">92234</span> <span class="m">1</span><span class="err">.</span><span class="m">0</span> <span class="m">92236</span> <span class="m">0</span><span class="err">.</span><span class="m">2</span> <span class="n">end</span>
  <span class="err">solution</span>
     <span class="err">mix=</span><span class="m">2</span>
     <span class="err">rho[uo</span><span class="m">2</span><span class="err">(no</span><span class="m">3</span><span class="err">)</span><span class="m">2</span><span class="err">]=</span> <span class="m">415</span><span class="err">.</span> <span class="m">92235</span> <span class="m">92</span><span class="err">.</span><span class="m">6</span> <span class="m">92238</span> <span class="m">5</span><span class="err">.</span><span class="m">9</span> <span class="m">92234</span> <span class="m">1</span><span class="err">.</span><span class="m">0</span>  <span class="m">92236</span> <span class="m">0</span><span class="err">.</span><span class="m">5</span>
     <span class="err">molar[hno</span><span class="m">3</span><span class="err">]=</span><span class="m">9</span><span class="err">.</span><span class="m">783</span><span class="err">-</span><span class="m">3</span>
     <span class="err">temperature=</span><span class="m">300</span>
  <span class="n">end</span><span class="err"> </span><span class="n">solution</span>
  <span class="err">plexiglass</span>     <span class="m">3</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">composition</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span>
  <span class="err">flx=yes</span> <span class="err">fdn=yes</span> <span class="err">nub=yes</span>
<span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">unit</span> <span class="m">1</span>
    <span class="err">com=</span><span class="s">&#39;uranyl nitrate solution in a plexiglas container&#39;</span>
    <span class="err">cylinder</span>  <span class="m">2</span> <span class="m">1</span> <span class="m">9</span><span class="err">.</span><span class="m">525</span> <span class="m">2</span><span class="err">p</span><span class="m">8</span><span class="err">.</span><span class="m">89</span>
    <span class="err">cylinder</span>  <span class="m">3</span> <span class="m">1</span> <span class="m">10</span><span class="err">.</span><span class="m">16</span> <span class="m">2</span><span class="err">p</span><span class="m">9</span><span class="err">.</span><span class="m">525</span>
    <span class="err">cuboid</span>  <span class="m">0</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">10</span><span class="err">.</span><span class="m">875</span> <span class="m">2</span><span class="err">p</span><span class="m">10</span><span class="err">.</span><span class="m">24</span>
  <span class="err">unit</span> <span class="m">2</span>
    <span class="err">com=</span><span class="s">&#39;uranium metal cylinder&#39;</span>
    <span class="err">cylinder</span>  <span class="m">1</span> <span class="m">1</span> <span class="m">5</span><span class="err">.</span><span class="m">748</span> <span class="m">2</span><span class="err">p</span><span class="m">5</span><span class="err">.</span><span class="m">3825</span>
    <span class="err">cuboid</span>  <span class="m">0</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">6</span><span class="err">.</span><span class="m">59</span> <span class="m">2</span><span class="err">p</span><span class="m">6</span><span class="err">.</span><span class="m">225</span>
  <span class="err">unit</span> <span class="m">3</span>
    <span class="err">com=</span><span class="s">&#39;1x2x2 array of solution units&#39;</span>
    <span class="err">array</span> <span class="m">1</span> <span class="m">3</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">0</span>
  <span class="err">unit</span> <span class="m">4</span>
    <span class="err">com=</span><span class="s">&#39;1x2x2 array of metal units padded to match solution array&#39;</span>
    <span class="err">array</span> <span class="m">2</span> <span class="m">3</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">0</span>
    <span class="err">replicate</span> <span class="m">0</span> <span class="m">1</span> <span class="m">2</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">0</span> <span class="m">2</span><span class="err">*</span><span class="m">8</span><span class="err">.</span><span class="m">57</span> <span class="m">2</span><span class="err">*</span><span class="m">8</span><span class="err">.</span><span class="m">03</span> <span class="m">1</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">5</span>
    <span class="err">array</span> <span class="m">3</span> <span class="m">3</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">0</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">read</span><span class="err"> </span><span class="n">array</span>
  <span class="err">ara=</span><span class="m">1</span> <span class="err">nux=</span><span class="m">1</span> <span class="err">nuy=</span><span class="m">2</span> <span class="err">nuz=</span><span class="m">2</span> <span class="err">fill</span> <span class="err">f</span><span class="m">1</span> <span class="n">end</span><span class="err"> </span><span class="n">fill</span>
  <span class="err">ara=</span><span class="m">2</span> <span class="err">nux=</span><span class="m">1</span> <span class="err">nuy=</span><span class="m">2</span> <span class="err">nuz=</span><span class="m">2</span> <span class="err">fill</span> <span class="err">f</span><span class="m">2</span> <span class="n">end</span><span class="err"> </span><span class="n">fill</span>
  <span class="err">gbl=</span><span class="m">3</span> <span class="err">ara=</span><span class="m">3</span> <span class="err">nux=</span><span class="m">2</span> <span class="err">nuy=</span><span class="m">1</span> <span class="err">nuz=</span><span class="m">1</span>
  <span class="err">com=</span><span class="s">&#39;composite array of solution and metal units&#39;</span>
  <span class="err">fill</span> <span class="m">4</span> <span class="m">3</span> <span class="n">end</span><span class="err"> </span><span class="n">fill</span>
<span class="n">end</span><span class="err"> </span><span class="n">array</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">end</span>
</pre></div>
</div>
<div class="figure align-center" id="id12">
<span id="fig2-1-1"></span><a class="reference internal image-reference" href="_images/fig12.png"><img alt="_images/fig12.png" src="_images/fig12.png" style="width: 400px;" /></a>
<p class="caption"><span class="caption-number">Fig. 11 </span><span class="caption-text">Critical assembly of four solution units and four metal units.</span><a class="headerlink" href="#id12" title="Permalink to this image"></a></p>
</div>
</div>
<div class="section" id="sample-problem-2-optimum-pitch-search-using-detailed-geometry">
<h3>Sample problem 2: optimum pitch search using detailed geometry<a class="headerlink" href="#sample-problem-2-optimum-pitch-search-using-detailed-geometry" title="Permalink to this headline"></a></h3>
<p>This problem represents an attempt to optimize the reactivity of
PWR-like fuel bundles in a storage pool. The storage array is an
infinite planar array of flooded fuel bundles. Each bundle consists of a
17 × 17 × 1 array of 2.35%-enriched UO<sub>2</sub> pins, density
9.21 g/cc, clad with Zircaloy-2. The fuel is 0.823 cm in diameter, the
clad diameter is 0.9627 cm, and the length of each pin is 366 cm. Each
fuel bundle is encased in a Boral sheath. There is a 1/4-in. gap flooded
with water between the bundle and the sheath. The Boral sheath is
3/8 in. thick. One inch of water separates the fuel bundle sheaths in
the horizontal plane, and 15 cm of water is present on the top and
bottom of the array.</p>
<p>The KENO V.a geometry represents each fuel pin in the bundle discretely.
The search should determine the optimum pitch within the fuel bundle.
The gap between the bundle and the Boral remains fixed, as does the
thickness of the sheath and the spacing between sheaths.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5s</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">2</span>  <span class="err">storage</span> <span class="err">array</span> <span class="err">of</span> <span class="err">pwr-like</span> <span class="err">fuel</span> <span class="err">bundles</span> <span class="err">in</span> <span class="err">poison</span> <span class="err">sheaths</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">composition</span>
  <span class="err">uo</span><span class="m">2</span>    <span class="m">1</span> <span class="err">.</span><span class="m">84</span> <span class="m">300</span><span class="err">..</span> <span class="m">92235</span> <span class="m">2</span><span class="err">.</span><span class="m">35</span> <span class="m">92238</span> <span class="m">97</span><span class="err">.</span><span class="m">65</span> <span class="n">end</span>
  <span class="err">zirc</span><span class="m">2</span>  <span class="m">2</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">3</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">b</span><span class="m">4</span><span class="err">c</span>    <span class="m">4</span> <span class="err">den=</span><span class="m">2</span><span class="err">.</span><span class="m">65</span> <span class="m">0</span><span class="err">.</span><span class="m">3517</span> <span class="n">end</span>
  <span class="err">al</span>     <span class="m">4</span> <span class="err">den=</span><span class="m">2</span><span class="err">.</span><span class="m">65</span> <span class="m">0</span><span class="err">.</span><span class="m">6483</span> <span class="n">end</span>
  <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">5</span> <span class="m">1</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">composition</span>
<span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
  <span class="err">latticecell</span>  <span class="err">squarepitch</span>  <span class="err">pitch=</span><span class="m">1</span><span class="err">.</span><span class="m">2751</span> <span class="m">3</span> <span class="err">fueld=.</span><span class="m">823</span> <span class="m">1</span> <span class="err">cladd=.</span><span class="m">9627</span> <span class="m">2</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span>
  <span class="err">nub=yes</span> <span class="err">far=yes</span> <span class="err">gen=</span><span class="m">103</span> <span class="err">npg=</span><span class="m">500</span> <span class="err">gas=no</span> <span class="err">fdn=yes</span>
<span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">unit</span> <span class="m">1</span>
    <span class="err">cylinder</span>  <span class="m">1</span> <span class="m">1</span> <span class="err">.</span><span class="m">4115</span> <span class="m">183</span><span class="err">.</span><span class="m">0</span> <span class="err">-</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
    <span class="err">cylinder</span>  <span class="m">2</span> <span class="m">1</span> <span class="err">.</span><span class="m">48135</span> <span class="m">183</span><span class="err">.</span><span class="m">1</span> <span class="err">-</span><span class="m">183</span><span class="err">.</span><span class="m">1</span>
    <span class="err">cuboid</span>    <span class="m">3</span> <span class="m">1</span> <span class="err">.</span><span class="m">63755</span> <span class="err">-.</span><span class="m">63755</span> <span class="err">.</span><span class="m">63755</span> <span class="err">-.</span><span class="m">63755</span> <span class="m">183</span><span class="err">.</span><span class="m">1</span> <span class="err">-</span><span class="m">183</span><span class="err">.</span><span class="m">1</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">2</span>
    <span class="err">array</span>     <span class="m">1</span> <span class="m">3</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">0</span>
    <span class="err">reflector</span> <span class="m">5</span> <span class="m">1</span> <span class="m">4</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">635</span>  <span class="m">2</span><span class="err">z</span>    <span class="m">1</span>
    <span class="err">reflector</span> <span class="m">4</span> <span class="m">1</span> <span class="m">4</span><span class="err">*</span><span class="m">0</span><span class="err">.</span><span class="m">9525</span> <span class="m">2</span><span class="err">z</span>    <span class="m">1</span>
    <span class="err">reflector</span> <span class="m">5</span> <span class="m">1</span> <span class="m">4</span><span class="err">*</span><span class="m">1</span><span class="err">.</span><span class="m">27</span>   <span class="m">2</span><span class="err">z</span>    <span class="m">1</span>
    <span class="err">reflector</span> <span class="m">5</span> <span class="m">2</span> <span class="m">4</span><span class="err">z</span>       <span class="m">2</span><span class="err">*</span><span class="m">3</span><span class="err">.</span><span class="m">0</span> <span class="m">5</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">read</span><span class="err"> </span><span class="n">array</span>
  <span class="err">ara=</span><span class="m">1</span> <span class="err">nux=</span><span class="m">17</span> <span class="err">nuy=</span><span class="m">17</span> <span class="err">nuz=</span><span class="m">1</span> <span class="err">fill</span> <span class="err">f</span><span class="m">1</span> <span class="n">end</span><span class="err"> </span><span class="n">fill</span>
<span class="n">end</span><span class="err"> </span><span class="n">array</span>
<span class="n">read</span><span class="err"> </span><span class="n">bounds</span>
  <span class="err">xyf=mirror</span>
<span class="n">end</span><span class="err"> </span><span class="n">bounds</span>
<span class="n">read</span><span class="err"> </span><span class="n">bias</span>
  <span class="err">id=</span><span class="m">500</span> <span class="m">2</span> <span class="m">6</span>
<span class="n">end</span><span class="err"> </span><span class="n">bias</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">read</span><span class="err"> </span><span class="n">search</span>
  <span class="err">optimum</span> <span class="err">pitch</span>
<span class="n">end</span><span class="err"> </span><span class="n">search</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-problem-3-optimum-pitch-search-using-homogenized-geometry">
<h3>Sample problem 3: optimum pitch search using homogenized geometry<a class="headerlink" href="#sample-problem-3-optimum-pitch-search-using-homogenized-geometry" title="Permalink to this headline"></a></h3>
<p>This problem illustrates the use of a cell-weighted mixture to represent
a PWR-like fuel bundle. The cask contains a 2 × 2 × 1 array of fuel
bundles. Each fuel bundle consists of a 17 × 17 × 1 array of Zircaloy-2
clad, 2.35%-enriched UO<sub>2</sub> fuel pins with a density of 9.21 g/cc
arranged in a square pitch. The pin diameter is 0.823 cm, and its length
is 366 cm. The clad is 0.06985 cm thick, and the pitch is 1.275 cm. Each
fuel bundle is contained in a 0.6625-cm-thick Boral sheath. The bundles
are separated by 1 cm of water, representing a flooded cask. The square
aluminum cask is 10-cm thick on all faces and is reflected by 15 cm of
water.</p>
<p>By using CELLMIX=, a cell-weighted cross section is created to represent
the fuel bundle. The KENO V.a geometry utilizes the cell-weighted
mixture (500) and the overall dimensions of the fuel bundle to represent
the entire fuel bundle as a single homogeneous region. The first
reflector entry represents the fuel cask, and the second reflector entry
represents the 15-cm reflector. Because this problem utilizes a
cell-weighted mixture, which is not applicable in the continuous energy
mode, the problem will end with an error message in the continuous
energy mode.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5s</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">3</span>  <span class="err">sample</span> <span class="err">square</span> <span class="err">fuel</span> <span class="err">cask</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">composition</span>
  <span class="err">uo</span><span class="m">2</span>    <span class="m">1</span> <span class="err">.</span><span class="m">84</span> <span class="m">300</span><span class="err">.</span> <span class="m">92235</span> <span class="m">2</span><span class="err">.</span><span class="m">35</span> <span class="m">92238</span> <span class="m">97</span><span class="err">.</span><span class="m">65</span> <span class="n">end</span>
  <span class="err">zirc</span><span class="m">2</span>  <span class="m">2</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">3</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">b</span><span class="m">4</span><span class="err">c</span>    <span class="m">4</span> <span class="err">den=</span><span class="m">2</span><span class="err">.</span><span class="m">65</span> <span class="m">0</span><span class="err">.</span><span class="m">3517</span> <span class="n">end</span>
  <span class="err">al</span>     <span class="m">4</span> <span class="err">den=</span><span class="m">2</span><span class="err">.</span><span class="m">65</span> <span class="m">0</span><span class="err">.</span><span class="m">6483</span> <span class="n">end</span>
  <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">5</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">al</span>     <span class="m">6</span> <span class="m">1</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">composition</span>
<span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
  <span class="err">latticecell</span>
  <span class="err">squarepitch</span>  <span class="err">pitch=</span><span class="m">1</span><span class="err">.</span><span class="m">275</span> <span class="m">3</span> <span class="err">fueld=.</span><span class="m">823</span> <span class="m">1</span> <span class="err">cladd=.</span><span class="m">9627</span> <span class="m">2</span> <span class="err">cellmix=</span><span class="m">500</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span>
  <span class="err">nub=yes</span> <span class="err">far=yes</span> <span class="err">gen=</span><span class="m">103</span> <span class="err">npg=</span><span class="m">500</span> <span class="err">gas=no</span> <span class="err">fdn=yes</span>
<span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">unit</span> <span class="m">1</span>
    <span class="err">cuboid</span>  <span class="m">500</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">10</span><span class="err">.</span><span class="m">8375</span> <span class="m">2</span><span class="err">p</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
    <span class="err">cuboid</span>    <span class="m">4</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">11</span><span class="err">.</span><span class="m">5</span>    <span class="m">2</span><span class="err">p</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
    <span class="err">cuboid</span>    <span class="m">5</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">12</span><span class="err">.</span><span class="m">0</span>    <span class="m">2</span><span class="err">p</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">2</span>
    <span class="err">array</span>     <span class="m">1</span> <span class="m">3</span><span class="err">*</span><span class="m">0</span>
    <span class="err">reflector</span> <span class="m">6</span> <span class="m">1</span> <span class="m">6</span><span class="err">*</span><span class="m">10</span><span class="err">.</span><span class="m">0</span> <span class="m">1</span>
    <span class="err">reflector</span> <span class="m">5</span> <span class="m">2</span> <span class="m">6</span><span class="err">*</span><span class="m">3</span> <span class="m">5</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">read</span><span class="err"> </span><span class="n">array</span>
  <span class="err">ara=</span><span class="m">1</span>  <span class="err">nux=</span><span class="m">2</span>  <span class="err">nuy=</span><span class="m">2</span>  <span class="err">nuz=</span><span class="m">1</span> <span class="err">fill</span> <span class="err">f</span><span class="m">1</span> <span class="n">end</span><span class="err"> </span><span class="n">fill</span>
<span class="n">end</span><span class="err"> </span><span class="n">array</span>
<span class="n">read</span><span class="err"> </span><span class="n">bias</span>
  <span class="err">id=</span><span class="m">500</span> <span class="m">2</span> <span class="m">6</span>
<span class="n">end</span><span class="err"> </span><span class="n">bias</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">read</span><span class="err"> </span><span class="n">search</span>
  <span class="err">optimum</span> <span class="err">pitch</span>
<span class="n">end</span><span class="err"> </span><span class="n">search</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-problem-4-search-for-a-specified-value-of-keff">
<h3>Sample problem 4: search for a specified value of <em>k</em><sub>eff</sub><a class="headerlink" href="#sample-problem-4-search-for-a-specified-value-of-keff" title="Permalink to this headline"></a></h3>
<p>Find the pitch at which a 2 × 2 × 2 array of cylinders of highly
enriched (93.2%) uranium metal with a density of 18.76 g/cc are
critical. Each cylinder has a radius of 5.748 cm and a height of
10.765 cm. The surface-to-surface spacing between the units is the same
in all directions. The initial guess for the critical surface-to-surface
spacing was 3.0 cm. The experimentally critical surface-to-surface
separation for this system is 2.248 cm. The input data for this problem
are given below.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5s</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">4</span>  <span class="err">critical</span> <span class="err">pitch</span> <span class="err">search</span> <span class="err">for</span> <span class="err">case</span> <span class="m">2</span><span class="err">c</span><span class="m">8</span> <span class="err">bare</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">comp</span>
<span class="err">uranium</span>  <span class="m">1</span> <span class="m">0</span><span class="err">.</span><span class="m">985</span> <span class="m">300</span><span class="err">.</span>  <span class="m">92235</span> <span class="m">93</span><span class="err">.</span><span class="m">2</span> <span class="m">92238</span> <span class="m">5</span><span class="err">.</span><span class="m">6</span> <span class="m">92234</span> <span class="m">1</span><span class="err">.</span><span class="m">0</span> <span class="m">92236</span> <span class="m">0</span><span class="err">.</span><span class="m">2</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">comp</span>
<span class="n">read</span><span class="err"> </span><span class="n">parameters</span><span class="err">  </span><span class="n">flx</span><span class="err">=</span><span class="n">yes</span><span class="err"> </span><span class="n">fdn</span><span class="err">=</span><span class="n">yes</span><span class="err"> </span><span class="n">far</span><span class="err">=</span><span class="n">yes</span><span class="err"> </span><span class="n">gas</span><span class="err">=</span><span class="n">no</span><span class="err"> </span><span class="n">rnd</span><span class="err">=656651</span><span class="n">ed</span><span class="err">24</span><span class="n">de</span>
<span class="n">end</span><span class="err"> </span><span class="n">parameters</span>
<span class="n">read</span><span class="err"> </span><span class="n">geometry</span>
<span class="err">unit</span> <span class="m">1</span>
<span class="err">cylinder</span> <span class="m">1</span> <span class="m">1</span> <span class="m">5</span><span class="err">.</span><span class="m">748</span> <span class="m">5</span><span class="err">.</span><span class="m">3825</span> <span class="err">-</span><span class="m">5</span><span class="err">.</span><span class="m">3825</span>
<span class="err">cuboid</span>  <span class="m">0</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">7</span><span class="err">.</span><span class="m">248</span> <span class="m">2</span><span class="err">p</span><span class="m">6</span><span class="err">.</span><span class="m">8825</span>
<span class="n">end</span><span class="err"> </span><span class="n">geometry</span>
<span class="n">read</span><span class="err"> </span><span class="n">array</span>
<span class="err">com=</span><span class="s">&#39;single unit problem with 1 array is filled with unit 1&#39;</span>
<span class="err">ara=</span><span class="m">1</span>  <span class="err">gbl=</span><span class="m">1</span> <span class="err">nux=</span><span class="m">2</span> <span class="err">nuy=</span><span class="m">2</span> <span class="err">nuz=</span><span class="m">2</span> <span class="err">fill</span> <span class="err">f</span><span class="m">1</span> <span class="n">end</span><span class="err"> </span><span class="n">fill</span>
<span class="n">end</span><span class="err"> </span><span class="n">array</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">read</span><span class="err"> </span><span class="n">search</span><span class="err">   </span><span class="n">critical</span><span class="err"> </span><span class="n">pitch</span><span class="err">   </span><span class="n">maxpitch</span><span class="err">=15.5  </span><span class="n">more</span>
<span class="err">alter</span>  <span class="err">unit=</span><span class="m">1</span> <span class="err">reg=</span><span class="m">2</span> <span class="err">+z=</span><span class="m">1</span><span class="err">.</span><span class="m">0531</span> <span class="err">-z=</span><span class="m">1</span><span class="err">.</span><span class="m">0531</span>
<span class="n">end</span><span class="err"> </span><span class="n">search</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-problem-5-solution-conc-search-for-a-specified-keff">
<h3>Sample problem 5: solution conc. search for a specified <em>k</em><sub>eff</sub><a class="headerlink" href="#sample-problem-5-solution-conc-search-for-a-specified-keff" title="Permalink to this headline"></a></h3>
<p>Consider a large spherical tank partially filled with
UO<sub>2</sub>F<sub>2</sub> solution. The tank has a radius of 34.6 cm and
is filled with solution to a height of 30.0 cm above the midpoint. The
tank is composed of a 0.759 cm thick Al shell. The
UO<sub>2</sub>F<sub>2</sub> solution is composed of three standard
compositions: UO2F2, HF acid, and H2O. The code combines these using a
set algorithm. This may or may not produce a solution at the desired
density. If the density of the solution is known it should be entered.
Also, extra acid can be added to the solution by specifying a non-zero
acid molarity.</p>
<p>A critical concentration search is performed on the solution yielding
system <em>k</em><sub>eff</sub> = 1.0 for various densities of UO<sub>2</sub>F<sub>2</sub>
in the solution. In the MORE search data, MIX=1 and SCNAME=UO2F2 specify
that the UO<sub>2</sub>F<sub>2</sub> component of the mixture 1 solution
is to be altered during the search. The code calculates the density of
the solution. The initial uranium fuel density is 300 gm/liter. The
maximum allowed uranium density is 600 gm/liter. The minimum allowed
uranium density is 150 gm/liter.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5s</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">5</span> <span class="err">soln</span> <span class="err">tank</span> <span class="err">-</span> <span class="err">crit.</span> <span class="err">conc.</span> <span class="err">search</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">composition</span>
  <span class="err">solution</span>
    <span class="err">mix=</span><span class="m">1</span>
    <span class="err">rho[uo</span><span class="m">2</span><span class="err">f</span><span class="m">2</span><span class="err">]=</span> <span class="m">300</span>  <span class="m">92235</span> <span class="m">80</span> <span class="m">92238</span> <span class="m">19</span><span class="err">.</span><span class="m">98</span> <span class="m">92234</span> <span class="m">0</span><span class="err">.</span><span class="m">02</span>
    <span class="err">temp=</span> <span class="m">300</span>
  <span class="n">end</span><span class="err"> </span><span class="n">solution</span>
  <span class="err">al</span>         <span class="m">2</span> <span class="m">1</span><span class="err">.</span><span class="m">0</span> <span class="m">300</span><span class="err">.</span><span class="m">0</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">composition</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">1</span>
    <span class="err">hemisphe-z</span>  <span class="m">1</span> <span class="m">1</span> <span class="m">16</span>   <span class="err">chord</span> <span class="m">15</span><span class="err">.</span><span class="m">5</span>
    <span class="err">sphere</span>      <span class="m">0</span> <span class="m">1</span> <span class="m">16</span>
    <span class="err">sphere</span>      <span class="m">2</span> <span class="m">1</span> <span class="m">16</span><span class="err">.</span><span class="m">1</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">read</span><span class="err"> </span><span class="n">search</span>
  <span class="err">critical</span>  <span class="err">concentration</span> <span class="err">kef=</span><span class="m">1</span><span class="err">.</span><span class="m">0</span>
  <span class="err">more</span>
    <span class="err">alter</span>  <span class="err">mix=</span><span class="m">1</span>  <span class="err">scname=uo</span><span class="m">2</span><span class="err">f</span><span class="m">2</span>  <span class="err">factor=</span><span class="m">1</span><span class="err">.</span><span class="m">0</span>
    <span class="err">-con=-</span><span class="m">0</span><span class="err">.</span><span class="m">5</span>  <span class="err">+con=</span><span class="m">1</span><span class="err">.</span><span class="m">0</span>
<span class="n">end</span><span class="err"> </span><span class="n">search</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-problem-6-dimension-chord-search-for-a-specified-keff">
<h3>Sample problem 6: dimension chord search for a specified <em>k</em><sub>eff</sub><a class="headerlink" href="#sample-problem-6-dimension-chord-search-for-a-specified-keff" title="Permalink to this headline"></a></h3>
<p>Consider a large spherical tank partially filled with
UO<sub>2</sub>F<sub>2</sub> solution. The tank has a radius of 34.6 cm and
is filled with solution to an initial height of 10.0 cm above the
midpoint. The tank is composed of a 0.759 cm thick Al shell. The
UO<sub>2</sub>F<sub>2</sub> solution is composed of three standard
compositions: UO2F2, HF acid, and H2O. The code combines these using a
set algorithm. This may or may not produce a solution at the desired
density. If the density of the solution is known it should be entered.
Also, extra acid can be added to the solution by specifying a non-zero
acid molarity.</p>
<p>A critical dimension search is performed on the chord length yielding
system <em>keff</em> = 0.98. In the MORE search data, UNIT=1 REG=1 CHORD=1.0
specify that the chord length in region 1 of unit 1 is to be altered
during the search. The constraints are set so the chord length varies
from −10.0 cm to just under 34.6 cm.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5s</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">6</span> <span class="err">soln</span> <span class="err">tank</span> <span class="err">-</span> <span class="err">crit.</span> <span class="err">dim.</span> <span class="err">search</span> <span class="err">on</span> <span class="err">chord</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">comp</span>
  <span class="err">solution</span>
    <span class="err">mix=</span><span class="m">1</span>
    <span class="err">rho[uo</span><span class="m">2</span><span class="err">f</span><span class="m">2</span><span class="err">]=</span> <span class="m">300</span>  <span class="m">92235</span> <span class="m">80</span> <span class="m">92238</span> <span class="m">19</span><span class="err">.</span><span class="m">98</span> <span class="m">92234</span> <span class="m">0</span><span class="err">.</span><span class="m">02</span>
    <span class="err">temp=</span> <span class="m">300</span>
  <span class="n">end</span><span class="err"> </span><span class="n">solution</span>
  <span class="err">al</span>         <span class="m">2</span> <span class="m">1</span><span class="err">.</span><span class="m">0</span> <span class="m">300</span><span class="err">.</span><span class="m">0</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">comp</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">1</span>
    <span class="err">hemisphe-z</span>  <span class="m">1</span> <span class="m">1</span> <span class="m">16</span>   <span class="err">chord</span> <span class="m">10</span><span class="err">.</span>
    <span class="err">sphere</span>      <span class="m">0</span> <span class="m">1</span> <span class="m">16</span>
    <span class="err">sphere</span>      <span class="m">2</span> <span class="m">1</span> <span class="m">16</span><span class="err">.</span><span class="m">1</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">read</span><span class="err"> </span><span class="n">search</span>
  <span class="err">critical</span>  <span class="err">dimension</span> <span class="err">kef=</span><span class="m">0</span><span class="err">.</span><span class="m">98</span>
  <span class="err">more</span>
    <span class="err">alter</span>  <span class="err">unit=</span><span class="m">1</span>  <span class="err">reg=</span><span class="m">1</span>  <span class="err">chord=</span><span class="m">1</span><span class="err">.</span><span class="m">0</span>
    <span class="err">-con=-</span><span class="m">0</span><span class="err">.</span><span class="m">23</span>  <span class="err">+con=</span><span class="m">0</span><span class="err">.</span><span class="m">23</span>
<span class="n">end</span><span class="err"> </span><span class="n">search</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-problem-7-two-material-conc-search-for-a-specified-keff">
<h3>Sample problem 7 two material conc. search for a specified <em>k</em><sub>eff</sub><a class="headerlink" href="#sample-problem-7-two-material-conc-search-for-a-specified-keff" title="Permalink to this headline"></a></h3>
<p>The fuel bundles in this problem represent 17 × 17 PWR fuel assemblies.
The fuel pin lattice is homogenized, making a cell-weighted mixture 100.
Because this problem utilizes a cell-weighted mixture, which is not
applicable in the continuous energy mode, the problem will end with an
error message in the continuous energy mode. The fuel pins consist of
4.35 wt % <sup>235</sup>U having a diameter of 0.823 cm, zirconium
cladding having an outer diameter of 0.9627 cm, and a pitch of 1.275 cm.
The fuel bundle is represented as a 10.8375 cm × 10.8375 cm × 366 cm
cuboid of mixture 100 surrounded by Boral and then water. The Boral has
a density of 2.61 g/cm<sup>3</sup> and has an initial composed of
50.0 wt % B<sub>4</sub>C and 50.0 wt % Al. The fuel bundles are at a
fixed pitch of 13.0 cm. Boral plates surrounding the X and Y sides of
each fuel assembly are 0.1625 cm thick. Full density water is between
the Boral plates.</p>
<p>A critical concentration search is performed on the Boral plates
searching for a system <em>keff</em> = 0.95. The Boral plates are at a fixed
density of 2.61 gm/cc. As the density of the B<sub>4</sub>C changes, the
density of the Al changes in the opposite direction maintaining a
constant Boral density. There are two entries in the MORE search data.
The first entry, MIX=4 SCNAME=b4c factor=1.0 specifies that the
B<sub>4</sub>C of mixture 4 is to be altered during the search. The
second entry, MIX=4 SCNAME=al factor=−1.0 specifies that aluminum is to
be changed in the opposite direction and proportionally to
B<sub>4</sub>C during the search. Both B<sub>4</sub>C and Al have the
same initial density of 0.5 * 2.61 = 1.305 gm/cc.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5s</span>
<span class="err">sample</span> <span class="err">problem</span> <span class="m">7</span> <span class="err">flux</span> <span class="err">trap</span> <span class="err">between</span> <span class="err">fuel</span> <span class="err">bundles</span> <span class="err">-</span> <span class="err">crit.</span> <span class="err">conc.</span> <span class="err">srch</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">composition</span>
  <span class="err">uo</span><span class="m">2</span>    <span class="m">1</span> <span class="err">.</span><span class="m">84</span> <span class="m">300</span><span class="err">.</span> <span class="m">92235</span> <span class="m">4</span><span class="err">.</span><span class="m">35</span> <span class="m">92238</span> <span class="m">95</span><span class="err">.</span><span class="m">65</span> <span class="n">end</span>
  <span class="err">zr</span>     <span class="m">2</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">3</span> <span class="m">1</span> <span class="n">end</span>
  <span class="err">arbmb</span><span class="m">4</span><span class="err">c</span>  <span class="m">2</span><span class="err">.</span><span class="m">61</span>  <span class="m">2</span>  <span class="m">0</span>  <span class="m">1</span>  <span class="m">0</span>  <span class="m">5000</span> <span class="m">4</span>  <span class="m">6000</span>  <span class="m">1</span>  <span class="m">4</span>  <span class="m">0</span><span class="err">.</span><span class="m">5</span>  <span class="m">300</span><span class="err">.</span><span class="m">0</span> <span class="n">end</span>
  <span class="err">al</span>     <span class="m">4</span> <span class="err">den=</span><span class="m">2</span><span class="err">.</span><span class="m">61</span> <span class="m">0</span><span class="err">.</span><span class="m">5</span> <span class="n">end</span>
  <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">5</span> <span class="m">1</span><span class="err">.</span><span class="m">0</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">composition</span>
<span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
  <span class="err">latticecell</span>  <span class="err">squarepitch</span>  <span class="err">pitch=</span><span class="m">1</span><span class="err">.</span><span class="m">275</span> <span class="m">3</span> <span class="err">fueld=.</span><span class="m">823</span> <span class="m">1</span>
    <span class="err">cladd=.</span><span class="m">9627</span> <span class="m">2</span> <span class="err">cellmix=</span><span class="m">100</span>  <span class="n">end</span>
  <span class="err">more</span> <span class="err">data</span>
     <span class="err">bal=none</span>
  <span class="n">end</span><span class="err"> </span><span class="n">more</span>
<span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span>
  <span class="err">far=no</span> <span class="err">gen=</span><span class="m">203</span> <span class="err">npg=</span><span class="m">1000</span>
<span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">1</span>
    <span class="err">cuboid</span> <span class="m">100</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">10</span><span class="err">.</span><span class="m">8375</span> <span class="m">2</span><span class="err">p</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
    <span class="err">cuboid</span>   <span class="m">4</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">11</span><span class="err">.</span><span class="m">0</span>    <span class="m">2</span><span class="err">p</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
    <span class="err">cuboid</span>   <span class="m">5</span> <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">13</span><span class="err">.</span><span class="m">0</span>    <span class="m">2</span><span class="err">p</span><span class="m">183</span><span class="err">.</span><span class="m">0</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">read</span><span class="err"> </span><span class="n">bounds</span>
  <span class="err">xfc=mirror</span> <span class="err">yfc=mirror</span>
<span class="n">end</span><span class="err"> </span><span class="n">bounds</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">read</span><span class="err"> </span><span class="n">search</span>
   <span class="err">critical</span> <span class="err">concentration</span>  <span class="err">kef=</span><span class="m">0</span><span class="err">.</span><span class="m">95</span>
   <span class="err">more</span>
     <span class="err">alter</span> <span class="err">mix=</span><span class="m">4</span>  <span class="err">scname=arbmb</span><span class="m">4</span><span class="err">c</span>   <span class="err">factor=</span><span class="m">1</span><span class="err">.</span><span class="m">0</span>
     <span class="err">alter</span> <span class="err">mix=</span><span class="m">4</span>  <span class="err">scname=al</span>        <span class="err">factor=-</span><span class="m">1</span><span class="err">.</span><span class="m">0</span>
     <span class="err">-con=-</span><span class="m">0</span><span class="err">.</span><span class="m">9</span>  <span class="err">+con=</span><span class="m">0</span><span class="err">.</span><span class="m">99</span>
<span class="n">end</span><span class="err"> </span><span class="n">search</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-problem-8-k-for-a-pebble-bed-fuel">
<h3>Sample problem 8: k<sub></sub> for a pebble bed fuel<a class="headerlink" href="#sample-problem-8-k-for-a-pebble-bed-fuel" title="Permalink to this headline"></a></h3>
<p>This problem demonstrates setting up a fuel pebble from a pebble bed
reactor, and calculating its k<strong></strong>. The pebble consists of a fuel
grain of UO<sub>2</sub> 0.025 cm in radius, coated with 0.003 cm of
pyrolitic carbon, a further coat of 0.0035 cm thick silicon carbide,
with a final coat of 0.004 cm thick pyrolitic carbon. 15000 grains are
packed with graphite into an internal fuel sphere of 2.5 cm radius clad
with a 0.5 cm thick covering of carbon and surrounded by helium. The
fuel is 8.2% enriched <sup>235</sup>U. The pebbles are stacked into an
infinite square pitched array with a pitch of 6 cm.</p>
<p>This problem uses DOUBLEHET cell type, which is applicable only in the
multigroup mode of KENO calculations. Therefore, the continuous energy
version of this problem will end with an error message.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=csas5             parm=(centrm)</span>
<span class="err">infinite</span> <span class="err">array</span> <span class="err">of</span> <span class="err">pebbles</span> <span class="err">on</span> <span class="err">a</span> <span class="err">square</span> <span class="err">pitch</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">composition</span>
<span class="c">&#39; fuel kernel</span>
  <span class="err">u-</span><span class="m">238</span>  <span class="m">1</span> <span class="m">0</span> <span class="m">2</span><span class="err">.</span><span class="m">12877</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
  <span class="err">u-</span><span class="m">235</span>  <span class="m">1</span> <span class="m">0</span> <span class="m">1</span><span class="err">.</span><span class="m">92585</span><span class="err">e-</span><span class="m">3</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
  <span class="err">o</span>      <span class="m">1</span> <span class="m">0</span> <span class="m">4</span><span class="err">.</span><span class="m">64272</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
<span class="c">&#39; inner pyro carbon</span>
  <span class="err">c</span>      <span class="m">3</span> <span class="m">0</span> <span class="m">9</span><span class="err">.</span><span class="m">52621</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
<span class="c">&#39; silicon carbide</span>
  <span class="err">c</span>      <span class="m">4</span> <span class="m">0</span> <span class="m">4</span><span class="err">.</span><span class="m">77240</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
  <span class="err">si</span>     <span class="m">4</span> <span class="m">0</span> <span class="m">4</span><span class="err">.</span><span class="m">77240</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
<span class="c">&#39; outer pyro carbon</span>
  <span class="err">c</span>      <span class="m">5</span> <span class="m">0</span> <span class="m">9</span><span class="err">.</span><span class="m">52621</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
<span class="c">&#39; graphite matrix</span>
  <span class="err">c</span>      <span class="m">6</span> <span class="m">0</span> <span class="m">8</span><span class="err">.</span><span class="m">77414</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
<span class="c">&#39; carbon pebble outer coating</span>
  <span class="err">c</span>      <span class="m">7</span> <span class="m">0</span> <span class="m">8</span><span class="err">.</span><span class="m">77414</span><span class="err">e-</span><span class="m">2</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
  <span class="err">he-</span><span class="m">3</span>    <span class="m">8</span> <span class="m">0</span> <span class="m">3</span><span class="err">.</span><span class="m">71220</span><span class="err">e-</span><span class="m">11</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
  <span class="err">he-</span><span class="m">4</span>    <span class="m">8</span> <span class="m">0</span> <span class="m">2</span><span class="err">.</span><span class="m">65156</span><span class="err">e-</span><span class="m">5</span> <span class="m">293</span><span class="err">.</span><span class="m">6</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">composition</span>
<span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
  <span class="err">doublehet</span>  <span class="err">right_bdy=white</span> <span class="err">fuelmix=</span><span class="m">10</span> <span class="n">end</span>
   <span class="err">gfr=</span><span class="m">0</span><span class="err">.</span><span class="m">025</span>  <span class="m">1</span> <span class="err">coatt=</span><span class="m">0</span><span class="err">.</span><span class="m">004</span> <span class="m">3</span> <span class="err">coatt=</span><span class="m">0</span><span class="err">.</span><span class="m">0035</span> <span class="m">4</span> <span class="err">coatt=</span><span class="m">0</span><span class="err">.</span><span class="m">004</span> <span class="m">5</span>
   <span class="err">matrix=</span><span class="m">6</span> <span class="err">numpar=</span><span class="m">15000</span> <span class="n">end</span><span class="err"> </span><span class="n">grain</span>
  <span class="err">pebble</span> <span class="err">sphsquarep</span> <span class="err">right_bdy=white</span> <span class="err">hpitch=</span><span class="m">3</span><span class="err">.</span><span class="m">0</span> <span class="m">8</span> <span class="err">fuelr=</span><span class="m">2</span><span class="err">.</span><span class="m">5</span> <span class="err">cladr=</span><span class="m">3</span><span class="err">.</span><span class="m">0</span> <span class="m">7</span> <span class="n">end</span>
  <span class="err">centrm</span> <span class="err">data</span>
    <span class="err">ixprt=</span><span class="m">1</span> <span class="err">isn=</span><span class="m">8</span> <span class="err">nprt=</span><span class="m">2</span>
  <span class="n">end</span><span class="err"> </span><span class="n">centrm</span>
<span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span>
  <span class="err">gen=</span><span class="m">210</span> <span class="err">npg=</span><span class="m">1000</span>
<span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">bounds</span>
  <span class="err">all=mirror</span>
<span class="n">end</span><span class="err"> </span><span class="n">bounds</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">1</span>
    <span class="err">sphere</span>   <span class="m">10</span> <span class="m">1</span> <span class="m">2</span><span class="err">.</span><span class="m">5</span>
    <span class="err">sphere</span>    <span class="m">7</span> <span class="m">1</span> <span class="m">3</span><span class="err">.</span><span class="m">0</span>
    <span class="err">cuboid</span>    <span class="m">8</span> <span class="m">1</span> <span class="m">6</span><span class="err">p</span><span class="m">3</span><span class="err">.</span><span class="m">0</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="warning-and-error-messages">
<h2>Warning and error messages<a class="headerlink" href="#warning-and-error-messages" title="Permalink to this headline"></a></h2>
<p>CSAS5 contains two types of warning and error messages. Warning messages
appear when a possible error is encountered. It is the responsibility of
the user to verify whether the data are correct when a warning message
is encountered. The functional modules activated by CSAS5 sequences will
be executed if no error messages are generated and a warning message has
been generated.</p>
<p>When an error is recognized, an error message is written and an error
flag is set so the functional modules will not be activated. The code
stops immediately if the error is too severe to allow continuation of
input. However, it will continue to read and check the data if it is
able. When the data reading is completed, execution is terminated if an
error flag was set when the data were being processed. If the error flag
has not been set, execution continues. When error messages are present
in the output, the user should focus on the first error message, because
subsequent messages may have been caused by the error that generated the
first message.</p>
<p>The following messages originate in the part of CSAS5 that reads,
checks, and prepares data for KENO V.a and the search module MODIFY.</p>
<dl class="simple">
<dt>CS-10   *** ERROR *** CONCENTRATION SEARCH MATERIAL WAS NOT SPECIFIED IN THE STANDARD COMPOSITION.</dt><dd><p>This self-explanatory message from subroutine CNCN indicates that the
indicated material is not in the standard composition data. Recheck the
standard composition data and the search data, correct the input, and
resubmit the problem.</p>
</dd>
<dt>CS-11   *** ERROR *** CONCENTRATION SEARCH DATA HAS BEEN DESTROYED. I= ______      ICMND= ______     IPNUM= ______     MIXUR= ______      SCNAME= ______</dt><dd><p>This message from subroutine CNCSRH indicates that the search data could
not be read properly. This usually indicates either: search data that is
required for the specified search type is missing or search data
inappropriate for the specified search type is present. Recheck the
search data, correct the input, and resubmit the problem.</p>
</dd>
<dt>CS-16   ***WARNING*** READ FLAG NOT FOUND.  ASSUME KENO V PARAMETER DATA FOLLOWS.</dt><dd><p>This message from subroutine CPARAM indicates that the word READ is not
the first word of KENO V.a data following the Material Information
Processor input data. If parameter data is to be entered, the code
expects the words READ PARAMETERS to precede the parameter input data.
If the word READ is not the first word, the code assumes the data are
parameter input data.</p>
</dd>
<dt>CS-21 A UNIT NUMBER WAS ENTERED FOR THE CROSS-SECTION LIBRARY. (LIB= IN PARAMETER DATA.) THE DEFAULT VALUE SHOULD BE USED IN ORDER TO UTILIZE THE CROSS SECTIONS GENERATED BY CSAS5. MAKE CERTAIN THE CORRECT CROSS-SECTION LIBRARY IS BEING USED.</dt><dd><p>This message is from subroutine CPARAM. It indicates that a value has
been entered for the cross-section library in the KENO V.a parameter
data. The cross-section library created by the analytical sequence
should be used. MAKE CERTAIN THAT THE CORRECT CROSS SECTIONS ARE BEING
USED.</p>
</dd>
<dt>CS-50   *** ERROR *** SEARCH COMMAND NUMBER ______ IS UNABLE TO PERFORM A PITCH SEARCH BECAUSE THE DIMENSIONS OF REGION ______ OF UNIT ______ ARE NOT EXPLICITLY DEFINED.</dt><dd><p>This message from subroutine PCHSRH indicates that the specified search
command is not valid for the specified region. An ARRAY or CORE region
cannot be altered; nor can a REPLICATE or REFLECTOR region immediately
following an ARRAY or CORE region.</p>
</dd>
<dt>CS-55   *** ERRORS WERE ENCOUNTERED IN PROCESSING THE CSAS-KENO5 DATA.  EXECUTION IS IMPOSSIBLE.  ***</dt><dd><p>This message from subroutine SASSY is printed if errors were found in
the KENO V.a input data for CSAS5. If a search is being made, data
reading will continue until all the data have been entered or a fatal
error terminates the data reading. When the data reading and checking
have been completed, the problem will terminate without executing. Check
the printout to locate the errors responsible for this message.</p>
</dd>
<dt>CS-62   *** ERROR *** MIXTURE ______ IN THE GEOMETRY WAS NOT CREATED IN THE STANDARD COMPOSITIONS SPECIFICATION DATA.</dt><dd><p>This message from subroutine MIXCHK indicates that a mixture specified
in the KENO V.a geometry was not created in the standard composition
data.</p>
</dd>
<dt>CS-68   *** ERROR *** AN INPUT DATA ERROR HAS BEEN ENCOUNTERED IN THE ______ DATA ENTERED FOR THIS PROBLEM.</dt><dd><p>This message from the main program, CSAS5, is printed if the subroutine
library routine LRDERR returns a value of “TRUE,” indicating that a
reading error has been encountered in the “KENO PARAMETER” data or the
CSAS5 “SEARCH” data. The appropriate data type is printed in the
message. Locate the unnumbered message stating “<a href="#id4"><span class="problematic" id="id5">**</span></a><strong>* ERROR IN INPUT.
CARD IMAGE PRINTED ON NEXT LINE ***</strong>.” Correct the data and resubmit
the problem.</p>
</dd>
<dt>CS-69   ***ERROR*** MIXTURE ______ IS AN INAPPROPRIATE MIXTURE NUMBER FOR USE IN THE KENO GEOMETRY DATA BECAUSE IT IS A COMPONENT OF THE CELL-WEIGHTED MIXTURE CREATED BY XSDRNPM.</dt><dd><p>This message from subroutine CMXCHK indicates that a mixture that is a
component of a cell-weighted mixture has been used in the KENO V.a
geometry data.</p>
</dd>
<dt>CS-70   ***** ERROR ***** SEARCH OR OPTIMIZATION DATA MUST BE ENTERED FOR CSAS5.  NO SEARCH DATA WAS ENTERED.</dt><dd><p>This message from subroutine RDOPT is self-explanatory. If the user does
not desire to run a search, another sequence such as CSAS5 should be
chosen.</p>
</dd>
<dt>CS-71   *** ERROR *** ______ IS NOT A VALID SEARCH TYPE.</dt><dd><p>This message is from subroutine RDOPT. The allowed search types include
PITCH, DIMENSION, and CONCENTRATION. The first four characters of the
search data after the words READ SEARCH must be PIT, PITC, DIM, DIME,
DMSN, CON, or CONC. The data may be misspelled or out of order.</p>
</dd>
<dt>CS-72   *** ERROR *** THE SEARCH TYPE IS INVALID.  I= ______.</dt><dd><p>This message is from subroutine RDOPT. The numerical index, I, should be
1 for an optimum pitch search, 2 for a dimension search, and 3 for a
concentration search. If it is none of these, the search type has been
incorrectly specified or a code error has been introduced.</p>
</dd>
<dt>CS-73   ***** AN END OF FILE WAS ENCOUNTERED BEFORE ALL THE SEARCH DATA WAS READ.</dt><dd><p>This self-explanatory message is from subroutine RDOPT. Check the input
data to be sure nothing was omitted or misspelled.</p>
</dd>
<dt>CS-74   ***** AN END SEARCH FLAG WAS READ BEFORE ALL THE SEARCH DATA WAS READ.</dt><dd><p>This self-explanatory message is from subroutine RDOPT. Check the input
data for omissions and correct order.</p>
</dd>
<dt>CS-75   *** ERROR *** READ SEARCH FLAG WAS NOT FOUND. ______ WAS READ INSTEAD.</dt><dd><p>This self-explanatory message is from subroutine RDOPT. READ SEARCH was
expected but was not found. Check the input data for omissions and
correct order.</p>
</dd>
<dt>CS-76   *** ERROR *** END SEARCH FLAG WAS NOT FOUND. ______ WAS READ INSTEAD.</dt><dd><p>This self-explanatory message from subroutine RDOPT indicates that an
end of file was encountered when looking for READ SEARCH. Check the
input data for omissions, correct order, and spelling.</p>
</dd>
<dt>CS-77   *** ERROR *** AN END OF FILE WAS FOUND WHEN THE READ SEARCH FLAG WAS EXPECTED.</dt><dd><p>This self-explanatory message is from subroutine RDOPT. Check the input
data for omissions, correct order, and spelling.</p>
</dd>
<dt>CS-78   *** ERROR *** ______ IS NOT A VALID SEARCH TYPE.</dt><dd><p>This message is from subroutines SRCHTYP. It indicates that an invalid
search type was read. The valid search names include PITCH,
CONCENTRATION, and DIMENSION. Either the data was entered improperly or
a code error has been introduced. A STOP 215 is executed when this
message is printed.</p>
</dd>
<dt>CS-80   *** ERROR *** SEARCH DATA HAS BEEN DESTROYED.  I= ______ ICMND= ______  IPNUM= ______ II= ______  IGEOM= ______</dt><dd><p>This message from subroutines DIMSRH indicates that the search data
cannot be interpreted. This usually indicates either: search data that
is required for the specified search type is missing or search data
inappropriate for the specified search type is present. Recheck the
search data, correct the input, and resubmit the problem.</p>
</dd>
<dt>CS-82 *** AN ERROR WAS ENCOUNTERED IN ONE OF THE FUNCTIONAL MODULES.</dt><dd><p>This message from CSAS5 or MODIFY indicates that an error was
encountered during execution of one of the functional modules such as
CRAWDAD, BONAMI, CENTRM, PMC, XSDRNPM, or KENO V.a. Check the printout
to locate and correct the error.</p>
</dd>
<dt>CS-83 ***** NO FEASIBLE SOLUTION WAS FOUND IN THE SEARCH PACKAGE. EXECUTION IS TERMINATED.</dt><dd><p>This message comes from the MODIFY search package, and indicates that it
is unable to find a solution to the problem as presented. This usually
occurs when a solution is not within the range specified. For this case
the user must decide what to change to improve the possibility of a
solution. Fairly rarely, for an optimum problem, there may be 2 maximums
within the range specified, and the package has found the wrong one. For
this case, the user would tighten the range to be searched to eliminate
the unwanted peak. The package uses least mean square fitted cubic
polynomials to make guesses as to where a solution is. If the
Keffectives have too much variance, the polynomials may not be a good
representation of the actual behavior of the system. For this case the
user could rerun the problem using more histories per pass to reduce the
variance.</p>
</dd>
<dt>CS-85 *** ERROR *** ALL OF THE ROOTS FOR K=_____ LIE OUTSIDE THE PARAMETER CONSTRAINTS</dt><dd><p>This message from MODIFY indicates that the polynomial fit to the
Keffectives already calculated only has solutions for the Keffective
asked for outside the parameter constraints specified. Keffectives with
large variances can lead to polynomials which fit the actual behavior of
a system poorly. The user could rerun the case with more histories to
reduce the variance, if this is the problem. If the variance is not the
problem, then extending the parameter range, or making some other change
to the problem definition to change the Keffective range will be
necessary.</p>
</dd>
<dt>CS-89 *** ERROR *** ______ IS AN INVALID DIMENSION SEARCH COMMAND.</dt><dd><p>This message from subroutine DMSN indicates that the dimension search
data are out of order, a search command is spelled incorrectly, or the
search data are specified incorrectly.</p>
</dd>
<dt>CS-90 *** ERROR *** ______ IS AN INVALID SEARCH PARAMETER.</dt><dd><p>This message printed from subroutines CNCTYP, DIMTYP, and PCHTYP
indicates that a parameter entered in the search type specification data
is not valid. The data could be misspelled or out of order. Omission of
the keyword MORE before entering the individual search commands can
cause this error.</p>
</dd>
<dt>CS-91 *** ERROR *** ______ IS AN INVALID CONCENTRATION SEARCH COMMAND.</dt><dd><p>This message from subroutine CNCN is caused by a misspelled or illegal
search command when attempting to do a concentration search.</p>
</dd>
<dt>CS-94 *** ERROR *** REG= ______ IS AN INVALID SEARCH DATA ENTRY. THE REGION NUMBER MUST BE GREATER THAN ZERO AND NO LARGER THAN THE NUMBER OF REGIONS IN THE UNIT.</dt><dd><p>This message from subroutine DMSN indicates that the region to be
altered is incorrectly specified. For example, if the unit being altered
contains five geometry regions, the value specified for REG= can be as
small as 1 and as large as 5.</p>
</dd>
<dt>CS-95 *** ERROR *** AN ERROR WAS ENCOUNTERED IN THE SEARCH DATA. THE LAST REGION NUMBER MUST BE AT LEAST AS LARGE AS THE FIRST REGION NUMBER. CHECK THE SEARCH DATA PRINTED BELOW. keyword UNIT ______ REGIONS ______ TO ______ PARAMETER= SEARCH CONSTANTS ARE ______</dt><dd><p>This message from subroutine DMSN indicates that the search data
specified an invalid region number for the final region to be altered.
Check the printed data and correct as appropriate.</p>
</dd>
<dt>CS-96 *** ERROR *** AN ERROR WAS ENCOUNTERED IN THE SEARCH DATA. THE REGION NUMBERS MUST BE GREATER THAN ZERO AND NO LARGER THAN THE NUMBER OF REGIONS IN THE UNIT. CHECK THE SEARCH DATA PRINTED BELOW. keyword UNIT ______ REGIONS ______ TO ______ PARAMETER= ______ SEARCH CONSTANTS ARE ______</dt><dd><p>This message from subroutine DMSN indicates that one of the specified
region numbers is incorrect. Check the printed data and correct as
appropriate.</p>
</dd>
<dt>CS-97 *** ERROR *** NO VALID SEARCH COMMANDS WERE FOUND IN THE DATA.</dt><dd><p>This message is accompanied by a STOP 235 and is printed from
subroutines PCHSRH, CNCSRH, and DIMSRH. A common cause of this error is
the omission of the MORE command before the individual search commands
are entered.</p>
</dd>
<dt>CS-99 *** ERROR *** THIS PROBLEM WILL NOT BE RUN BECAUSE PARM=CHECK WAS ENTERED IN THE ANALYTICAL SEQUENCE SPECIFICATION.</dt><dd><p>This message from subroutine CSAS5 indicates that the problem data were
read and checked and no errors were found. To execute the problem,
remove the PARM=CHECK or PARM=CHK from the analytical sequence indicator
data entry.</p>
</dd>
<dt>CS-100 *** ERROR *** THIS PROBLEM WILL NOT BE RUN BECAUSE ERRORS WERE ENCOUNTERED IN THE INPUT DATA.</dt><dd><p>This message from subroutine CSAS5 is self-explanatory. Examine the
printout to locate the error or errors in the input data. Correct them
and resubmit the problem.</p>
</dd>
<dt>CS-101  *** ERROR <a href="#id6"><span class="problematic" id="id7">**</span></a>* THE CONSTRAINTS ARE NOT VALID FOR PARAMETER SET. −CON= ______  +CON= ______</dt><dd><p>This message is printed from either subroutine CNCN or DMSN if the
parameter set is invalid. For a parameter set to be valid, −CON must be
less than 0.0 and +CON must be greater than 0.0. They can be explicitly
set or calculated using default or provided data.</p>
</dd>
<dt>CS-102 *** ERROR *** THE UNIT CELL SPECIFICATION FOR UNIT ______ IS OUT OF BOUNDS. CELL NUMBER ______ WAS SPECIFIED. THE SPECIFIED CELL MUST BE BETWEEN 1 AND THE NUMBER OF CELLS ______.</dt><dd><p>This self-explanatory message from subroutine DMSN indicates that the
unit cell specified is not between 1 and the number of unit cells
present in the problem. Recheck the unit cell number specified in the
search data, correct the input, and resubmit the problem.</p>
</dd>
<dt>CS-103 *** ERROR *** THE UNIT CELL SPECIFICATION FOR MIXTURE ______  IS OUT OF BOUNDS. CELL NUMBER ______ WAS SPECIFIED. THE SPECIFIED CELL MUST BE BETWEEN 1 AND THE NUMBER OF UNIT CELLS ______ .</dt><dd><p>This self-explanatory message from subroutine CNCN indicates that the
unit cell specified for the indicated mixture is not between 1 and the
number of unit cells present in the problem. Recheck the unit cell
number specified in the search data, correct the input, and resubmit the
problem.</p>
</dd>
</dl>
<p id="bibtex-bibliography-CSAS5-0"><dl class="citation">
<dt class="bibtex label" id="lorek-improved-1979"><span class="brackets"><a class="fn-backref" href="#id1">LDPW79</a></span></dt>
<dd><p>M. J. Lorek, H. L. Dodds, L. M. Petrie, and R. M. Westfall. Improved criticality search techniques for low and high enriched systems. Technical Report, Tennessee Univ., 1979.</p>
</dd>
<dt class="bibtex label" id="thomas-critical-1964"><span class="brackets"><a class="fn-backref" href="#id3">Tho64</a></span></dt>
<dd><p>J. T. Thomas. CRITICAL THREE-DIMENSIONAL ARRAYS OF NEUTRON-INTERACTING UNITS. PART II. U (93.2) METAL. Technical Report, Oak Ridge National Lab., Tenn., 1964.</p>
</dd>
<dt class="bibtex label" id="thomas-critical-1973"><span class="brackets"><a class="fn-backref" href="#id2">Tho73</a></span></dt>
<dd><p>Joseph T. Thomas. Critical three-dimensional arrays of U (93.2)-metal cylinders. <em>Nuclear Science and Engineering</em>, 52(3):350–359, 1973. Publisher: Taylor &amp; Francis.</p>
</dd>
</dl>
</p>
</div>
</div>


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