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Taylor, Benjamin
SCALE manual
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.. _CSAS5:
CSAS5: Control Module For Enhanced Criticality Safety Analysis Sequences With KENO V.a
=======================================================================================
*L. M. Petrie, K. B. Bekar, S. Goluoglu,*\ :sup:`\*` *D. F. Hollenbach,*\ :sup:`\*` *N. F. Landers*
The **C**\ riticality **S**\ afety **A**\ nalysis **S**\ equences with
KENO V.a (CSAS5) provides reliable and efficient means of performing
*k*\ :sub:`eff` 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 *k*\ :sub:`eff`
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 *k*\ :sub:`eff` for the modified dimensions or
densities.
\*Formerly with Oak Ridge National Laboratory.
Acknowledgments
---------------
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.
Special appreciation is expressed to S. J. Poarch and S. Y. Walker for their efforts in formatting this document.
.. _CSAS5-intro:
Introduction
------------
Criticality Safety Analysis Sequence with KENO V.a (CSAS5) provides
reliable and efficient means of performing *k*\ :sub:`eff` calculations for
systems that are routinely encountered in engineering practice,
especially in the calculation of *k*\ :sub:`eff` 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 *k*\ :sub:`eff` 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 *k*\ :sub:`eff` and (2) a critical search seeking a fixed
value of *k*\ :sub:`eff`.
All the control sequences in the CSAS5 control module are listed in
:numref:`tab2-1` with the modules they invoke. The first four sequences are
subsets of the CSAS5 sequence.
.. _tab2-1:
.. table:: CSAS5 sequences for criticality safety
:align: center
+-------------------+-----------------------------------+--------------------------+----------+--------+
| Control sequence | Function | Functional modules | | |
| | | executed by the | | |
| | | control sequence | | |
| | | for multigroup libraries | | |
+===================+===================================+==========================+==========+========+
| CSAS5 | :math:`k_{eff}` (3-D) | XSProc | KENO V.a | |
+-------------------+-----------------------------------+--------------------------+----------+--------+
| CSAS5S | :math:`k_{eff}` (3-D) search | XSProc | KENO V.a | MODIFY |
+-------------------+-----------------------------------+--------------------------+----------+--------+
Sequence Capabilities
---------------------
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.
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
*k*\ :sub:`eff` or neutron multiplication factor using the cross-section
library that was prepared by the control sequence. MODIFY may be invoked
to perform a search :cite:`lorek_improved_1979` 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.
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 :math:`k_{eff}` as a function of pitch,
dimensions or densities or (2) the pitch, dimensions, or densities
corresponding to a specified value of :math:`k_{eff}`. 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.
Optimum (minimum/maximum) search
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Because only an initial value of :math:`k_{eff}` 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 :math:`k_{eff}`. The optimum search
procedure is summarized as follows:
#. Calculate :math:`k_{eff}` for the specified problem.
#. Calculate :math:`k_{eff}` for the minimum constraint.
#. Calculate :math:`k_{eff}` for the maximum constraint.
#. Calculate :math:`k_{eff}` for a fourth point that lies approximately
equidistant between the initial guess and the constraint that is
farthest from it.
#. Utilize a weighted least-squares fit to a cubic polynomial on the
data points.
#. Determine the type of cubic. For a type A cubic, go to step 11.
#. Take the first derivative of the least-squares cubic.
#. Solve the quadratic for its roots.
#. 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) :math:`k_{eff}`.
#. Calculate the :math:`k_{eff}` corresponding to the next guess. Go to
step 5. Repeat this procedure until convergence is achieved.
#. 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.
Convergence is defined as occurring when a *k*\ :sub:`eff` 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
*k*\ :sub:`eff` 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.
.. Note::
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.
Critical search
~~~~~~~~~~~~~~~
The critical search option searches for the pitch, dimensions, or
material densities corresponding to a specified value of *k*\ :sub:`eff`. If
the calculated value of *k*\ :sub:`eff` is within the specified search
tolerance (EPS) of the desired *k*\ :sub:`eff`, the search is considered to be
complete. The critical search procedure is summarized as follows:
1. Calculate *k*\ :sub:`eff` for the specified problem. If it is within EPS of
the specified *k*\ :sub:`eff`, convergence has been achieved.
2. Calculate *k*\ :sub:`eff` for one of the constraints. If the specified
*k*\ :sub:`eff` of the system does not fall between the initial value and
the *k*\ :sub:`eff` of the constraint, calculate the *k*\ :sub:`eff` of the other
constraint. If the calculated *k*\ :sub:`eff` is within EPS of the specified
*k*\ :sub:`eff`, convergence has been achieved.
3. Calculate *k*\ :sub:`eff` for a point chosen from a linear fit of the two
existing points closest to the specified *k*\ :sub:`eff`.
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` is within EPS of the
specified *k*\ :sub:`eff`.
5. If convergence is achieved, calculate *k*\ :sub:`eff` for a point determined
from fitting the previous points to a cubic and solving the cubic for
the point closest to the desired *k*\ :sub:`eff`. 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.
.. Note::
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.
Multigroup CSAS5 limitations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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:
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
Continuous energy CSAS5 limitations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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:
1. 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.
2. Only VACUUM, MIRROR, PERIODIC, and WHITE boundary conditions are
allowed. Other albedos, e.g., WATER, CARBON, POLY, etc. are for
multigroup only.
3. Problems with DOUBLEHET cell data are not allowed as they inherently
utilize CELLMIX feature.
Input Data Guide
----------------
This section describes the input data required for CSAS5. Several
subsets of the CSAS5 sequences listed in :numref:`tab2-1` are available to
achieve several different levels of processing.
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.
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`.
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. *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.*
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.
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.
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.
To check the input data without actually processing the cross sections,
the words “PARM=CHECK” or “PARM=CHK” should be entered, as shown below.
| =CSAS5 PARM=CHK
| or
| #CSAS5 PARM=CHK
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.
XSProc data
~~~~~~~~~~~
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.
KENO V.a data
~~~~~~~~~~~~~
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.
:numref:`tab2-2` 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 :numref:`tab2-2`. 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.
.. _tab2-2:
.. table:: Outline of KENO data
:align: center
+-----------------+-----------------+-----------------+-----------------+
| **Type of | **Starting | **Comments** | **Termination |
| data** | flag** | | flag** |
+-----------------+-----------------+-----------------+-----------------+
| Parameters\* | READ PARAMETER | Enter | END PARAMETER |
| | | desired | |
| | | parameter | |
| | | data | |
+-----------------+-----------------+-----------------+-----------------+
| Geometry | READ GEOMETRY | Enter | END GEOMETRY |
| | | desired | |
| | | geometry | |
| | | data | |
+-----------------+-----------------+-----------------+-----------------+
| Array data | READ ARRAY | Enter | END ARRAY |
| | | desired | |
| | | array data | |
+-----------------+-----------------+-----------------+-----------------+
| Boundary | READ BOUNDS | Enter | END BOUNDS |
| conditions | | desired | |
| | | boundary | |
| | | conditions | |
+-----------------+-----------------+-----------------+-----------------+
| Energy group | READ ENERGY | Enter | END ENERGY |
| boundaries | | desired | |
| | | neutron | |
| | | energy group | |
| | | boundaries | |
+-----------------+-----------------+-----------------+-----------------+
| Start data | READ START | Enter | END START |
| or initial | | desired | |
| source | | start data | |
+-----------------+-----------------+-----------------+-----------------+
| Plot data | READ PLOT | Enter | END PLOT |
| | | desired plot | |
| | | data | |
+-----------------+-----------------+-----------------+-----------------+
| Grid | READ GRID | Enter | END GRID |
| geometry | | desired mesh | |
| data | | data | |
+-----------------+-----------------+-----------------+-----------------+
| Reaction | READ REACTION | Enter desire | END REACTION |
| | | reaction | |
| | | tallies (CE | |
| | | mode only) | |
+-----------------+-----------------+-----------------+-----------------+
| KENO V.a | END DATA | | Enter to | |
| data | | signal the | |
| terminus | | end of all | |
| | | | KENO V.a | |
| | | data | |
+-----------------+-----------------+-----------------+-----------------+
| Search data | READ SEARCH | Enter for | END SEARCH |
| | | CSAS5 | |
+-----------------+-----------------+-----------------+-----------------+
| \*Must precede | | | |
| all other data | | | |
| blocks in this | | | |
| table. | | | |
+-----------------+-----------------+-----------------+-----------------+
Search data
~~~~~~~~~~~
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.
Search type specification
^^^^^^^^^^^^^^^^^^^^^^^^^
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.
SEARCH DESCRIPTOR is used to define the search mode.
Use OPTIMUM if the maximum value of *k*\ :sub:`eff` is to be determined.
Use CRITICAL if a specified value of *k*\ :sub:`eff` is to be obtained.
Use MINIMUM if the minimum value of *k*\ :sub:`eff` is to be determined.
SEARCH TYPE is used to specify the variable that is to be changed during the search procedure.
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.
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.
An OPTIMUM PITCH search determines the pitch that gives the maximum
value of *k*\ :sub:`eff`.* 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.
An OPTIMUM DIMENSION search determines the maximum value of *k*\ :sub:`eff` 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.
An OPTIMUM CONCENTRATION search determines the maximum value of *k*\ :sub:`eff`
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.
A CRITICAL PITCH search alters the spacing between units in the same
manner as an optimum pitch search to achieve the specified value of
*k*\ :sub:`eff`. 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.
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 *k*\ :sub:`eff`.* 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.
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 *k*\ :sub:`eff`. 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.
A MINIMUM PITCH search determines the pitch that gives the minimum value
of *k*\ :sub:`eff`. 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.
A MINIMUM DIMENSION search determines the minimum value of *k*\ :sub:`eff` 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.
A MINIMUM CONCENTRATION search determines the minimum value of *k*\ :sub:`eff`
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.
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.
PAS=nn
is used to set the maximum number of times the search will
calculate *k*\ :sub:`eff`.* The first pass calculates the *k*\ :sub:`eff` corresponding
to the initial geometry dimensions. The second pass calculates the
*k*\ :sub:`eff` 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.
NPM=nn
is used to set the number of search parameters. The default value
of nn is 1 and should not be overridden.
EPS=ff
is used to set the search convergence tolerance (the amount by
which *k*\ :sub:`eff` is allowed to vary from the desired *k*\ :sub:`eff`)\ *.* An
optimum or minimum search is terminated when the calculated *k*\ :sub:`eff` 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 *k*\ :sub:`eff` is within EPS of the specified
*k*\ :sub:`eff`. The default value of ff is 0.005.
KEF=ff
is used only for a CRITICAL search. The default value of ff is
1.000.
MINPITCH=ff
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.
MAXPITCH=ff
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.
MORE
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.
.. _tab2-3:
.. table:: Outline of search type specification
:align: center
+-----------------+-----------------+-----------------+-----------------+
| **Entry** | **Type of | **Data entry** | **Comments** |
| | data** | | |
| **No.** | | | |
+-----------------+-----------------+-----------------+-----------------+
| 1 | Search | OPTIMUM | Initiates a |
| | descriptor | | search for the |
| | | | maximum value |
| | | | of *k\ eff*. |
+-----------------+-----------------+-----------------+-----------------+
| | | CRITICAL | Initiates a |
| | | | search for a |
| | | | specified value |
| | | | of *k\ eff*. |
+-----------------+-----------------+-----------------+-----------------+
| | | MINIMUM | Initiates a |
| | | | search for the |
| | | | minimum value |
| | | | of *k\ eff*. |
+-----------------+-----------------+-----------------+-----------------+
| 2 | Search type | PITCH | Vary the pitch |
| | | | of an array. |
+-----------------+-----------------+-----------------+-----------------+
| | | DIMENSION | Vary one or |
| | | | more dimensions |
| | | | in one or more |
| | | | regions of one |
| | | | or more units. |
+-----------------+-----------------+-----------------+-----------------+
| | | CONCENTRATION | Vary the |
| | | | concentration |
| | | | of one or more |
| | | | standard |
| | | | compositions in |
| | | | one or more |
| | | | mixtures. |
+-----------------+-----------------+-----------------+-----------------+
| 3 | Optional search | | Optional search |
| | parameters | | parameters |
| | | | allow changing |
| | | | default values. |
| | | | Any or all may |
| | | | be entered in |
| | | | any order. |
+-----------------+-----------------+-----------------+-----------------+