.. _sec-origami:

============================================================
ORIGAMI: A Code for Computing Assembly Isotopics with ORIGEN
============================================================

.. codeauthor:: S. E. Skutnik, M. L. Williams, I. C. Gauld, W. A. Wieselquist, and R. A. Lefebvre

.. include:: <isonum.txt>
.. program:: origami

ORIGAMI computes detailed isotopic compositions for light water reactor
assemblies containing UO\ :sub:`2` fuel by using the ORIGEN
transmutation code with pre-generated ORIGEN libraries, for a specified
assembly power distribution. The fuel may be modeled using either lumped
or pinwise representations with the option of including axial zones. In
either case, ORIGAMI performs ORIGEN burnup calculations for each of the
specified power regions to obtain the spatial distribution of isotopes
in the burned fuel. Multiple cycles with varying burn-times and
downtimes may be used. ORIGAMI produces several types of output files,
including one containing stacked ORIGEN binary output data ("ft71 file")
for each depletion zone; files with nuclide concentrations at the last
time-step for each axial depletion region, in the format of SCALE
standard composition input data or as MCNP material cards; a file
containing the axial decay heat at the final time-step; and gamma and
neutron radiation source spectra.


Acknowledgments
===============

ORIGAMI is based on the PinDeplete code developed by Steve Skutnik and also 
includes techniques taken from the Orella code written by Ian Gauld (retired).
Support for development of ORIGAMI was provided by the U.S. Department of Energy,
Office of Nuclear Energy, Nuclear Fuels Storage and Transportation Planning Project.

Introduction
============

ORIGAMI (**ORIG**\ EN **A**\ sse\ **m**\ bly **I**\ sotopics) provides
the capability to perform isotopic depletion and decay calculations for
a light water reactor fuel assembly model using one or more ORIGEN
calculations. The assembly may be modeled using either lumped or pinwise
representations with the option of including axial zones. ORIGAMI
automates the performance of ORIGEN depletion calculations for each
region and thus simulates zero-, one-, two-, and three -dimensional (0D,
1D, 2D, and 3D) modeling of a fuel assembly. Multiple cycles with
different specific powers and exposure and decay times may be treated,
and the power distribution is described in terms of fractional pin
powers in the XY plane and axial distributions along the Z axis, which
define the burnup regions for the ORIGEN computations. ORIGAMI allows
for easy and flexible material composition specification through the
standard SCALE mixture processor for composition input, the same as in
TRITON (see :ref:`XSPROC chapter <sec-xsproc>`). While ORIGAMI cannot presently treat
axially non-uniform lattice features (e.g. axially varying enrichment or
the partial-length rods found in many boiling water reactor designs)
within a single input, these problems can still be easily modeled by
splitting the problem across sequential ORIGAMI input cases residing on
the same file.

The ORIGEN calculations performed by ORIGAMI use the methodology
originally established for the SCALE sequence ORIGEN-ARP
(see the :ref:`ARP section <sect-arp>`). This approach provides an efficient
mechanism to perform stand-alone reactor depletion calculations using
pre-generated  ORIGEN libraries which contain self-shielded, collapsed one-group
cross sections as a function of selected independent variables, such as burnup,
enrichment, and moderator density, for different reactor systems. Typically the
data in these libraries are obtained from 2D, multigroup lattice transport
calculations (e.g., TRITON) coupled with depletion calculations for burnup.
The library cross sections may be flux-weighted over the lattice to obtain data
representative of the entire homogenized assembly for lumped depletion; or
alternatively, it is also possible to generate multiple ORIGEN libraries
corresponding to individual or groups of pins within the lattice for multi-pin
depletion. The burnup-dependent ORIGEN libraries are analogous to the
parameterized cross section data produced by lattice physics codes for reactor
core simulators, except that data for many more nuclides and reactions are
included to allow ORIGEN to compute detailed isotopics for more than 2200
nuclides.

ORIGAMI extends the capabilities previously provided by ORIGEN-ARP to
perform a suite of ORIGEN calculations in order to represent the
isotopic distribution of fuel within an assembly in more detail. The
pre-generated ORIGEN libraries provided with SCALE tabulate the
assembly-average one-group cross sections, in order to accurately
reproduce assembly-average isotopics. When performing pin-by-pin
calculations in ORIGAMI, users can increase the fidelity with respect to
proximity to features such as assembly edges, water holes, burnable
poison rods, etc. by creating and employing zone-specific libraries for
different pins. By specifying the individual library assignments for
each pin, users can capture these local spectrum changes in the ORIGAMI
calculation through the use of one-group libraries based on these local
conditions. Currently, the specification of individual libraries is
limited to pin-level specification only (i.e., the same library is used
for all axial zones corresponding to a pin for 3D cases) with an allowed
axial moderator density distribution and radial and axial power
distributions.

ORIGAMI can produce the following output files in addition to the
standard ORIGEN output for each depletion zone:

   * isotopics in ORIGEN binary concentration (ft71) files

      * in each depletion zone at times specified by the :command:`options` block,
        :option:`ft71` key

      * in each axial zone (summed over all pins at a particular axial
        level) at the final time;

   * nuclide concentrations by axial zone, written as a SCALE "standard
     composition block" that can be used directly as input for SCALE
     transport codes such as the KENO Monte Carlo criticality code;

   * axially-dependent decay heat source for input to a thermal analysis
     code such as COBRA, so that the temperature distribution within a
     storage cask can be computed;

   * nuclide concentrations for each axial zone, given in the format of
     MCNP material cards;

   * space-dependent radiation source energy spectra and magnitudes in a
     simple text file.


ORIGAMI is tightly integrated with the SCALE Graphical User Interface,
Fulcrum. Using Fulcrum and the "UO2 express form (configurable)", one
can create a simple UO\ :sub:`2` assembly depletion case in seconds (see
:numref:`fig-origami-uox-express`). Finally, ORIGAMI has the ability to
perform the depletion/decay calculations for each zone in parallel using the
MPI (Message Passing Interface), however this requires a special SCALE
installation built with MPI in order to do so :cite:`ORIGAMI-shlg2013`.

.. _fig-origami-uox-express:
.. figure:: ../figs/ORIGAMI/ss-uox-express.png

   Fulcrum UO\ :sub:`2` express form for creating ORIGAMI input.


Computational Methods
=====================

ORIGAMI assembly model
----------------------

The basic model for ORIGAMI is a fuel assembly, which may be modeled in
several ways with varying degrees of complexity. The most primitive
model represents the assembly materials as a single mass lump that is
depleted using the value of the specific power input in the
power-history block. In this case, a single ORIGEN calculation is
performed to obtain isotopics representing the entire assembly. This 0D
model is equivalent to the current ORIGEN-ARP procedure. A more detailed
model applies an input axial power profile to the (radially) lumped
assembly materials. This lumped axial depletion model produces a 1D
axially varying burnup distribution, but no allowance is made for
variations in the relative pin powers within the assembly. Thus, if the
axial power distribution is defined by N\ :sub:`Z` axial zones, ORIGEN
calculations are performed for N\ :sub:`Z` different depletion regions.
The 1D axial depletion model has been found to be adequate for most
criticality and decay heat analysis of spent fuel
assemblies :cite:`ORIGAMI-rgiw2012`. Note that both the 0D and 1D modes are fully
consistent with the 2D TRITON calculations used to generate ORIGEN
reactor libraries distributed with SCALE, in that these modes employ
spatially-homogenized cross-sections to represent assembly-averaged flux
and cross-sections. For 2D and 3D depletion models (wherein individual
pin-specific libraries may optionally be specified), the user is advised
that the ORIGEN reactor data libraries distributed with SCALE are
representative of an assembly axial plane as a whole; in as much, the
user is advised to generate their own zone-specific libraries (i.e.,
based on individual material zones) within TRITON if they wish to
capture regional neutronic effects within the assembly (such as
proximity to water holes, burnable absorbers, etc.)

By specifying a radial pin-power map, a 2D or 3D calculation may be
performed. Currently the axial and radial power shapes are fixed for the
entire calculation but do still result in a fully 3D isotopic
distribution :cite:`ORIGAMI-shlg2013,ORIGAMI-sgrt2012`. If there are N\ :sub:`P` pins in the
assembly and each has N\ :sub:`Z` axial zones, ORIGAMI will perform ORIGEN
calculations for N\ :sub:`P` :math:`\times` N\ :sub:`Z` depletion regions. For
example, an assembly with a 17 :math:`\times` 17 array with 264 fuel pins and
N\ :sub:`Z` = 24 axial zones requires 6336 independent ORIGEN
calculations. For these types of simulations, the parallel mode with MPI
is highly recommended.

Definition of initial composition
---------------------------------

The initial mass in metric tons of heavy metal is M\ :sub:`mtu`, set by the
input parameter :option:`mtu`. The default value of :option:`mtu` is equal to 1.0, so
that by default the ORIGEN calculations are performed on the basis of
"per metric ton of heavy metal". Given that the sum over all zones must
have the total heavy metal content (M\ :sub:`mtu`), one arrives at zone-wise
heavy metal masses of:

.. math::
   M_{xy,z} = \dfrac{M_{\text{mtu}}}
  { \sum \limits_{z = 1}^{N_{z}}{ f_{z} } \sum \limits_{xy = 1}^{N_{P}}{ m_{xy}} } \cdot f_{z} \cdot m_{xy}
  :label: eq-origami-mass-norm

where the relative amount of heavy metal in each radial position,
:m\ :sub:`xy`, is calculated from the mixture specification;
fractional axial height, f\ :sub:`z`, from the zone specification;
and N\ :sub:`P` and N\ :sub:`Z` are the total number of fuel pins and axial zones,
respectively. Note that some pin locations in the assembly may not
contain fuel, and these are not included in the value of N\ :sub:`P`.
The fractional axial height is given

    :math:`f_z = \frac{\Delta Z }{Z_{\text{tot}}}` is the fraction of
    the active fuel height occupied by axial zone Z
    :math:`\Delta Z` is the length of axial zone

    Z\ :sub:`tot` is the total length of the active fuel.


Whenever an axial zone mesh is input (with array :option:`meshz`), the value of
f\ :sub:`Z` is computed from the values of the zone boundaries (see input
description in :numref:`sect-origami-print-opts-blk`). If an axial mesh array
is not input, the axial zones are assumed to be uniformly distributed. In this
case, the axial zones all have the same height, so that :math:`f=\frac{1}{N_Z}`,
where N\ :sub:`Z` is the number of uniform axial zones in the assembly.

The uranium mass in a single axial zone for all N\ :sub:`P` fuel pins in
the assembly (M\ :sub:`z`) is thus:

.. math::
   M_Z = N_P \times M_{XY, Z} = M_{\text{mtu}} \times f_Z
  :label: eq-origami-mass-ax-norm


In addition to the fuel mixture in an assembly, non-fuel materials
(e.g., structural materials) may also be present. These materials
contribute to the overall power production due to the energy produced by
neutron capture reactions.. For a given value of the total assembly
power, this reduces the power from the fuel mass and thus may slightly
alter the fuel burnup and isotopics. In addition, activation of non-fuel
materials produces additional radiation source terms in the spent fuel,
which contribute to the decay heat and activity. Therefore ORIGAMI
provides an option for including the non-fuel elements in the input
array, :option:`nonfuel`. The units of the non-fuel element masses are kg per
MTU, and the materials are distributed uniformly within all fuel
depletion zones. Note that the input non-fuel materials should not
include oxygen in UO\ :sub:`2` if UO\ :sub:`2` is specified as the fuel
material, as oxygen is already included in proportion to the uranium
mass basis. Finally, because ORIGAMI accesses the StdComp library, any
SCALE StdComp composition, e.g. "zirc4" for reactor cladding material
Zircaloy-4, may be used in either structural or fuel materials.

.. _sect-origami-restart-case:

Restart cases
-------------

ORIGAMI also allows the initial nuclide concentrations to be obtained
from a previously produced ORIGEN binary output file. A restart case is
indicated by setting :command:`restart=yes` in the parameter array. The restart
file has the name :file:`assembly_restart.f71` and must be copied (or linked)
to the SCALE temporary directory used for calculations. The restart file
is normally obtained from an earlier ORIGAMI calculation, which always
produces an ORIGEN restart file named :file:`${OUTBASENAME}.assm.f71`, where
:envvar:`${OUTBASENAME}` is an output prefix defined by the name of the input file
and any user-specified prefix with the :command:`prefix` key. Generally the
restart file from ORIGAMI contains stacked concentrations, corresponding
to each axial zone and then a final entry for the lumped assembly
concentrations; hence, the initial composition for a restart case varies
with axial zone, unlike the case for fresh fuel. ORIGAMI does not
currently allow pin-dependent restart calculations. A restart case may
be useful for performing decay-only calculations of spent fuel
inventory, using the burned fuel composition previously computed for the
assembly exposure during reactor operation. For decay-only cases, a
value for the input parameter :option:`nz` must be input in order to indicate
the number of axial depletion regions in the previous burnup
calculation.

.. _sect-origami-power-dist:

Definition of power distribution
--------------------------------

The radial power distribution is defined by the XY fractional pin powers in the
input array :option:`pxy`, and the axial fractional powers in the input array :option:`pz`.
The input values in arrays :option:`pxy` and :option:`pz` are normalized to unity by the code.
The fractional power for a fuel pin "XY" is designated here to be
r\ :sub:`XY`, with the normalization :math:`\sum_{XY = 1}^{N_{P}}r_{XY}`.
Similarly the fractional axial power for an axial zone Z is a\ :sub:`Z`,
which is normalized to :math:`\sum_{Z = 1}^{N_{Z}}a_{Z}`. The shapes of
both the radial XY and axial Z distributions must be obtained prior to the
ORIGAMI calculation, either from neutron transport calculations or experimental
measurements. The input distributions remain constant during the ORIGEN burn
calculations for all cycles; but in reality, the power distributions may vary
with time---for example, the initial axial power distribution tends to flatten
after a period of burnup since the higher power zones deplete the fuel faster.
For this reason it is strongly recommended to use the relative burnup
distribution (at final discharge) rather than the relative power density
distribution for the input values. The burnup shape corresponds to the
shape of the time-averaged flux distribution during the exposure period. This
ensures that the final burnup distribution matches the desired shape.

.. Note::
  When comparing depletion calculations to an equivalent case from 
  TRITON/NEWT or TRITON/KENO, it is important to note the difference
  between the *total system power* (which will include small contributions
  from the recoverable energy from non-fission capture reactions by the
  moderator and any structural materials) with the *fuel power* (used for 
  the fuel depletion calculation). Because of the small contributions to
  the total system power from non-fuel regions, the fuel power will likely
  be smaller than the total system power, as specified in the `burn` block.

  Thus, users wishing to compare the results of an ORIGAMI calculation to
  an equivalent TRITON calculation should ensure that that they are using
  the equivalent fuel mixture power from TRITON in ORIGAMI (and not the 
  total system power); see :numref:`sect-triton-power-balance` for further 
  details.


For a given cycle, the assembly-specific power P\ :sup:`(SP)` is equal
to the value of input variable :option:`power`, read in the power-history block
(see :numref:`sect-origami-hist-block`). The assembly-specific power has units
of megawatts per MTU (MW/MTU). Therefore, the total power produced by the fuel
assembly is:

.. math::
  P_{\text{tot}} = P_{A}^{\left( \text{SP} \right) } \cdot M_{\text{mtu}}
  :label: eq-origami-tot-pow

where P\ :sub:`tot` is the assembly total power, and
:math:`P_{A}^{\left( \text{SP} \right)}` is the specific power for the
assembly, read from input.

The absolute power (MW) in fuel pin "XY" is:

.. math::
   P_{P} = P_{\text{tot}} \cdot r_{xy} = P_{A}^{\left( \text{SP} \right)}
      \cdot M_{\text{mtu}} \cdot r_{xy}
   :label: eq-origami-pin-pow


and the power produced in axial zone Z of this fuel pin XY is:

.. math::
  P_{XY,Z} = P_{\text{tot}} \cdot r_{xy} \cdot a_{Z} = P_{A}^{\left( \text{SP}
     \right)} \cdot M_{\text{mtu}} \cdot r_{xy} \cdot a_{Z}
  :label: eq-origami-node-pow

The absolute power produced in a single axial zone Z for all pins is:

.. math::
   P_{Z} = \sum_{XY = 1}^{N_{P}}{P_{XY,Z} = P_{\text{tot}}
   \times a_{Z} = P_{A}^{\left( \text{SP} \right)} \times M_{\text{mtu}}
   \times a_{Z}}
   :label: eq-origami-ax-zone-pow

The ORIGEN depletion calculations are performed with the absolute powers
defined in :eq:`eq-origami-pin-pow` and :eq:`eq-origami-ax-zone-pow`
for each depletion region in the 2D/3D pin-wise or 0D/1D axial depletion models,
respectively. However, cross sections in the ORIGEN libraries are parameterized
as a function of burnup, which depends on the specific power rather than absolute
power for a given depletion region. The specific power (MW/MTU) in axial zone Z
of pin XY is equal to:

.. math::
   P_{XY,Z}^{(SP)} = \frac{P_{XY,Z}}{M_{XY,Z}}
   :label: eq-origami-pin-sp-pow

Substituting :eq:`eq-origami-mass-norm` and :eq:`eq-origami-node-pow` into
:eq:`eq-origami-pin-sp-pow` gives:

.. math::
   P_{XY,Z}^{(SP)} = \frac{P_{A}^{(SP)} \cdot r_{\text{xy}} \cdot a_{Z}
      \cdot N_{P}}{f_{Z}}


In a similar manner, it can be shown that the specific power for all
fuel pins in axial plane Z is:

.. math::
    P_{Z}^{(SP)} = \frac{P_{A}^{(SP)} \cdot a_{Z}}{f_{Z}}
    :label: eq-origami-ax-zone-sp-pow

ORIGAMI permits two modes for user-specified power distributions along the
axial and radial meshes: *absolute* fractions (i.e., where powers along the
axial mesh points are expressed as fractions of the total assembly power in
MW) and *relative* normalization (i.e., in which *specific powers*\ ---
in MW/MTU --- of axial zones are expressed as a relative modifiers of the
assembly specific powers input in the power history block). Relative power
shape modifiers assume that the specific powers expressed in the power history
block represent the *average* assembly specific power(s) thus, ORIGAMI will
convert these factors into axial & pin power *fractions* --- i.e., the factors
r\ :sub:`xy` and a\ :sub:`z` found in :eq:`eq-origami-pin-pow` and
:eq:`eq-origami-ax-zone-pow` used to calculate the absolute pin power
and axial zone power, respectively. The conversion from *relative* specific
power modifiers to *absolute* power fractions is accomplished through the
following normalization procedure :eq:`eq-origami-rel-pow-norm`:


.. math::
   \left( a_{Z} \right)_{i} =
   \frac{ \left( R_{Z} \right)_{i} \cdot M_{\text{MTU}} \cdot \left( \frac{\Delta Z}{Z_{\text{tot}}} \right)_{i}}
   {\sum{\left( R_{Z} \right)_{i} \cdot M_{\text{MTU}} \cdot \left( \frac{\Delta Z}{Z_{\text{tot}}} \right)_{i}}}
   = \frac{\left( R_{Z} \right)_{i} \cdot \left( \frac{\Delta Z}{Z_{\text{tot}}} \right)_{i}}{\sum{\left( R_{Z} \right)_{i}
   \cdot \left( \frac{\Delta Z}{Z_{\text{tot}}} \right)_{i}}}
   :label: eq-origami-rel-pow-norm


where :math:`\left( a_{Z} \right)_{i}` is the axial power fraction for axial
zone *i* and :math:`\left( R_{Z} \right)_{i}` is the relative axial zone
specific power modifier for axial zone *i.* Obviously, for a uniformly-spaced
axial mesh, the conversion from relative specific powers (using relative power
modifiers) is precisely the same as that for absolute fractional axial zone
powers; i.e., the relative power modifiers simply become axial power fractions
by virtue of the fact that the term
:math:`\left( \frac{\Delta Z}{Z_{\text{tot}}} \right)_{i}` becomes a constant,
thereby reducing :eq:`eq-origami-rel-pow-norm` back to a direct
calculation of the fractional axial power based on a relative power modifier
following normalization.

Because it is assumed that the assembly mass is uniformly distributed across
the pins, it can similarly be shown that the use of relative power modifiers
for the XY pin map :math:`\left( r_{XY} \right)_{i}` will always produce the
same result as using pre-normalized absolute fractional powers in the pin map,
i.e. :eq:`eq-origami-pin-pow-norm`:

 .. math::
   \left( r_{XY} \right)_{i} = \frac{\left( R_{XY} \right)_{i} \cdot
   \frac{M_{\text{MTU}}}{N_{P}}}{\sum_{}^{}{\left( R_{XY} \right)_{i}
   \cdot \frac{M_{\text{MTU}}}{N_{P}}}} =
   \frac{\left( R_{XY} \right)_{i}}{\sum_{}^{}\left( R_{XY} \right)_{i}}
   :label: eq-origami-pin-pow-norm


This option is provided as the :option:`relnorm` option in the parameters block
(discussed further in :numref:`sect-origami-options-blk`). The motivation
for providing an alternative normalization for axial power shape factors is
twofold. First, it is generally assumed that information on the axial power
shape is obtained from axial measurements relative to an assembly-average
value (i.e., axial gamma scans to determine the burnup profile based
upon the gross gamma intensity or isotopic ratios of burnup indicators
such as :sup:`134`\ Cs / :sup:`137`\ Cs, etc.). Therefore, by using the
relative normalization option (i.e., treating axial power shape factors
as *relative* modifiers of the assembly specific power), users can
directly input shape factors obtained from techniques such as
non-destructive analysis (NDA) fuel measurements into ORIGAMI to model
assembly isotopic distributions.

The second motivation for the relative normalization option comes from
potential problems that can arise if treating axial power shape factors
as absolute fractional powers (:command:`relnorm=no`) in conjunction with
non-uniform axial mesh spacing defined by the user in the :command:`z` array (see
:numref:`sect-origami-input-arrays` for details).

.. Important::
   If using the :command:`relnorm=no` option, the fractional axial powers **must** be
   consistent with the axial mesh sizes defined or else **incorrect**
   zone-specific powers will result from :eq:`eq-origami-ax-zone-sp-pow`,
   therefore leading to incorrect results and likely causing the ARP sequence
   to fail (and therefore the ORIGAMI calculation to halt) due to calculated
   burnup values for the depletion zone being out of the library range.

   Users are thus **strongly cautioned** when using absolute fractional
   axial powers (:command:`relnorm=no`) to ensure proper consistency between the axial
   power fractions and the axial mesh sizes.

   For this reason, relative power shape factor normalization is
   **turned on** by default (:command:`relnorm=yes`).

.. _sect-origami-n-gamma-calc:

Computation of neutron and gamma energy spectra
-----------------------------------------------

ORIGAMI includes an option to generate multi-group neutron and gamma
source spectra due to radioactive decay, for each depletion zone.
Multi-group values are calculated by binning the discrete line and
continuum spectra produced by radioactive decay and nuclear reactions
into arbitrary energy group structures defined by user input. Whenever
neutron energy group boundaries are input in array :option:`ngrp`, neutron
source spectra due to spontaneous fission, delayed neutron emission, and
:math:`\left( \alpha, n\right)` reactions are calculated.

Similarly, gamma source spectra are computed if gamma energy group bounds are
input in array :option:`ggrp`. The gamma source includes photons produced by all types
of radioactive decays, and also may include bremsstrahlung radiation produced
by beta interactions. Input options can specify the type of nuclides included in
the source term (i.e., light elements, actinides, fission products, or all
nuclides), and the materials used for :math:`\left( \alpha,n \right)`
reactions and bremsstrahlung production. If source spectra are calculated, the
values are always included in the ORIGEN output ft71 binary file; and
optionally the source spectra may also be output in a text file. The source
text file only includes the average over all pins for each axial zone, while
the ft71 file includes sources for all pins and axial zones.

The source spectra output by ORIGAMI are calculated in ORIGEN using the
expression outlined in :eq:`eq-origami-spectra`:


.. math::
   S_{\text{Z.g}}^{(p)} = \sum_{i = 1}^{\text{itot}}{Y_{i,g}^{(p)}\lambda_{i}
   \frac{M_{Z}^{(i)}}{A^{(i)}} \cdot N_{A}}
   :label: eq-origami-spectra

where

   :math:`S_{\text{Z.g}}^{(p)}` = source spectrum (p/s) in energy group *g*
   for particles of type *p* and axial zone *Z*;

   :math:`Y_{i,g}^{(p)}` = number of particles of type *p* emitted per
   decay of nuclide *i*; with energy in group *g*;

   :math:`M_{Z}^{(i)}` = mass (g) of nuclide *i* in axial zone *Z*,
   obtained from ORIGEN calculation;

   N\ :sub:`A` = Avogadro's number (number atoms of nuclide *i* per mole);

   A\ :sup:`(i)` = mass (g) of 1 mole of nuclide *i*;

   :math:`\lambda_i` = decay constant (s\ :sup:`-1`) for nuclide *i*,

   itot = total number of nuclides in burned fuel.


More details on the ORIGEN calculation of the source spectra can be
found in the ORIGEN section (:numref:`sect-origen-rad-emissions`) of
the SCALE documentation.

.. _sect-origami-input:

ORIGAMI Input Description
=========================

ORIGAMI uses free-form, keyword-driven input with the SCALE Object
Notation (SON) syntax also used for ORIGEN input, and is described in
more detail there. The general outline of ORIGAMI input is as follows.

   (a) Case Identifier

   (b) Options

   (c) Fuel Composition

   (d) Power-History

   (e) Source-Options

   (f) Output-Print Options

   (g) Input Data

The above input data may be entered in any order. Data blocks and
parameters which are not needed, or for which default values are
desired, can be omitted. :numref:`ex-origami-input` provides a template
containing all of the ORIGAMI input data blocks and arrays, with example
values assigned. Note that much of the information shown in the template is
optional, and typically is not needed for many cases. The following
subsections provide a more detailed description of the input.

.. code-block:: scale
  :caption: Template for ORIGAMI input data
  :name: ex-origami-input

   =origami
   % Case identifier information
     title= 'input template example'
     prefix= example
     asmid=1
   % Parameter options
     options{
       pitch= 19.718
       mtu= 0.4
       decayheat=yes
       fracnf=0.08
       nburn=15
       ndecay=12
       temper=300.0
       stdcomp=yes
       restart=no
       interp=spline
       output=cycle
       ft71=all
     }
   % Array containing ORIGEN library names
     libs=[ ce14x14 ce16x16 ]
   % Fuel Composition
     fuelcomp{
       uox(fuel1){ enrich=3.21 }
       uox(fuel2){ enrich=3.50 }
       uox(fuel3){ enrich=2.80 }
       mix(1){ comps[ fuel1=98.2 Gd2O3=1.8 ] }
       mix(2){ comps[ fuel2=100 ] }
       mix(3){ comps[ fuel2=97.5 Gd2O3=2.5 ] }
       mix(4){ comps[ fuel3=96.9 Gd2O3=3.1 ] }
     }
   % Map ORIGEN library names to XY pin layout
     libmap=[ 1 2
              2 1 ]
   % Map individual compositions XY pin layout
     compmap=[ 1 2
               3 4 ]
   % XY relative power distribution (code renormalizes to unity)
     pxy=[ 0.2 0.3
           0.4 0.5 ]
   % Z-axial relative power distribution (code renormalizes to unity)
     pz=[ 0.6 0.4 ]
   % Axial interval boundaries (for MTU mass distribution & plotting)
     meshz=[ 0.0 15.0 30.0 ]
   % Non-fuel nuclides distributed within fuel material
     nonfuel=[ cr=3.366 mn=0.1525 fe=6.309 co=0.0302
               ni=2.366 zr=516.3 sn=8.412 gd=2.860 ]
   % Axial variation of moderator density fraction
     modz=[ 0.73 0.715 ]
   % Irradiation/decay information
     hist[
       cycle{ power=35.0 burn=200.0 nlib=7 down=50.0 }
     ]
   % Optional neutron/gamma source information
     ggrp=[ 10.0e6 2.0e6 1.0e6 0.5e6 0.01 ]
     ngrp=[ 20.0e6 1.0e6 1.0e5 1.0e4 1.0e3 10.0 0.01 ]
     srcopt{ sublib=ac brem_medium=uo2 alphan_medium=case print=yes }
   % Output edit options
     print{
       nuc{sublibs=[lt ac] total=no units=[grams] }
     }
   % Nuclides included in comp file (OPTIONAL: overrides default)
     nuccomp=[
        92232 92233 92234 92235 92236 92237 92238 92239 92240
        92241 93235 93236 93237 93238 93239 94236 94237 94238
        94239 94240 94241 94242 94243 94244 94246 95241 95242
        95243 95244 95246 96241 96242 96243 96244 96245 96246
        96247 96248 96249 96250 97249 97250 98249 98250 98251
        98252 98253 98254 99253 99254 99255
     ]
   end


Case and identifier information
-------------------------------

ORIGAMI has three optional identifiers for the case. The :option:`title` is
included as a descriptor in the printed output file. The character string
:option:`prefix` is added to the front of the  output file names described in
:numref:`sect-origami-io-files` and in :numref:`tab-origami-io-files`. Finally,
the integer variable :option:`asmid` is an arbitrary assembly identifier used
in defining mixture numbers in the SCALE standard composition output file.
:eq:`eq-origami-mix-num` in :numref:`sect-origami-stdcomp-file` describes how
the mixture ID is determined.

.. option:: title= <string>

   Title (up to 50 characters) describing the case. Enclosed in quotes if
   using embedded blanks.

   (**Default:** none)

.. option:: prefix= <string>

   Prefix (up to 16 characters) to append to output file names.

   (**Default:** none)

.. option:: asmid= <integer>

   Integer used to identify mixture ID in generated SCALE standard composition
   block [see :eq:`eq-origami-mix-num`].

   (**Default:** 1)

.. tabularcolumns:: |\Y{0.08}|\Y{0.65}|\Y{0.12}|
.. table:: Keywords for case identifier
   :class: longtable
   :widths: 13 65 12
   :name: tab-origami-id-kw

  +-------------+----------------------------------------+-------------+
  | **Keyword** | **Description**                        | **Default** |
  +=============+========================================+=============+
  | title=      | up to 50 characters describing the     | blank       |
  |             | case title, quoted if embedded blanks  |             |
  +-------------+----------------------------------------+-------------+
  | prefix=     | up to 16 characters (no embedded       | blank       |
  |             | blanks) appended to output file names  |             |
  +-------------+----------------------------------------+-------------+
  | asmid=      | integer used to identify mixture ID in | 1           |
  |             | generated SCALE standard composition   |             |
  |             | block [see :eq:`eq-origami-mix-num`]   |             |
  +-------------+----------------------------------------+-------------+

.. _sect-origami-options-blk:

Options block
-------------

The ``options`` block has the following form:

.. option:: options {… keyword blocks …}

   The :option:`options` block allows the user to control problem features such
   as the total mass basis (:option:`mtu`), non-fuel mass (:option:`fracnf`),
   axial power normalization (:option:`relnorm`), exercise fine-grained control
   over depletion calculations (:option:`solver`, :option:`interp`,
   option:`nburn`, :option:`ndecay`), perform restart calculations from a prior
   ORIGAMI run (:option:`restart`), specify the number of axial zones
   (:option:`nz`), specify optional parameters used for visualization and
   post-processing (:option:`pitch`, :option:`temper`, :option:`fdens`),
   and control which outputs to generate (:option:`small`, :option:`mcnp`,
   :option:`stdcomp`, :option:`decayheat`).

.. :numref:`tab-origami-options-kw` shows the keywords for allowable parameters.

Each of the allowable parameter keywords is explained below. An example parameter block would be: ::

   options{ stdcomp=yes decayheat=yes }


.. option:: mtu= <number>

   Metric tons of heavy metal in the assembly.

   (**Default:** `1.0`)


.. option:: fracnf= <number>

  Total non-fuel mass in the assembly, given as a fraction of the heavy metal
  mass defined in :option:`mtu`.

  .. seealso::`nonfuel`

  (**Default:** `none`)


.. option:: nz= <integer>

  Number of axial intervals. If not input, :option:`nz` is equal to the number of
  entries in the input axial power array :option:`pz`.

  **Required** for decay-only restarts.

  (**Default:** Determined by code via :option:`pz`)


.. option:: nburn= <integer>

   Number of substeps used in ORIGEN burn calculations

   (**Default:** 10)


.. option:: ndecay= <integer>

   Number of substeps used in ORIGEN decay calculations

   (**Default:** 10)

.. option:: pitch= <real number>

   Assembly pitch (cm), if > 0.0. Only used to define XY mesh in viewing
   results. If this parameter is input, array :option:`pxy` must also be
   entered.

   (**Default:** 0.0)


.. option:: temper= <real number>

   Temperature (in degrees Kelvin) for mixtures output to the SCALE Standard
   Composition output (:file:`compBlock`).

   (**Default:** 293.0)


.. option:: fdens= <real number>

   Fuel density in g/cm\ :sup:`3`. Used to calculate the effective fuel 
   volume based on the total mass basis (thus facilitating conversion to
   volumetric units of concentration, such as atoms/bn-cm). Used in 
   calculating atom densities for the SCALE Standard Composition output
   (:file:`compBlock`).

   (**Default:** 10.4)


.. option:: offsetz= <integer>

   Axial numbering offset; used for sequential ORIGAMI cases to uniquely
   identify axial zones (i.e., such as when using sequential cases to modify
   changing axial geometry).

   (**Default:** 0)

.. option:: relnorm= <yes | no>

  Normalization of axial power shaping factors (:option:`pz`) to be used

  **no** |rarr| axial power shape factors treated as absolute fractions (does
         not normalize all axial burnups to 1.0)

  **yes** |rarr|  axial power shape factors treated as relative modifiers of
          assembly specific power (i.e., power= entries in the power history block)

  (**Default:** `yes`)


.. option:: mcnp= <yes | no>

   Generate MCNP input stubs containing data on material concentrations and/or
   gamma and neutron emissions for each depletion node in the problem.

   (**Default:** `yes`)


.. option:: stdcomp= <yes | no>

   Generate a text-based standard composition file containing burnup-credit
   nuclide number densities for each axial zone.

   (**Default:** `no`)


.. option:: decayheat= <yes | no>

    Produce a decay heat file containing decay powers (in W) for each axial
    zone.

   (**Default:** `no`)


.. option:: restart= <yes | no>

   Perform a restart calculation using initial compositions from a
   previously-generated ORIGEN ft71 file.

   (**Default:** `no`)


.. option:: solver= <matrex | cram>

   Use the standard ("MATREX") solver or the Chebyshev Rational Approximation
   Method (CRAM) solver.

   (**Default:** `matrex`)


.. option:: small= <yes | no>

   keep .out file small by suppressing all spectra and concentrations output
   except for lumped, assembly-averaged concentrations and spectra

    .. note::

       Full results are still written to other relevant files

   (**Default:** `no`)


.. option:: interp= <lagrange | spline>

   Method for interpolating cross sections in ARP; Lagrangian polynomial (`lagrange` or monotonic cubic spline `spline`)

   (**Default:** `lagrange`)


.. .. option:: output= <last | cycle | all>

   Time steps for printed output
   (**Default:** `last`)


.. .. option:: ft71= <last | cycle | all>

   Time steps included in output ft71 file
   (**Default:** `last`)

.. option:: ft71=<last,cycle,all>, output=<last,cycle,all>

   Controls output of saved / printed output concentrations.

   ``last`` saves / prints results only for the substeps in last step of the
   last cycle (**default**)

   ``cycle`` saves results for substeps in the last irradiation and decay
   steps in every cycle

   ``all`` saves results for all substeps of all irradiation and decay steps
   in every cycle

   (**Default:** ``last``)

.. tabularcolumns:: |\Y{0.13}|\Y{0.72}|\Y{0.15}|
.. table:: Keywords in ORIGAMI options
  :class: longtable
  :widths: 13 72 15
  :name: tab-origami-options-kw

  +-------------+---------------------------------+--------------------+
  | **Keyword** | **Description**                 | **Default**        |
  +=============+=================================+====================+
  | mtu=        | Metric tons of heavy metal in   | 1.0                |
  |             | the assembly                    |                    |
  +-------------+---------------------------------+--------------------+
  | fracnf=     | Total non-fuel mass in          | none               |
  |             | assembly, given as fraction of  |                    |
  |             | heavy metal mass defined by     |                    |
  |             | input *mtu=* . See description  |                    |
  |             | of input array                  |                    |
  |             | :option:`nonfuel`               |                    |
  +-------------+---------------------------------+--------------------+
  | nz=         | Number of axial intervals. If   | Determined by code |
  |             | not input, *nz* is equal to the |                    |
  |             | number of entries in the input  |                    |
  |             | axial power array :option:`pz`. |                    |
  |             | Required for decay-only         |                    |
  |             | restarts.                       |                    |
  +-------------+---------------------------------+--------------------+
  | nburn=      | Number of substeps used in      | 10                 |
  |             | ORIGEN burn calculations        |                    |
  +-------------+---------------------------------+--------------------+
  | ndecay=     | Number of substeps used in      | 10                 |
  |             | ORIGEN decay calculations       |                    |
  +-------------+---------------------------------+--------------------+
  | pitch=      | Assembly pitch (cm), if > 0.0.  | 0.0                |
  |             | Only used to define XY mesh in  |                    |
  |             | viewing results. If this        |                    |
  |             | parameter is input, array       |                    |
  |             | :option:`pxy` must also be      |                    |
  |             | entered.                        |                    |
  +-------------+---------------------------------+--------------------+
  | temper=     | Temperature (Kelvin) assigned   | 293.0              |
  |             | to materials in standard        |                    |
  |             | composition file                |                    |
  +-------------+---------------------------------+--------------------+
  | offsetz=    | Axial numbering offset; used    | 0                  |
  |             | for sequential ORIGAMI cases to |                    |
  |             | uniquely identify axial zones   |                    |
  |             | (i.e., such as when using       |                    |
  |             | sequential cases to modify      |                    |
  |             | changing axial geometry).       |                    |
  |             | [integer]                       |                    |
  +-------------+---------------------------------+--------------------+
  | relnorm=    | Normalization of axial power    | Yes                |
  |             | shaping factors (:option:`pz`)  |                    |
  |             | to be used                      |                    |
  |             |                                 |                    |
  |             | **no:** axial power shape       |                    |
  |             | factors treated as absolute     |                    |
  |             | fractions (does not normalize   |                    |
  |             | all axial burnups to 1.00)      |                    |
  |             |                                 |                    |
  |             | **yes:** axial power shape      |                    |
  |             | factors treated as **relative** |                    |
  |             | modifiers of assembly specific  |                    |
  |             | power (i.e., *power=* entries   |                    |
  |             | in the power history block)     |                    |
  |             | [yes/no]                        |                    |
  +-------------+---------------------------------+--------------------+
  | mcnp=       | no/yes |rarr| do not / do       | Yes                |
  |             | generate an MCNP material and   |                    |
  |             | gamma/neutron file              |                    |
  +-------------+---------------------------------+--------------------+
  | stdcomp=    | no/yes |rarr| do not / do       |  No                |
  |             | generate a standard composition |                    |
  |             | file containing burnup-credit   |                    |
  |             | nuclide number densities for    |                    |
  |             | each axial zone.                |                    |
  +-------------+---------------------------------+--------------------+
  | decayheat=  | no/yes |rarr| do not / do       |  No                |
  |             | produce a decay heat file       |                    |
  |             | containing decay powers (in W)  |                    |
  |             | for each axial zone.            |                    |
  +-------------+---------------------------------+--------------------+
  | restart=    | no/yes |rarr| do not / do       |  No                |
  |             | restart using initial           |                    |
  |             | compositions from a             |                    |
  |             | previously-generated ORIGEN     |                    |
  |             | ft71 file.                      |                    |
  +-------------+---------------------------------+--------------------+
  | solver=     | matrex/cram |rarr| use the      | Matrex             |
  |             | standard ("MATREX") solver or   |                    |
  |             | the Chebyshev Rational          |                    |
  |             | Approximation Method (CRAM)     |                    |
  |             | solver.                         |                    |
  +-------------+---------------------------------+--------------------+
  | small=      | no/yes |rarr| keep .out file    | No                 |
  |             | small by suppressing all        |                    |
  |             | spectra and concentrations      |                    |
  |             | output except for lumped,       |                    |
  |             | assembly-averaged               |                    |
  |             | concentrations and spectra      |                    |
  |             | (**Note:** all results are      |                    |
  |             | still written to other relevant |                    |
  |             | files).                         |                    |
  +-------------+---------------------------------+--------------------+
  | interp=     | lagrange/spline |rarr| method   | Lagrange           |
  |             | for interpolating cross         |                    |
  |             | sections in ARP                 |                    |
  +-------------+---------------------------------+--------------------+
  | output=     | last/cycle/all |rarr| time      | Last               |
  |             | steps for output print edits    |                    |
  +-------------+---------------------------------+--------------------+
  | ft71=       | last/cycle/all |rarr| time      | Last               |
  |             | steps included in output ft71   |                    |
  |             | file                            |                    |
  +-------------+---------------------------------+--------------------+


Additional notes on input parameters:

  (a) :option:`pitch` is only used for visualization of the results, and may be
      omitted if this is not of interest;

  (b) :option:`mtu` is discussed in :numref:`sect-origami-options-blk`

  (c) :option:`nz` is not required except decay-only restart cases; it must equal
      the number of entries in the array :option:`pz`;

  (d) :option:`nburn` and :option:`ndecay` are discussed in :numref:`sect-origami-hist-block`;

  (e) :option:`fracnf` is discussed in :numref:`sect-origami-input-arrays`, where the
      input array of non-fuel materials is described;

  (f) :option:`relnorm` is discussed in :numref:`sect-origami-power-dist`, in the
      definition of the assembly power distribution;

  (g) :option:`stdcomp`, :option:`fdens`, and :option:`temper` are discussed
      in :numref:`sect-origami-io-files`;

  (h) :option:`offsetz` is an optional feature designed to allow for ORIGAMI
      cases to be split across multiple inputs to capture axially-dependent
      features (such as partial-length rods); its use is discussed in further
      detail in the context of output generation in
      :numref:`sect-origami-io-files`;

  (i) :option:`decayheat` is discussed in :numref:`sect-origami-decay-heat-calc`;

  (j) :option:`restart` is discussed in :numref:`sect-origami-restart-case`.

  (k) :option:`output`, :option:`ft71`, are discussed in
      :numref:`sect-origami-power-dist`.


.. _sect-origami-fuel-comps:

Fuel composition block
----------------------

The purpose of the :option:`fuelcomp` block is to create a set of mixtures (via
the :command:`mix` blocks inside) to specify the pin-wise distribution of initial
isotopics. The example below, defines three mixtures (with IDs 1, 2, and
3); these are referenced in the :option:`compmap` array for this 2x2 array of
fuel pins.

.. option:: fuelcomp= { mixture blocks }

   Specifies fuel mixtures to be used by ORIGAMI in the :option:`compmap`
   array. *Numbered* :option:`mix` blocks are used by :option:`compmap`,
   which can be composed of other named mixtures.


.. option:: mix= { SCALE standard composition }

   Mixture blocks identify specific pin-wise composition to be used by ORIGAMI,
   using the standard SCALE mixture composition syntax. Mixtures must be given
   an integer identifier (e.g., ``mix(1)``, ``mix(2)``, etc.)

.. option:: compmap= [ mixture IDs ]

   Specifies the distribution of fuel compositions / mixtures for each pin for
   2-D and 3-D depletion cases. Mixture ID numbers correspond to those in the
   :option:`fuelcomp` block.

   **Required** if :option:`libmap` is explicitly specified beyond one element.

   (**Default:** ``[1]``)

.. code-block:: scale
  :name: ex-origami-fuel-comps
  :caption: Example specification of uranium oxide-based fuel mixtures in
             ORIGAMI, including 1) Mixed urania-gadolina fuel, 2) 4\% enriched
             UO\ :sub:`2` fuel, and 3) 2\% enriched UO\ :sub:2 fuel.

   fuelcomp{
      uox(fuel_3pct){ enrich=3.20 dens=10.42 }
      uox(fuel_4pct){ enrich=4.00 dens=10.45 }
      uox(fuel_2pct){ enrich=2.10 dens=10.43 }
      mix(1){ comps[ fuel_3pct=99.0 Gd2O3=1.0 ] }
      mix(2){ comps[ fuel_4pct=100] }
      mix(3){ comps[ fuel_2pct=100] }
   }
   compmap=[ 1 2
             2 3 ]



The *mix* block defines an array of compositions by their weight %.
For example, in the case of mix 2 and 3, it is 100% the "fuel_4pct" and
"fuel_2pct" compositions defined on the *uox* blocks above. In the case
of mix 1, it is 99% by weight `fuel_3pct` and 1% by weight the SCALE
StdComp `Gd2O3` (gadolinia). Each mixture number (defined by numbered
*mix* objects) is then referenced in the *compmap* array to define an
individual pin composition. For UO\ :sub:`x`-based fuels, ORIGAMI
automatically calculates the pin enrichment for cross-section library
interpolation via ARP. (Interpolation for MOX-based fuels is not
supported by ORIGAMI at this time.)

The *uox* keyword is an ORIGAM-specific shortcut to allow for easy
specification of UO\ :sub:`2`-based fuels along with their enrichment;
ORIGAMI automatically expands the *uox* keyword into a SCALE StdComp
block with a UO\ :sub:`2` base and explicitly-calculated uranium
isotopics per :numref:`tab-origami-uox-formula`. For example, the *uox* block
"fuel_3pct"expands to the following (:numref:`ex-origami-stdcmp-uox`):

.. code-block:: scale
  :name: ex-origami-stdcmp-uox
  :caption: Equivalent explicit expansion of the "fuel_3pct" block

   stdcomp(fuel_3pct){
      base=uo2
      iso[92234=0.02848 92235=3.2 92236=0.01472 92238=96.7568]
   }


For *uox*-based entries, the uranium isotopic distribution is calculated
from the user-specified enrichment per the formula outlined in
:numref:`tab-origami-uox-formula` :cite:`ORIGAMI-hpr1994,ORIGAMI-rgi2014`:

.. table:: Uraniumm isotope dependent on X wt% :sup:`235`\ U
  :class: longtable
  :name: tab-origami-uox-formula

  ============= ===============
  **Isotope**   **Isotope wt%**
  ============= ===============
  :sup:`234`\ U 0.0089 X
  :sup:`235`\ U 1.0000 X
  :sup:`236`\ U 0.0046 X
  :sup:`238`\ U 100 - 1.0135 X
  ============= ===============


Users may also specify materials directly using SCALE mixture processor
conventions; for example, the user could simply enter fuel mixture 2
directly as a StdComp as shown in :numref:`ex-origami-mix-direct` and
:numref:`ex-origami-mix-indirect`:

.. code-block:: scale
  :caption: Direct specification of materials in ORIGAMI (i.e., within the mixture block)
  :name: ex-origami-mix-direct

   mix(2){
     stdcomp(fuel_4pct){
       base=uo2
       iso[92234=XXX 92235=XXX 92236=XXX 92238=XXX]
      }
   }

Or similarly, one can refer to a composition by its alias:

.. code-block:: scale
  :caption: Indirect specification of fuel material mixtures (outside the mixture block)
  :name: ex-origami-mix-indirect

   stdcomp(fuel_4pct){
      base=uo2
      iso[92234=XXX 92235=XXX 92236=XXX 92238=XXX]
   }
   mix(2){ comps[ fuel_4pct=100.0 ] }


The *uox* keyword is thus useful when a user wishes to quickly specify a
UO\ :sub:`2`-based fuel; however, in cases where the user wishes to
specify the isotopic fractions of each uranium isotope, the use of a
StdComp object is recommended.


.. Caution::
   The mixture composition system in ORIGAMI is very flexible but the user is
   cautioned that ORIGAMI does not rigorously check that the specified
   composition is neutronically similar to that used to generate the ORIGEN
   library used in the calculation.

   For example, use of gadolinia burnable absorbers in the ORIGAMI input will
   yield incorrect results if the ORIGEN library was generated without
   gadolinia, due to the extreme thermal flux depression that gadolinia
   creates. It is therefore **up to the user** to verify that the libraries
   specified for the depletion zone are matched neutronically to the
   compositions specified.

.. _sect-origami-hist-block:

Power history block
-------------------

The data contained in the power history block is the same as in the
*BURNDATA* block of the TRITON lattice physics depletion sequence in
SCALE (see the :ref:`TRITON chapter <sec-triton>`, :ref:`BURNDATA block <sec-triton.burndata>`).
The power-history block describes the burnup and decay of the assembly and has the
following general form:

.. code-block:: scale
  :caption: Origami power history block
  :name: ex-origami-history-kw

   hist[
      cycle{ keywords for cycle-1 }
      cycle{ keywords for cycle-2 }
      … *(repeat for total number of cycles) …*
   ]


Because the cycles must be processed in order, the array syntax with
"[]" is used for the "hist" block. (The block syntax "{}" implies no
order for its contents.) The "hist" array consists of one or more
"cycle" blocks, each describing the assembly irradiation and/or decay
for some period of time. Each cycle is defined by (a) the assembly total
specific power; (b) number of exposure days at this power; (c) the
number of ORIGEN library burnup interpolations during the exposure
period; and (d) number of days of decay following the exposure period.

The keywords defining this information are:

.. given in :numref:`tab-origami-hist-kw`.


.. option:: power= <real number>

   Assembly specific power (MW/MTU) for the cycle

   (**Default:** 0.0)


.. option:: burn= <real number>

   Length of cycle exposure period in days

   (**Default:** 0.0)


.. option:: down= <real number>

   Downtime (decay) in days following exposure

   (**Default:** 0.0)

.. option:: nlib= <integer>

   Number of ORIGEN library burnup-interpolations during the cycle

   (**Default:** 1)


.. tabularcolumns:: |\Y{0.13}|\Y{0.65}|\Y{0.10}|
.. table:: Keywords in the power history (hist) block hist-repeat_
  :class: longtable
  :widths: 13 65 10
  :name: tab-origami-hist-kw

  +-------------+----------------------------------------+-------------+
  | **Keyword** | **Description**                        | **Default** |
  +=============+========================================+=============+
  | power=      | assembly specific power (MW/MTU) for   | 0.0         |
  |             | the cycle                              |             |
  +-------------+----------------------------------------+-------------+
  | burn=       | length of the cycle exposure period in | 0.0         |
  |             | days                                   |             |
  +-------------+----------------------------------------+-------------+
  | nlib=       | number of ORIGEN library               | 1           |
  |             | burnup-interpolations during the cycle |             |
  +-------------+----------------------------------------+-------------+
  | down=       | downtime in days following the         | 0.0         |
  |             | exposure                               |             |
  +-------------+----------------------------------------+-------------+
.. [#hist-repeat] Keywords are repeated for each cycle.


:numref:`ex-origami-history` demonstrates the use of the power-history block for four cycles:

.. code-block:: scale
  :name: ex-origami-history
  :caption: Example of the ORIGAMI "hist" block for irradiation cycle history

   hist[
     cycle{ power=35.6 burn=400 nlib=6 down=30 }
     cycle{ power=38.2 burn=350 nlib=6 down=30 }
     cycle{ power=30.0 burn=200 nlib=4 down=30 }
     cycle{ down=10000 }
   ]


ORIGAMI discretizes time intervals first by *cycles* (composed of a
fixed power over a set burn time interval and / or decay time), where
each *cycle* is composed of a number of *substeps*. The power-history
block, along with values of :option:`nburn` and :option:`ndecay` from the input
parameter block, define various types of nested time intervals
(substeps) for the ORIGEN calculations. The entire time period for an
ORIGAMI case is first of all divided into the cycles defined within the
power-history block. Each cycle is divided into an exposure interval
(:option:`burn`) and a decay (:option:`down`) interval. The exposure interval has a
constant specific power, but it is further subdivided into a number of
equally spaced burnup steps defined by :option:`nlib` in the power-history
block. This parameter specifies the number of burnup-dependent ORIGEN
libraries to use during the exposure interval. Cross section values for
each burnup step are interpolated using the burnup at the midpoint of
the step and remain constant throughout the burnup step. The burnup
period associated with a single ORIGEN library, or a decay period, is
called a time "step." Finally, each burnup step, as well as the entire
decay step, is divided into a number of computational "substeps"---the
actual time steps used in the ORIGEN solver kernel. The number of
substeps in each burnup step is given by the value of :option:`nburn`, while
the number of decay substeps is equal to the value :option:`ndecay`. The
default number of substeps for both burnup and decay is equal to 10. The
substeps for irradiation are equally spaced but for decay follow the
rule of threes, i.e. each substep increases in duration by a factor of
three over the previous substep.

For the example given above, there are four cycles. The first three
cycles include both exposure and decay intervals, while the last cycle
is decay only. In the first cycle, the assembly-specific power is
35.6 MW/MTU, which remains constant over the 400-day exposure interval;
therefore, the total burnup for the exposure period is 400*35.6 = 14240
MWD/MTU. This exposure period is divided into six burnup steps of 66.67
days, each with a cross-section library based on the midpoint burnup of
that step. Thus, ORIGEN libraries are interpolated at 1186.7, 3560.0,
5933.3, 8306.7, 10680.0, and 13053.3 MWD/MTU. Each of the six burnup
steps is further subdivided into 10 computational substeps. Likewise,
the decay interval of 30 days is divided into 10 computational substeps.

.. _sect-origami-srcopt-block:

Source options block
--------------------

This block defines options used in computing neutron and gamma sources.
The block is only used if the input energy group boundary arrays :option:`ggrp`
or :option:`ngrp` is given, which indicates that radiation decay source spectra
are to be computed. The general form of this block is:

.. option:: srcopt { … keyword-value pairs … }

   Where the following blocks are permitted:

      * :option:`sublibs`
      * :option:`brem_medium`
      * :option:`alphan_medium`
      * :option:`print`


The following (:numref:`ex-origami-srcopt`) is an example of the
:option:`srcopt` input block:

.. code-block:: scale
  :name: ex-origami-srcopt
  :caption: Template of the ORIGAMI "srcopt" block options

  srcopt{
     sublib= …
     brem_medium= …
     alphan_medium= …
     print= …

  }

If `print=yes`, then text files with axial neutron and gamma sources are
created.

.. option:: sublib= [ lt / fp / ac / all ]

   Gamma sources from light elements / fission products / actinides / all
   nuclides.

   (**Default:** all)


.. option:: brem_medium= [ H2O / UO2 /  none ]

   Medium for Bremsstrahlung production based on water (H2O), uranium oxide
   (UO2), or no Bremsstrahlung calculation (none)

   (**Default:** UO2)


.. option:: alphan_medium= [ UO2 / borosilicate / case ]

   Target medium used for :math:`\left(\alpha,n\right)` source caclulation;
   UO\ :sub:`2`, borosilicate glass, or case-specific mixture.

   (**Default:** case)


.. option:: print= [ yes / no ]

   Write text-based output file containing source information / only write
   radiation source terms to binary ft71 file.

   (**Default:** no)

.. tabularcolumns:: |\Y{0.20}|\Y{0.60}|\Y{0.10}|
.. table:: Keywords in the ORIGAMI source options (srcopt) block
  :class: longtable
  :widths: 20 60 10
  :name: tab-origami-srcopt-kw

  +----------------+-------------------------------------+-------------+
  | **Keyword**    | **Description**                     | **Default** |
  +================+=====================================+=============+
  | sublib=        | *lt / fp / ac / all* |rarr| gamma   | all         |
  |                | sources from:                       |             |
  |                |                                     |             |
  |                | light elements / fission products / |             |
  |                | actinides / all nuclides            |             |
  +----------------+-------------------------------------+-------------+
  | brem_medium=   | *none* / *H2O* / *UO2* / |rarr|     | uo2         |
  |                | bremsstrahlung production based on: |             |
  |                |                                     |             |
  |                | no bremsstrahlung / water /         |             |
  |                | UO\ :sub:`2`                        |             |
  +----------------+-------------------------------------+-------------+
  | alphan_medium= | *UO2* / *borosilicate*/ *case*      | case        |
  |                | |rarr| (alpha,n) source computed    |             |
  |                | for:                                |             |
  |                |                                     |             |
  |                | UO­\ :sub:`2`/ borosilicate glass / |             |
  |                | case-specific mixture               |             |
  +----------------+-------------------------------------+-------------+
  | print=         | *yes* / *no* |rarr| write output    | no          |
  |                | text file containing sources / only |             |
  |                | write sources in binary output ft71 |             |
  |                | file                                |             |
  +----------------+-------------------------------------+-------------+

.. _sect-origami-print-opts-blk:

Output print-options block
--------------------------

This block defines the desired ORIGEN output response edits to be
printed by ORIGAMI.

The following is an example input which edits response values for the
mass in grams, activities in Curies, and concentrations in
atoms/barn-cm, for all nuclides (isotopes) broken down by actinides or
fission products as well as curies by element, totaled over all nuclide
sub-libraries (sublibs).

.. code-block:: scale
  :caption: Example of Origami's "print" block for specifying output print
             options

     print{
        nuc{ units=[grams curies atoms-per-barn-cm] sublibs=[fp ac] }
        ele{ units=[curies] total=yes }
     }


.. option:: nuc= { }, ele={ }

   Block to specify print options for output by individual nuclides / elements


.. option::
   units= [ moles / gram-atoms / grams / curies / becquerels / watts
 / g-watts / m3_air / m3_water / weight_ppm / atoms_ppm / atoms-per-barn-cm ]

   Output concentrations in units of gram-atoms (moles), grams, curies,
   becquerels, total thermal power (alpha, beta, and gamma), thermal
   power from gammas only, radiotoxicity / dilution factors for air and water,
   mass fraction (in ppm), atom fraction (in ppm), atoms / barn-cm [#bncm]_\ ,
   respectively.

   One or more output units may be specified, separated by commas.

   (**Default:** gram-atoms)

.. [#bncm] Requires volume input


.. option:: sublibs= [ le / fp / ac / all ]

   Output concentration units for light element sublibrary, fission product
   sublibrary, actinide sublibrary, or all nuclides.

   (**Default:** all)

.. option:: total= [ no / yes ]

   Print out total concentration for nuclides / elements for each selected unit
   type.

   (**Default:** yes)

.. tabularcolumns:: |\Y{0.13}|\Y{0.77}|\Y{0.10}|
.. table:: Keywords in ORIGAMI "print" block
  :class: longtable
  :widths: 13 77 10
  :name: tab-origami-print-kw

  +-------------+------------------------------------------+-------------+
  | **Keyword** | **Description**                          | **Default** |
  +=============+==========================================+=============+
  | nuc / ele   | Specify print options for output by      | N/A         |
  |             | individual nuclides / elements           |             |
  +-------------+------------------------------------------+-------------+
  | units=      | *moles / gram-atoms / grams / curies /*  | all         |
  |             | *becquerels / watts / g-watts / m3_air*  |             |
  |             | */ m3_water / weight_ppm / atoms_ppm /*  |             |
  |             | *atoms-per-barn-cm*                      |             |
  |             |                                          |             |
  |             | Output concentrations in units of        |             |
  |             | gram-atoms (moles), grams, curies,       |             |
  |             | becquerels, total thermal power          |             |
  |             | (alpha, beta, and gamma), thermal        |             |
  |             | power from gammas only, radiotoxicity    |             |
  |             | / dilution factors for air and water,    |             |
  |             | mass fraction (in ppm), atom fraction    |             |
  |             | (in ppm), atoms / barn-cm,               |             |
  |             | respectively.                            |             |
  +-------------+------------------------------------------+-------------+
  | sublibs=    | *le / fp / ac / all* |rarr| output       | all         |
  |             | concentration units for light element    |             |
  |             | / fission product / actinide             |             |
  |             | sub-libraries                            |             |
  +-------------+------------------------------------------+-------------+
  | total=      | *yes / no* |rarr| print out total        | yes         |
  |             | concentration for nuclides / elements    |             |
  |             | for each output unit type                |             |
  +-------------+------------------------------------------+-------------+


.. _sect-origami-input-arrays:

Input data arrays
-----------------

.. :numref:`tab-origami-input-arrays` shows the remaining input arrays for ORIGAMI.

For all other input arrays in ORIGAMI, the input values are entered in either
of the general  forms (with or without ``=``)::

   array[ … values … ]

   array=[ … values … ]

The array :option:`libs`, which defines the ORIGEN library files, is the only
one that is strictly required for all cases. Cases that simulate 0D or
1D lumped-assembly models typically only require one entry for a single
ORIGEN library (assuming uniform axial enrichment), while the simulated
3D depletion model may utilize multiple libraries if specific ORIGEN
libraries are pre-generated for different pin locations (e.g., adjacent
to a water hole, Gd rods, etc.). If multiple libraries are used, the
array :option:`libmap` is required to identify the pin locations associated
with the input libraries. The numbering of these libraries in the libmap
array corresponds to the ordering of libraries in the :option:`libs` array;
i.e., a "1" corresponds to the first library specified, "2" to the
second, and so on. A zero-value entry in the array indicates that the
location is not to be depleted (i.e., a non-fuel region, such as a water
hole or guide tube).

For **single** array values, the array bracket syntax is not required.
For example, each of the following is equivalent: ::

   compmap=[1]

   compmap[1]

   compmap=

Note that the assignment operator (``=``) is likewise optional for arrays
when using the square-bracket syntax.

Unless the 0D lumped-assembly model (i.e., lumped mass with no axial
power variation) is used, at least one of the arrays (:option:`pz`,
:option:`pxy`) describing the power variations must also be entered. The 1D
axial depletion model requires that the :option:`pz` array be entered, while
the pin-wise depletion model additionally requires the array :option:`pxy` .
The data in arrays :option:`pxy` and :option:`pz` correspond to the variables
r\ :sub:`xy` and a\ :sub:`z`, respectively, described in
:numref:`sect-origami-power-dist`. The axial and XY power distributions are
normalized to unity inside the code, so that only the ratios of the input
array values are significant. As discussed in :numref:`sect-origami-power-dist`,
it is generally recommended to use the final burnup distributions rather than
the relative power distributions for the values in the :option:`pxy` and
:option:`pz` arrays.

The array :option:`nuccomp` defines the nuclides to be included in the output
compBlock file, described in more detail in :numref:`sect-origami-io-files`.
The nuclides in the array are identified by their seven digit IZZZAAA
identifier defined as ID = I \* 1000000 + Z \* 1000 + A, where Z is the atomic
number; A is the mass number, and I is the isomeric state (I=0 for ground; I=1
for first metastable; etc.). For example, identifiers for :sup:`16`\ O and
:sup:`242m`\ Am are 8016 and 1095242, respectively. If this array is
omitted, the nuclides in :numref:`tab-origami-stdcmp-default` are used.
This is described in more detail in :numref:`sect-origami-stdcomp-file`.

The optional array describing the non-fuel elements in the assembly
contains pairs of values (element, mass), where "element" is the
chemical symbol for a particular element, and "mass" is the mass of the
element in kilograms per MTU. For example, the::

   nonfuel=[ zr=520.3 sn=8.4 ]

indicates that the assembly contains 520.3 kilograms of zirconium and
8.4 kilograms of tin for each metric ton of uranium (MTU) in the
assembly. Note that elemental masses are specified — the isotopic masses
are computed internally by the code using natural abundances in the data
library. It is also possible to normalize the total mass of non-fuel
elements to a specified fraction of the MTU mass using the parameter
:option:`fracnf` in the parameter block. In this case, only the relative
amounts of each non-fuel element are needed for the :option:`nonfuel` array.
Non-fuel masses are distributed uniformly among all the fuel depletion
regions.

.. option:: libs= [ ... ]

   List of ORIGEN one or more library file names for fuel in assembly

   **Required**

.. option:: libmap= [ integer(s) ]

   XY map of library identifiers associated with each pin in assembly. Library
   identifiers correspond to the order of the ORIGEN libraries entered in the
   :option:`libs` array (i.e., index positions)

   (**Default:** ``[1]``)

   .. seealso:: :option:`libs`


.. option:: commap= [ integer(s) ]

   XY map of mixture identifiers that correspond to the mixture ID in the fuelcomp block.

   (**Default:** ``[1]``)

   .. seealso:: :option:`fuelcomp`


.. option:: pxy= [ real number(s) ]

   XY map of pin power shaping factors / fractional powers. Must be a square
   array (e.g., 15×15). Defaults to lumped assembly model (no individual pins).

   (**Default:** ``[1.0]``)


.. option:: pz= [ real number(s) ]

   Axial (Z) power shaping factors / fractional power distribution for the
   assembly.

   (**Default:** ``[1.0]``)


.. option:: meshz= [ real number(s) ]

   Axial mesh boundaries (cm) for the axial relative power zones. Only
   required to define axial mesh for viewing results; but if entered, it must
   be consistent with axial power shape. The number of entries should be one
   greater than number of entries in :option:`pz` array.

   (**Default:** `none`)

   .. seealso:: :option:`pz`


.. option:: modz= [ real number(s) ]

   Axial variation in water density (g/cc) corresponding to the axial power zones.

   (**Default:** ``[0.723]``)


.. option:: nonfuel= [ key-value pairs ]

   Non-fuel materials contained in assembly. Values are entered in pairs of
   ``element-symbol=mass`` (kg per mtu of HM ). If parameter :option:`fracnf`
   is input, mass of non-fuel materials is normalized to this fraction of fuel
   :option:`mtu`.

   .. note::

     Oxygen mass in UO\ :sub:`2` should not be entered here (i.e., this is
     pre-supplied by ORIGAMI).

    (**Default:** `None`)


.. option:: ggrp= [ real numbers ]

   Energy boundaries (eV) for defining decay gamma source spectrum, in monotonically
   increasing order.

   (**Default:** `None`)


.. option:: ngrp= [ real numbers ]

   Energy boundaries (eV) for defining :math:`\left(\alpha,n\right)` and
   fission neutron source spectrum.

   (**Default:** Nuclides in :numref:`tab-origami-stdcmp-default`)


.. option:: nuccomp= [ IZZZAAA values ]

   User-specified list of nuclides (in IZZZAAA format) to be included in the
   :file:`compBlock` file.

   (**Default:** Nuclides specified in :numref:`tab-origami-stdcmp-default`).


.. tabularcolumns:: |\Y{0.15}|\Y{0.65}|\Y{0.20}|
.. table:: Description of ORIGAMI input arrays
  :class: longtable
  :widths: 15 65 20
  :name: tab-origami-input-arrays

  +----------------+------------------------------------+---------------------------------------+
  | **Array Name** | **Description**                    | **Default**                           |
  +================+====================================+=======================================+
  | **libs** \*    | List of ORIGEN library file names  | None                                  |
  |                | for fuel in assembly. [characters] |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | libmap         | XY map of library identifiers      | 1                                     |
  |                | associated with each pin in        |                                       |
  |                | assembly. Library identifiers      |                                       |
  |                | correspond to the order of the     |                                       |
  |                | ORIGEN libraries entered in the    |                                       |
  |                | *libs* block. [integers]           |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | compmap        | XY map of mixture identifiers that | 1                                     |
  |                | correspond to the mixture ID in    |                                       |
  |                | the :option:`fuelcomp` block.      |                                       |
  |                | [integers]                         |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | pxy            | XY map of pin power shaping        | 1.0                                   |
  |                | factors / fractional powers. Must  |                                       |
  |                | be a square array (e.g., 15×15).   |                                       |
  |                | Defaults to lumped assembly model  |                                       |
  |                | (no individual pins). [real        |                                       |
  |                | numbers]                           |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | pz             | Axial (Z) power shaping factors /  | 1.0                                   |
  |                | fractional power distribution for  |                                       |
  |                | the assembly. [real numbers]       |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | meshz          | Axial mesh boundaries (cm) for the | None                                  |
  |                | axial relative power zones. Only   |                                       |
  |                | required to define axial mesh for  |                                       |
  |                | viewing results; but if entered,   |                                       |
  |                | it must be consistent with axial   |                                       |
  |                | power shape. The number of entries |                                       |
  |                | should be one greater than number  |                                       |
  |                | of entries in :option:`pz` array.  |                                       |
  |                | [real numbers]                     |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | modz           | Axial variation in water density   | 0.723                                 |
  |                | (g/cc) corresponding to the axial  |                                       |
  |                | power zones. [real numbers]        |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | nonfuel        | Non-fuel materials contained in    | None                                  |
  |                | assembly. Values are entered in    |                                       |
  |                | pairs of (element-symbol=mass(kg)  |                                       |
  |                | per mtu of HM ). If parameter      |                                       |
  |                | *fracnf* is input, mass of         |                                       |
  |                | non-fuel materials is normalized   |                                       |
  |                | to this fraction of fuel mtu.      |                                       |
  |                | **NOTE:** Oxygen mass in           |                                       |
  |                | UO\ :sub:`2` should **not** be     |                                       |
  |                | entered here (i.e., this is        |                                       |
  |                | pre-supplied by ORIGAMI).          |                                       |
  |                | [character / real number pairs]    |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | ggrp           | Energy boundaries (eV) for         | None                                  |
  |                | defining decay gamma source        |                                       |
  |                | spectrum. [real numbers]           |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | ngrp           | Energy boundaries (eV) for         | None                                  |
  |                | defining                           |                                       |
  |                | :math:`\left(\alpha,n\right)` and  |                                       |
  |                | fission neutron source spectrum.   |                                       |
  |                |                                    |                                       |
  |                | [real numbers]                     |                                       |
  +----------------+------------------------------------+---------------------------------------+
  | nuccomp        | List of nuclide IZZZAAAs to be     | :numref:`tab-origami-stdcmp-default`  |
  |                | included in output *compBlock*     |                                       |
  |                | file.                              | Nuclides                              |
  +----------------+------------------------------------+---------------------------------------+
  | \* indicates required                                                                       |
  +---------------------------------------------------------------------------------------------+


.. _sect-origami-io-files:

ORIGAMI Input/Output Files
==========================

:numref:`tab-origami-io-files` gives the input and output files for ORIGAMI.
ORIGAMI produces printed output results as well as several optional output
files described in this section. In order to reduce the potentially voluminous
amount of printout, by default ORIGAMI only prints the concentrations in
grams for selected actinides in each axial zone of every pin, and only
for the last time step (e.g., decay step) of the last cycle in the
power-history block. Time-dependent results are given for all substeps
in the last step (i.e, there are :option:`nburn` and :option:`ndecay` substeps within a
burn step or decay step, respectively) In addition, the blended actinide
concentrations over all pins are printed for each axial zone, and for
the entire lumped assembly. Additional types of printed output can be
specified in the :option:`print` block. The concentrations, as well as optional
neutron and gamma source spectra information, for all nuclides, in all
pins and axial zones are also stored in the ORIGEN binary output file,
often called an "ft71" file. The contents and format of the binary file
are described in the ORIGEN documentation of the SCALE manual. The
binary file information can be edited by the OPUS module in SCALE. Like
the printed output, the ft71 file is written by default only for the
last step of the last cycle. However, both the printed output and binary
file results can be obtained at additional time steps by specifying the
input variables output and ft71, respectively, in the OPTIONS input
block. These input parameters can have the keywords:

The output files are written in the user output directory for the
calculation (i.e., the same directory where the printed output file is
written — the default is the directory from where the case was
submitted). File names are prefixed by an extension consisting of the
input file base-name appended to an optional character string given by
the input keyword :option:`prefix` . For example, if the ORIGAMI input file is
named file:`ORIGAMICase.inp`, the base-name is :file:`ORIGAMICase`. Thus, if the
keyword :option:`prefix` is not included in the input, the file containing the
axial decay heat results is named file:`ORIGAMICase_AxialDecayHeat`. On the
other hand, if the input contains the keyword :command:`prefix=CE16X16`, the file
is named :file:`ORIGAMICase_CE16X16_AxialDecayHeat`.

In order to capture axially dependent features of an assembly (such as
partial-length rods), users may elect to construct sequential ORIGAMI
cases that modify the XY pin map features (e.g., library and enrichment
maps) between cases. In order to allow for these types of "continuation"
cases (in which the sequential case represents an adjacent axial span of
the assembly), the :option:`offsetz` feature is provided, which adjusts the
axial numbering for ORIGAMI outputs (such as for MCNP materials &
spectra cards, axial decay heat, etc.). The :option:`offsetz` parameter offsets
the axial numbering for these output files, where the (integer) value
provided corresponds to the *last* axial zone number calculated by
ORIGAMI (default: 0). For more details on the syntax of the :command:`options`
block, see :numref:`sect-origami-power-dist`.

.. tabularcolumns:: |\Y{0.20}|\Y{0.60}|\Y{0.10}|\Y{0.10}|
.. table:: ORIGAMI input/output files
  :class: longtable
  :widths: 20 60 10 10
  :name: tab-origami-io-files

  +--------------------------------+---------------------+----------+------------+
  | **File Name** [#prefix]_       | **Description**     | **Type** | **Format** |
  +================================+=====================+==========+============+
  | :file:`compBlock`              | Mixture             | out      | text       |
  |                                | compositions in     |          |            |
  |                                | standard            |          |            |
  |                                | composition format  |          |            |
  |                                | for input to SCALE  |          |            |
  |                                | codes such as KENO  |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`MCNP_matls.inp`         | Nuclide identifiers | out      | text       |
  |                                | and weight          |          |            |
  |                                | fractions in format |          |            |
  |                                | for MCNP material   |          |            |
  |                                | cards               |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`MCNP_gamma.inp`         | Total gamma source  | out      | text       |
  |                                | intensity in MCNP   |          |            |
  |                                | source format. Only |          |            |
  |                                | output if gamma     |          |            |
  |                                | energy group        |          |            |
  |                                | boundaries are      |          |            |
  |                                | entered in input    |          |            |
  |                                | array               |          |            |
  |                                | :option:`ggrp`      |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`MCNP_neutron.inp`       | Total neutron       | out      | text       |
  |                                | source intensity in |          |            |
  |                                | MCNP source format. |          |            |
  |                                | Only output if      |          |            |
  |                                | neutron energy      |          |            |
  |                                | group boundaries    |          |            |
  |                                | are entered in      |          |            |
  |                                | input array         |          |            |
  |                                | :option:`ngrp`      |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`AxialGammaSpec`         | Gamma spectrum      | out      | text       |
  |                                | (photons/sec) by    |          |            |
  |                                | axial zone, enabled |          |            |
  |                                | by "srcopt{         |          |            |
  |                                | print=yes }".       |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`AxialNeutSpec`          | Neutron spectrum    | out      | text       |
  |                                | (neutron/sec) by    |          |            |
  |                                | axial zone, enabled |          |            |
  |                                | by "srcopt{         |          |            |
  |                                | print=yes }".       |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`AxialDecayHeat`         | Decay heat source   | out      | text       |
  |                                | (watts) by axial    |          |            |
  |                                | zone, enabled by    |          |            |
  |                                | "options{           |          |            |
  |                                | decayheat=yes }"    |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`assm.f71`               | Output stacked      | out      | binary     |
  |                                | ORIGEN ft71 files   |          |            |
  |                                | for each axial zone |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`assembly_restart.f71`   | Input stacked       | in       | binary     |
  |                                | ORIGEN ft71 files   |          |            |
  |                                | for each axial zone |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`.f71`                   | Output of stacked   | out      | binary     |
  |                                | ORIGEN ft71 files   |          |            |
  |                                | for each pin and    |          |            |
  |                                | axial zone          |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`actinideMesh.3dmap`     | Binary MeshView     | out      | binary     |
  |                                | file of selected    |          |            |
  |                                | actinide masses by  |          |            |
  |                                | depletion cell      |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`actinideMesh.ASCII.txt` | Plaintext MeshView  | out      | text       |
  |                                | file of selected    |          |            |
  |                                | actinide masses by  |          |            |
  |                                | depletion cell      |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`fpMesh.3dmap`           | Binary MeshView     | out      | binary     |
  |                                | file of selected    |          |            |
  |                                | fission product     |          |            |
  |                                | masses by depletion |          |            |
  |                                | cell                |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`fpMesh.ASCII.txt`       | Plaintext MeshView  | out      | text       |
  |                                | file of selected    |          |            |
  |                                | fission product     |          |            |
  |                                | masses by depletion |          |            |
  |                                | cell                |          |            |
  +--------------------------------+---------------------+----------+------------+
  | :file:`burnupMesh.3dmap`       | Binary MeshView     | out      | binary     |
  |                                | file of depletion   |          |            |
  |                                | node burnups        |          |            |
  +--------------------------------+---------------------+----------+------------+

.. [#prefix] Note that all file names are prefixed by an identifier
   :envvar:`${OUTBASENAME}`, where :envvar:`${OUTBASENAME}` is a prefix
   constructed from the input file base name followed by the character string
   given by input keyword ``prefix= *.*`` For example, the input file
   named "my.inp" with :command:`prefix=sample` would give an output prefix
   ``my_sample``; e.g., :file:`my_sample.f71`, :file:`my_sample.assm.f71`,
   :file:`my_sample_MCNP_matls.inp`, etc.


.. _sect-origami-stdcomp-file:

Generation of SCALE standard composition data file
--------------------------------------------------

If input parameter ``stdcomp=yes`` is specified, ORIGAMI produces a text
file containing a SCALE standard composition description for each axial
interval. The file is written in the form of a ``stdcomp`` block that can
be directly used as input to any SCALE module that requires a
composition block. If a 1D axial depletion model is used for the
assembly, the composition for each axial zone is given a unique mixture
number defined for an axial node "\ *Z*\ " as:

.. math::
  \begin{align}
  \text{(1D\ axial\ model)}\ \ &\ \text{mix} = 1000 + (\textit{asmid} -1) \times N_Z + Z
  \end{align}

where N\ :sub:`Z` is the number of axial zones and :option:`asmid` is the input
identifier. For example, if there are 12 axial zones and the input for
:option:`asmid` is 20, then the mixture number associated with axial zone number
1 is mix = 1229, and the mixture for zone 12 is mix= 1240. If an
assembly is represented by a 3D multiple-pin model, the mixture number
is defined,

.. math::
   \begin{align}
      \text{(3D\ model)}\ \ &\ \text{mix} = 1000 + (\textit{asmid} -1) \times N_Z +
                   Z + X \times 100000 + Y \times 10000000
   \end{align}
   :label: eq-origami-mix-num


where X and Y correspond to the row and column numbers of the pin.

The nuclides components of the mixtures may be specified in the input
array :option:`nuccomp`, or by default the mixture may consist of the nuclides
given in :numref:`tab-origami-stdcmp-default`, which are the nuclides
recommended in :cite:`ORIGAMI-rgiw2012` for burnup credit analysis, plus :sup:`16`\ O.

The  temperatures of the mixtures are set by the value of parameter
:option:`temper`, which defaults to a value of 293 Kelvin. The number densities
of the nuclides in the mixtures are calculated using the following expressions:

.. math::
   N_{Z}^{ \left( i \right) } & =
      \rho \frac{M_{Z}^{(i)}}{M_{Z} \cdot 10^6} \cdot \frac{N_{A}}{A^{\left( i \right)}} \cdot 0.8814 \cdot 10^{-24} \\
    &  =   \rho \frac{ M_{Z}^{(i)} }{ M_{Z} \cdot A^{\left( i \right)} } \cdot 5.309 \cdot 10^{-7}
   :label: eq-origami-num-dens

Where:

   :math:`N_{Z}^{\left( i \right)}` = number density of nuclide "i" in zone
   Z, in units of atoms of "i" per barn-cm of UO\ :sub:`2`;

   :math:`\rho` = density of UO\ :sub:`2` (g/cc), defined by the input parameter
   :option:`fdens` (default is 10.4 g/cc);

   :math:`M_{Z}^{(i)}` = mass (g) of nuclide i in axial zone Z , obtained
   from ORIGEN calculation;

   :math:`M_{Z} \cdot 10^{6}` = mass (g) of uranium in axial zone Z, where
   M\ :sub:`Z` is given by :eq:`eq-origami-mass-ax-norm`;

   A\ :sup:`(i)` = mass (g) of 1 mole of nuclide i;

   0.8814 = weight fraction of uranium in UO\ :sub:`2`;

   10\ :sup:`-24` = cm\ :sup:`3` per barn-cm.


The definitions of other parameters appearing in this equation are given
in :numref:`sect-origami-power-dist`. An example of the standard composition
file produced by ORIGAMI is given in :numref:`sect-origami-sample-probs`,
:numref:`ex-origami-prob2-stdcmp` (illustrated in sample problem 2,
:numref:`ex-origami-sample2`).


.. table:: Default burnup credit nuclides in Standard Composition output
  :class: longtable
  :name: tab-origami-stdcmp-default

  ============== ======== ================
  **Nuclide**    **ZAID** **Nuclide type**
  ============== ======== ================
  :sup:`16`\ O   8016     light element
  :sup:`234`\ U  92234    actinide
  :sup:`235`\ U  92235    actinide
  :sup:`236`\ U  92236    actinide
  :sup:`238`\ U  92238    actinide
  :sup:`237`\ Np 93237    actinide
  :sup:`238`\ Pu 94238    actinide
  :sup:`239`\ Pu 94239    actinide
  :sup:`240`\ Pu 94240    actinide
  :sup:`241`\ Pu 94241    actinide
  :sup:`242`\ Pu 94242    actinide
  :sup:`241`\ Am 95241    actinide
  :sup:`243`\ Am 95243    actinide
  :sup:`95`\ Mo  42095    fission product
  :sup:`99`\ Tc  43099    fission product
  :sup:`101`\ Ru 44101    fission product
  :sup:`103`\ Rh 45103    fission product
  :sup:`109`\ Ag 47109    fission product
  :sup:`133`\ Cs 55133    fission product
  :sup:`143`\ Nd 60143    fission product
  :sup:`145`\ Nd 60145    fission product
  :sup:`147`\ Sm 62147    fission product
  :sup:`149`\ Sm 62149    fission product
  :sup:`150`\ Sm 62150    fission product
  :sup:`151`\ Sm 62151    fission product
  :sup:`152`\ Sm 62152    fission product
  :sup:`151`\ Eu 63151    fission product
  :sup:`153`\ Eu 63153    fission product
  :sup:`155`\ Gd 64155    fission product
  ============== ======== ================

MCNP data files
---------------

If the input parameter ``mcnp=yes`` is set in the ``options`` block, the
computed weight fractions for the materials in each axial zone also are
output in a file in the format of MCNP material cards. These material
cards are designed to be coupled to a corresponding MCNP assembly
geometry using the same numbering convention for the depletion zones.
:numref:`sect-origami-sample-probs` shows an example of the MCNP material
information produced by ORIGAMI. The numbering convention of the MCNP
materials cards works by combining the axial and pin numbers into a material
card, where pins are counted sequentially by row, starting with the bottom-left
row of input, counting from left to right across each row to the top-right pin
(i.e., the bottom-left pin is pin #1, etc.). The pin numbers reset with
each axial zone, starting from the bottom zone, counting up from 1. The
naming convention for materials cards is thus the pin number (1-999)
followed by the zone number (1-99); for example, pin #15 of axial zone
#12 would be **m1512**. Accompanying each material card is a list of
ZAID numbers and final concentrations (following depletion/decay) for the
cell expressed in weight fractions. The weight fractions are given as negative
values in accordance with MCNP convention. The fuel density, which may be used
in the MCNP cell card, is equal to the value of the input parameter
:option:`fdens`.

When parameter ``mcnp=yes`` is set, ORIGAMI also produces output files
containing the fuel assembly radiation source magnitude by depletion
zone, to support modeling with MCNP. The gamma/neutron source term cards
correspond to the total gamma or neutron intensity (particles/s) from
each respective depletion region, using the same numbering convention as
that for the MCNP material cards. The source magnitude is computed by
summing over the MG source spectra defined in :eq:`eq-origami-spectra`.

 .. math::
    S_{Z}^{\left( p \right)} = \sum_{g}^{}{S_{Z,g}^{\left( p \right)}\ }
    :label: eq-origami-ax-rad-source


Where:

   :math:`S_{Z}^{\left( p \right)}` = total source magnitude (p/s) for
   particles of type *p*;

   :math:`S_{Z,g}^{\left( p \right)}` = multigroup source magnitude (p/s)
   for energy group *g*, and particles of type *p*

More details on the ORIGEN calculation of the source terms can be found
in the ORIGEN section of SCALE documentation.

.. _sect-origami-decay-heat-calc:

Decay heat calculation
----------------------

When input parameter ``decayheat=yes`` is specified in the input, a text
file containing the decay heat source by axial zone, summed over all
pins, is generated as output. The decay heat in zone *Z* is given in
watts and is computed from the


 .. math::
    H_{Z} = \sum_{i = 1}^{\text{itot}}{Q_{i}\lambda_{i}\frac{M_{Z}^{(i)}}{A^{(i)}}
    \cdot 1.602 \cdot 10^{-13} \cdot N_{A}} = 9.65 \cdot 10^{10}
    \sum_{i = 1}^{\text{itot}}{Q_{i}\lambda_{i}\frac{M_{Z}^{(i)}}{A^{(i)}}}
    :label: eq-origami-ax-dh

where:

   Q\ :sub:`i` = decay energy in MeV for nuclide *i*;

   :math:`\lambda_i` = decay constant (s\ :sup:`-1`) for nuclide *i*;

   :math:`M_{Z}^{(i)}` = mass (g) of nuclide *i* in axial zone *Z*,
   obtained from ORIGEN calculation;

   A\ :sup:`(i)` = mass (g) of 1 mole of nuclide *i*;

   itot = total number of nuclides in burned fuel,

   1.602×10\ :sup:`-19` = number of joules per MeV.

An example output decay heat file produced by ORIGAMI is shown in
:numref:`sect-origami-sample-probs`, :numref:`ex-origami-prob2-dh-file` (from
sample problem 2).


ORIGEN results files
--------------------

The ORIGEN computation for each depletion region produces an ORIGEN
binary concentrations output file, historically called an "ft71" because
it was written on "Fortran tape" number 71. The file named
:file:`${OUTBASENAME}.f71` contains the concentrations for all depletion
regions, stacked within a single binary file, where :envvar:`${OUTBASENAME}` is
the base of the output file name, e.g. the "my" in :file:`my.out`.

The order of stored cases on the f71 file corresponds to the order in
which ORGAMI processes individual depletion cases, starting with the
bottom-left row in the user-supplied power map (pin #1) and looping left
to right, progressively up through the series of rows. This process
repeats for each axial zone, starting from the bottom of the assembly
and working upward (i.e., starting with pin #1, axial zone #1, looping
through each pin on axial zone #1, and then proceeding to pin #1 on
axial zone #2, etc.). This convention is the same as that used for
TRITON arrays.

In addition, the compositions are blended over all pins for each axial
zone to obtain the axially-dependent compositions for the lumped
assembly, stored in a file named :file:`${OUTBASENAME}.assm.f71`. If saved,
this file may be input as a restart file, as discussed in
:numref:`sect-origami-restart-case`.

.. _sect-origami-plotting:

Plotting features
-----------------

ORIGAMI creates three separate mesh summaries of material inventories
for individual depletion regions, useful for 3D visualization and
inspection. These include maps of (1) depletion region burnups, (2)
selected actinide concentrations (including isotopes of U, Pu, A m, and
Cm), and (3) selected fission products typically used for burnup
evaluation, including isotopes of Cs, Y, Ag, Rh, Ru, Eu, Sm, Nd, Gd, and
others). Additionally, ORIGAMI outputs a separate mesh tally of
individual node burnups. These outputs are described in
:numref:`tab-origami-io-files`.

.. note::

  The mesh files are only created if the user specifies the (optional) input
  arguments for assembly pitch (:option:`pitch`) and axial zone locations
  (:option:`meshz`).

These output mesh-dependent maps can be visualized using the Java-based
Mesh File Viewer program included with SCALE. An example MeshView
visualization of one of these outputs is shown in :numref:`fig-origami-mv-xz`
and :numref:`fig-origami-mv-xy`. MeshView is installed in :file:`${SCALE}/Meshview`,
where :envvar:`${SCALE}` is the installation directory. A script to run MeshView is
located at :file:`${SCALE}/cmds/meshview`.


.. _fig-origami-mv-xz:
.. figure:: ../figs/ORIGAMI/meshview_xz.png
   :width: 50%

   MeshView plot of total plutonium content in the 3D depletion regions (XZ plane)

.. _fig-origami-mv-xy:
.. figure:: ../figs/ORIGAMI/meshview_xy.png
   :width: 50%

   MeshView plot of total plutonium content in the 3D depletion regions (XY plane).


Parallel Execution on Linux Clusters
====================================

For large 3D depletion problems it is advantageous to execute the ORIGEN
calculations for different depletion regions in parallel. This can be
done on Linux clusters using MPI. When parallel execution mode is
enabled, ORIGAMI distributes the individual depletion cases across the
pin rows, columns, and axial zones across several processors; the
depletion calculation is thus split across several processors. ORIGAMI
then collects the inventories from each calculation node and
concatenates the output.

To execute ORIGAMI in parallel mode, a parallel-enabled MPI build of
SCALE must be used and ORIGAMI should be invoked with the percent (%)
prefix: ::

   =%

   <normal ORIGAMI input follows>

Additionally, for parallel jobs spanning multiple computational nodes
(as opposed to those just using multiple processors on the same node, it
is recommended to use the :command:`–T` option to specify a common temporary
directory (such as a network-mounted directory accessible to all nodes).
This is due to the way ORIGAMI divides the problem space in parallel
mode; each computational node stores its respective binary dump file of
the individual pin/zone concentrations. Upon completion of execution,
the master node must be able to locate these individual problem
node-generated binary dump files; thus, by using a common temporary
directory, ORIGAMI can correctly re-assembly the individual pinwise
dumpfiles into a single consolidated "master" dump file.

The following is a typical execution command line to execute ORIGAMI in
parallel.

:command:`scalerte –N [number of nodes] -M [machine file] –T [tmpdir] [input_file.inp]`

For more information on executing SCALE in parallel, see the SCALE
Readme file.

.. _sect-origami-sample-probs:

Sample Problems
===============

This section shows sample problems for each of the three types of
simulated assembly models: 0D fully lumped, 2D lumped axial depletion,
and 3D pinwise depletion, and also demonstrates a restart case.

Sample problem 1: fully lumped assembly model
---------------------------------------------

The first example, :numref:`ex-origami-prob1`, corresponds to a fully-lumped
assembly model in which the materials are depleted with a space-independent
(i.e., assembly average) flux distribution. The assembly contains 0.38 MTU,
and the fuel is 2.8 wt% enriched. The assembly also includes several non-fuel
materials corresponding to cladding and other structural materials. Note
that the non-fuel concentrations are specified in kg/MTU, and thus are
not the actual total non-fuel masses in the 0.38 MTU assembly. The
assembly is depleted for three cycles with specific powers of 40.0,
38.6, and 25.2 MW/MTU, respectively. The ORIGEN library data are
interpolated for eight different burnup steps during the irradiation
periods of the first two cycles, and for six burnup steps in the last
cycle.

:numref:`tab-origami-prob1-results` gives the calculated actinide
concentrations at the end of the third cycle.

.. code-block:: scale
   :caption: Input for ORIGAMI sample problem 1
   :name: ex-origami-prob1

    =origami
      title='fully lumped assembly model'
      libs=[ ce14x14 ]
      fuelcomp{
        stdcomp(fuel){
           base=uo2 iso[92234=0.02848 92235=3.2 92236=0.01472 92238=96.7568] }
           mix(1){ comps[fuel=100] }
       }
       options{ mtu=0.38 ft71=all }
       nonfuel=[ cr=3.366 mn=0.1525 fe=6.309 co=0.0302
                 ni=2.366 zr=516.3 sn=8.412 gd=2.860 ]
       hist[
          cycle{ power=40 burn=284 nlib=4 down=54 }
          cycle{ power=38.6 burn=300 nlib=4 down=28 }
          cycle{ power=25.2 burn=250 nlib=3 down=30 }
       ]
       print{
          nuc {
              sublibs=[ac fp]
              units=[grams moles]
              total=no }
          }
    end


.. table:: Calculated Actinide inventories for sample problem 1
  :class: longtable
  :name: tab-origami-prob1-results

  ===============  =========
  Nuclide \*       Mass (g)
  ===============  =========
  :sup:`234`\ U    6.820E+01
  :sup:`235`\ U    3.621E+03
  :sup:`236`\ U    1.487E+03
  :sup:`238`\ U    3.598E+05
  :sup:`237`\ Np   1.348E+02
  :sup:`238`\ Pu   3.862E+01
  :sup:`239`\ Pu   1.919E+03
  :sup:`240`\ Pu   7.820E+02
  :sup:`241`\ Pu   3.960E+02
  :sup:`242`\ Pu   1.394E+02
  :sup:`241`\ Am   1.474E+01
  :sup:`243`\ Am   2.491E+01
  :sup:`242`\ Cm   2.663E+00
  :sup:`244`\ Cm   5.698E+00
  TOTAL            6.820E+01
  ===============  =========

\* Actinides with concentrations less than 0.0001 are not shown.


Sample problem 2: lumped axial depletion assembly model
-------------------------------------------------------

The second example has the same lumped assembly and power history as
sample problem 1, except in this case an axial power distribution is
provided for eight zones, so that the fuel burnup will vary axially;
the ORIGAMI input for this case is provided as :numref:`ex-origami-sample2`.
Also, the options to generate standard composition and decay output
files are requested.

:numref:`tab-origami-prob2-results` gives the computed actinide
concentrations in grams for the first four of the eight axial zones.
Since the input axial power distribution is symmetrical about the assembly
midplane, the last four zones have identical concentrations as the first four.
The last column in the table shows actinide masses for the entire assembly.

:numref:`ex-origami-prob2-stdcmp` is a listing of the contents of the
compBlock file, which contains standard composition input for the eight
axial zones in the assembly at the end of cycle 3. A complete description of
the SCALE standard composition input format is given in the
:ref:`XSPROC chapter <SECT-XSCOMP-STDCOMP>` The first entry on each line in
:numref:`ex-origami-prob2-stdcmp` corresponds to the SCALE nuclide identifier.
Only the default burnup credit analysis are included. The second entry is the
mixture number associated with a particular axial zone. The mixture number for
an axial zone is obtained using :eq:`eq-origami-mix-num`. The third entry is
always zero in this file, and the fourth entry corresponds to the number density
in atoms per barn-cm. The next entry on the line is the temperature, which has
the default value of 293.0 since the input parameter :option:`temper` was not
specified. The final entry is an "end" statement. The information in this file
can be used as the ``read comp`` input block for any SCALE module.

:numref:`ex-origami-prob2-dh-file` shows a listing of the file AxialDecayHeat,
which contains the heat source at the end of the third cycle. The entries in
the file correspond to the decay power in watts for the eight axial zones,
which are computed using :eq:`eq-origami-ax-dh`.

.. code-block:: scale
  :caption: Input for ORIGAMI sample problem 2
  :name: ex-origami-sample2

   =origami
   title= 'lumped axial-deplete assembly model'
   libs=[ ce14x14 ]
   fuelcomp{
      uox(fuel2){ enrich=3.2 }
      mix(1){ comps[fuel2=100] }
   }
   options{
      mtu=0.38 stdcomp=yes decayheat=yes
    }
   pz=[ 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 ]
   nonfuel=[ cr=3.366 mn=0.1525 fe=6.309 co=0.0302
             ni=2.366 zr=516.3 sn=8.412 gd=2.860 ]
   hist[
      cycle{ power=40 burn=284 nlib=4 down=54 }
      cycle{ power=38.6 burn=300 nlib=4 down=28 }
      cycle{ power=25.2 burn=250 nlib=3 down=30 }
   ]
   end

.. tabularcolumns:: |\Y{0.15}|\Y{0.17}|\Y{0.17}|\Y{0.17}|\Y{0.17}|\Y{0.17}|
.. table:: Calculated actinide inventories by axial zone for sample problem 2
  :class: longtable
  :widths: 15 17 17 17 17 17
  :name: tab-origami-prob2-results

  +----------------+--------------+--------------+--------------+--------------+------------+
  | Nuclide        | Axial Zone 1 | Axial Zone 2 | Axial Zone 3 | Axial Zone 4 | TOTAL      |
  |                |              |              |              |              |            |
  |                | Mass (g)     | Mass (g)     | Mass (g)     | Mass (g)     | Mass (g)   |
  +================+==============+==============+==============+==============+============+
  | :sup:`234`\ U  | 1.1384E+01   | 9.4326E+00   | 7.6666E+00   | 6.11E+00     | 6.92E+01   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`235`\ U  | 9.7324E+02   | 5.9453E+02   | 3.3795E+02   | 1.78E+02     | 4.17E+03   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`236`\ U  | 1.0392E+02   | 1.6544E+02   | 2.0053E+02   | 2.15E+02     | 1.37E+03   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`238`\ U  | 4.5604E+04   | 4.5202E+04   | 4.4752E+04   | 4.43E+04     | 3.60E+05   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`237`\ Np | 4.7874E+00   | 1.2622E+01   | 2.0984E+01   | 2.83E+01     | 1.33E+02   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`238`\ Pu | 5.5445E-01   | 2.9024E+00   | 7.1722E+00   | 1.26E+01     | 4.65E+01   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`239`\ Pu | 1.7378E+02   | 2.2968E+02   | 2.4438E+02   | 2.46E+02     | 1.79E+03   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`240`\ Pu | 3.3124E+01   | 7.7894E+01   | 1.1457E+02   | 1.40E+02     | 7.30E+02   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`241`\ Pu | 1.2974E+01   | 3.8401E+01   | 5.8714E+01   | 7.09E+01     | 3.62E+02   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`242`\ Pu | 1.4543E+00   | 1.0115E+01   | 2.6393E+01   | 4.75E+01     | 1.71E+02   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`241`\ Am | 5.3938E-01   | 1.5121E+00   | 2.0433E+00   | 2.12E+00     | 1.24E+01   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`243`\ Am | 9.5029E-02   | 1.4341E+00   | 5.6093E+00   | 1.29E+01     | 4.00E+01   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`242`\ Cm | < 0.0001     | 2.0213E-01   | 4.7744E-01   | 7.56E-01     | 2.93E+00   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`244`\ Cm | < 0.0001     | 2.4685E-01   | 1.6315E+00   | 5.54E+00     | 1.49E+01   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | :sup:`245`\ Cm | < 0.0001     | < 0.0001     | 5.8836E-02   | 2.40E-01     | 6.11E-01   |
  +----------------+--------------+--------------+--------------+--------------+------------+
  | TOTAL          | 4.6920E+04   | 4.6346E+04   | 4.5780E+04   | 4.5221E+04   | 3.6854E+05 |
  +----------------+--------------+--------------+--------------+--------------+------------+




.. code-block:: scale
  :caption: Sample Problem 2: Standard composition file
             (default burnup credit nuclides)
  :name: ex-origami-prob2-stdcmp

   o-16   1001 0 4.6395E-02 293.0 end
   u-234  1001 0 5.6529E-06 293.0 end
   u-235  1001 0 4.8120E-04 293.0 end
   u-236  1001 0 5.1165E-05 293.0 end
   u-238  1001 0 2.2263E-02 293.0 end
   np-237 1001 0 2.3470E-06 293.0 end
   pu-238 1001 0 2.7067E-07 293.0 end
   pu-239 1001 0 8.4481E-05 293.0 end
   pu-240 1001 0 1.6036E-05 293.0 end
   pu-241 1001 0 6.2547E-06 293.0 end
   pu-242 1001 0 6.9823E-07 293.0 end
   am-241 1001 0 2.6003E-07 293.0 end
   am-243 1001 0 4.5435E-08 293.0 end
   mo-95  1001 0 1.5700E-05 293.0 end
   tc-99  1001 0 1.7475E-05 293.0 end
   ru-101 1001 0 1.5272E-05 293.0 end
   rh-103 1001 0 9.4877E-06 293.0 end
   ag-109 1001 0 7.6473E-07 293.0 end
   cs-133 1001 0 1.8563E-05 293.0 end
   nd-143 1001 0 1.4504E-05 293.0 end
   nd-145 1001 0 1.0445E-05 293.0 end
   sm-147 1001 0 1.5451E-06 293.0 end
   sm-149 1001 0 8.0469E-08 293.0 end
   sm-150 1001 0 3.3359E-06 293.0 end
   sm-151 1001 0 3.5230E-07 293.0 end
   sm-152 1001 0 1.7469E-06 293.0 end
   eu-151 1001 0 1.5582E-09 293.0 end
   eu-153 1001 0 9.1077E-07 293.0 end
   gd-155 1001 0 1.3966E-09 293.0 end
   o-16   1002 0 4.6394E-02 293.0 end
   u-234  1002 0 4.6837E-06 293.0 end
   u-235  1002 0 2.9395E-04 293.0 end
   u-236  1002 0 8.1452E-05 293.0 end
   u-238  1002 0 2.2067E-02 293.0 end
   np-237 1002 0 6.1878E-06 293.0 end
   pu-238 1002 0 1.4169E-06 293.0 end
   pu-239 1002 0 1.1165E-04 293.0 end
   pu-240 1002 0 3.7710E-05 293.0 end
   pu-241 1002 0 1.8513E-05 293.0 end
   pu-242 1002 0 4.8561E-06 293.0 end
   am-241 1002 0 7.2896E-07 293.0 end
   am-243 1002 0 6.8566E-07 293.0 end
   mo-95  1002 0 2.9706E-05 293.0 end
   tc-99  1002 0 3.3424E-05 293.0 end
   ru-101 1002 0 3.0467E-05 293.0 end
   rh-103 1002 0 1.8486E-05 293.0 end
   ag-109 1002 0 2.2784E-06 293.0 end
   cs-133 1002 0 3.5311E-05 293.0 end
   nd-143 1002 0 2.4869E-05 293.0 end
   nd-145 1002 0 1.9393E-05 293.0 end
   sm-147 1002 0 2.4415E-06 293.0 end
   sm-149 1002 0 1.0154E-07 293.0 end
   sm-150 1002 0 7.3182E-06 293.0 end
   sm-151 1002 0 4.4543E-07 293.0 end
   sm-152 1002 0 3.4915E-06 293.0 end
   eu-151 1002 0 1.1064E-09 293.0 end
   eu-153 1002 0 2.5199E-06 293.0 end
   gd-155 1002 0 2.5157E-09 293.0 end
   o-16   1003 0 4.6392E-02 293.0 end
   u-234  1003 0 3.8068E-06 293.0 end
   u-235  1003 0 1.6709E-04 293.0 end
   u-236  1003 0 9.8728E-05 293.0 end
   u-238  1003 0 2.1847E-02 293.0 end
   np-237 1003 0 1.0287E-05 293.0 end
   pu-238 1003 0 3.5014E-06 293.0 end
   pu-239 1003 0 1.1880E-04 293.0 end
   pu-240 1003 0 5.5465E-05 293.0 end
   pu-241 1003 0 2.8306E-05 293.0 end
   pu-242 1003 0 1.2671E-05 293.0 end
   am-241 1003 0 9.8507E-07 293.0 end
   am-243 1003 0 2.6819E-06 293.0 end
   mo-95  1003 0 4.2205E-05 293.0 end
   tc-99  1003 0 4.7742E-05 293.0 end
   ru-101 1003 0 4.5361E-05 293.0 end
   rh-103 1003 0 2.6134E-05 293.0 end
   ag-109 1003 0 4.1770E-06 293.0 end
   cs-133 1003 0 5.0069E-05 293.0 end
   nd-143 1003 0 3.1519E-05 293.0 end
   nd-145 1003 0 2.6993E-05 293.0 end
   sm-147 1003 0 2.8511E-06 293.0 end
   sm-149 1003 0 1.2277E-07 293.0 end
   sm-150 1003 0 1.1691E-05 293.0 end
   sm-151 1003 0 5.2472E-07 293.0 end
   sm-152 1003 0 5.0112E-06 293.0 end
   eu-151 1003 0 9.0563E-10 293.0 end
   eu-153 1003 0 4.4446E-06 293.0 end
   gd-155 1003 0 4.0054E-09 293.0 end
   o-16   1004 0 4.6390E-02 293.0 end
   u-234  1004 0 3.0343E-06 293.0 end
   u-235  1004 0 8.7951E-05 293.0 end
   u-236  1004 0 1.0588E-04 293.0 end
   u-238  1004 0 2.1605E-02 293.0 end
   np-237 1004 0 1.3864E-05 293.0 end
   pu-238 1004 0 6.1605E-06 293.0 end
   pu-239 1004 0 1.1946E-04 293.0 end
   pu-240 1004 0 6.7542E-05 293.0 end
   pu-241 1004 0 3.4172E-05 293.0 end
   pu-242 1004 0 2.2786E-05 293.0 end
   am-241 1004 0 1.0210E-06 293.0 end
   am-243 1004 0 6.1463E-06 293.0 end
   mo-95  1004 0 5.3319E-05 293.0 end
   tc-99  1004 0 6.0395E-05 293.0 end
   ru-101 1004 0 5.9831E-05 293.0 end
   rh-103 1004 0 3.2151E-05 293.0 end
   ag-109 1004 0 6.2338E-06 293.0 end
   cs-133 1004 0 6.2779E-05 293.0 end
   nd-143 1004 0 3.4995E-05 293.0 end
   nd-145 1004 0 3.3350E-05 293.0 end
   sm-147 1004 0 2.9202E-06 293.0 end
   sm-149 1004 0 1.4469E-07 293.0 end
   sm-150 1004 0 1.6101E-05 293.0 end
   sm-151 1004 0 6.0099E-07 293.0 end
   sm-152 1004 0 6.3684E-06 293.0 end
   eu-151 1004 0 8.1899E-10 293.0 end
   eu-153 1004 0 6.4006E-06 293.0 end
   gd-155 1004 0 5.5315E-09 293.0 end
   o-16   1005 0 4.6390E-02 293.0 end
   u-234  1005 0 3.0343E-06 293.0 end
   u-235  1005 0 8.7951E-05 293.0 end
   u-236  1005 0 1.0588E-04 293.0 end
   u-238  1005 0 2.1605E-02 293.0 end
   np-237 1005 0 1.3864E-05 293.0 end
   pu-238 1005 0 6.1605E-06 293.0 end
   pu-239 1005 0 1.1946E-04 293.0 end
   pu-240 1005 0 6.7542E-05 293.0 end
   pu-241 1005 0 3.4172E-05 293.0 end
   pu-242 1005 0 2.2786E-05 293.0 end
   am-241 1005 0 1.0210E-06 293.0 end
   am-243 1005 0 6.1463E-06 293.0 end
   mo-95  1005 0 5.3319E-05 293.0 end
   tc-99  1005 0 6.0395E-05 293.0 end
   ru-101 1005 0 5.9831E-05 293.0 end
   rh-103 1005 0 3.2151E-05 293.0 end
   ag-109 1005 0 6.2338E-06 293.0 end
   cs-133 1005 0 6.2779E-05 293.0 end
   nd-143 1005 0 3.4995E-05 293.0 end
   nd-145 1005 0 3.3350E-05 293.0 end
   sm-147 1005 0 2.9202E-06 293.0 end
   sm-149 1005 0 1.4469E-07 293.0 end
   sm-150 1005 0 1.6101E-05 293.0 end
   sm-151 1005 0 6.0099E-07 293.0 end
   sm-152 1005 0 6.3684E-06 293.0 end
   eu-151 1005 0 8.1899E-10 293.0 end
   eu-153 1005 0 6.4006E-06 293.0 end
   gd-155 1005 0 5.5315E-09 293.0 end
   o-16   1006 0 4.6392E-02 293.0 end
   u-234  1006 0 3.8068E-06 293.0 end
   u-235  1006 0 1.6709E-04 293.0 end
   u-236  1006 0 9.8728E-05 293.0 end
   u-238  1006 0 2.1847E-02 293.0 end
   np-237 1006 0 1.0287E-05 293.0 end
   pu-238 1006 0 3.5014E-06 293.0 end
   pu-239 1006 0 1.1880E-04 293.0 end
   pu-240 1006 0 5.5465E-05 293.0 end
   pu-241 1006 0 2.8306E-05 293.0 end
   pu-242 1006 0 1.2671E-05 293.0 end
   am-241 1006 0 9.8507E-07 293.0 end
   am-243 1006 0 2.6819E-06 293.0 end
   mo-95  1006 0 4.2205E-05 293.0 end
   tc-99  1006 0 4.7742E-05 293.0 end
   ru-101 1006 0 4.5361E-05 293.0 end
   rh-103 1006 0 2.6134E-05 293.0 end
   ag-109 1006 0 4.1770E-06 293.0 end
   cs-133 1006 0 5.0069E-05 293.0 end
   nd-143 1006 0 3.1519E-05 293.0 end
   nd-145 1006 0 2.6993E-05 293.0 end
   sm-147 1006 0 2.8511E-06 293.0 end
   sm-149 1006 0 1.2277E-07 293.0 end
   sm-150 1006 0 1.1691E-05 293.0 end
   sm-151 1006 0 5.2472E-07 293.0 end
   sm-152 1006 0 5.0112E-06 293.0 end
   eu-151 1006 0 9.0563E-10 293.0 end
   eu-153 1006 0 4.4446E-06 293.0 end
   gd-155 1006 0 4.0054E-09 293.0 end
   o-16   1007 0 4.6394E-02 293.0 end
   u-234  1007 0 4.6837E-06 293.0 end
   u-235  1007 0 2.9395E-04 293.0 end
   u-236  1007 0 8.1452E-05 293.0 end
   u-238  1007 0 2.2067E-02 293.0 end
   np-237 1007 0 6.1878E-06 293.0 end
   pu-238 1007 0 1.4169E-06 293.0 end
   pu-239 1007 0 1.1165E-04 293.0 end
   pu-240 1007 0 3.7710E-05 293.0 end
   pu-241 1007 0 1.8513E-05 293.0 end
   pu-242 1007 0 4.8561E-06 293.0 end
   am-241 1007 0 7.2896E-07 293.0 end
   am-243 1007 0 6.8566E-07 293.0 end
   mo-95  1007 0 2.9706E-05 293.0 end
   tc-99  1007 0 3.3424E-05 293.0 end
   ru-101 1007 0 3.0467E-05 293.0 end
   rh-103 1007 0 1.8486E-05 293.0 end
   ag-109 1007 0 2.2784E-06 293.0 end
   cs-133 1007 0 3.5311E-05 293.0 end
   nd-143 1007 0 2.4869E-05 293.0 end
   nd-145 1007 0 1.9393E-05 293.0 end
   sm-147 1007 0 2.4415E-06 293.0 end
   sm-149 1007 0 1.0154E-07 293.0 end
   sm-150 1007 0 7.3182E-06 293.0 end
   sm-151 1007 0 4.4543E-07 293.0 end
   sm-152 1007 0 3.4915E-06 293.0 end
   eu-151 1007 0 1.1064E-09 293.0 end
   eu-153 1007 0 2.5199E-06 293.0 end
   gd-155 1007 0 2.5157E-09 293.0 end
   o-16   1008 0 4.6395E-02 293.0 end
   u-234  1008 0 5.6529E-06 293.0 end
   u-235  1008 0 4.8120E-04 293.0 end
   u-236  1008 0 5.1165E-05 293.0 end
   u-238  1008 0 2.2263E-02 293.0 end
   np-237 1008 0 2.3470E-06 293.0 end
   pu-238 1008 0 2.7067E-07 293.0 end
   pu-239 1008 0 8.4481E-05 293.0 end
   pu-240 1008 0 1.6036E-05 293.0 end
   pu-241 1008 0 6.2547E-06 293.0 end
   pu-242 1008 0 6.9823E-07 293.0 end
   am-241 1008 0 2.6003E-07 293.0 end
   am-243 1008 0 4.5435E-08 293.0 end
   mo-95  1008 0 1.5700E-05 293.0 end
   tc-99  1008 0 1.7475E-05 293.0 end
   ru-101 1008 0 1.5272E-05 293.0 end
   rh-103 1008 0 9.4877E-06 293.0 end
   ag-109 1008 0 7.6473E-07 293.0 end
   cs-133 1008 0 1.8563E-05 293.0 end
   nd-143 1008 0 1.4504E-05 293.0 end
   nd-145 1008 0 1.0445E-05 293.0 end
   sm-147 1008 0 1.5451E-06 293.0 end
   sm-149 1008 0 8.0469E-08 293.0 end
   sm-150 1008 0 3.3359E-06 293.0 end
   sm-151 1008 0 3.5230E-07 293.0 end
   sm-152 1008 0 1.7469E-06 293.0 end
   eu-151 1008 0 1.5582E-09 293.0 end
   eu-153 1008 0 9.1077E-07 293.0 end
   gd-155 1008 0 1.3966E-09 293.0 end


.. code-block:: scale
  :caption: Sample problem 2: Decay heat file with axial decay heat by zone
             (Watts)
  :name: ex-origami-prob2-dh-file

   7.11397E+02
   1.43786E+03
   2.18631E+03
   2.95428E+03
   2.95428E+03
   2.18631E+03
   1.43786E+03
   7.11397E+02


.. _sect-origami-sample3:

Sample problem 3: restart decay calculation for lumped axial depletion assembly model
-------------------------------------------------------------------------------------

The third example shows a restart decay-only calculation, using the
ORIGEN ft71 binary file obtained from sample problem 2. This case
calculates the composition of the burned fuel produced in sample problem
2 after 100,000 additional days of decay. The input this problem is
given in :numref:`ex-origami-prob4`. Because the input parameter
:command:`restart=yes` is specified, the initial composition of the assembly is
obtained from a file named :file:`assembly_restart.f71`. The shell input that
precedes the ORIGAMI input in :numref:`ex-origami-prob4` copies the output ft71
file  produced in sample problem 2, which was named :file:`assembly_dump.f71`,
into a file  named :file:`assembly_restart.f71` in the temporary directory for
SCALE calculations. The restart file contains the complete inventory of
nuclide compositions for  eight axial zones. Because this restart case is
decay only (i.e., :option:`power` value is not given in the power-history
block), it is necessary to provide the input parameter :command:`nz=8` because
this value is used to determine how many axial zones were used in the previous
burnup calculations.

:numref:`tab-origami-prob3-act-results` shows the actinide composition of the
first four axial of the (symmetrical) eight zones after 100,000 days of decay.
The initial masses of these nuclides before decay are the values given in
numref:`ex-origami-prob2-stdcmp`. The last column in
:numref:`tab-origami-prob3-act-results` shows actinide masses for the entire
assembly after the decay period.

.. code-block:: scale
  :name: ex-origami-prob3-input
  :caption: Sample problem 3: restart decay for a lumped axial depletion model

   =origami
      title= 'lumped axial-deplete assembly model'
      libs=[ ce14x14 ]
      fuelcomp{
         %3.2 w/o
         uox(fuel){ enrich=3.2 }
         mix(1){ comps[fuel=100] }
      }
      options[ mtu=0.38 relnorm=no ]
      pz=[ 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 ]
      nonfuel=[ cr=3.366 mn=0.1525 fe=6.309 co=0.0302
                ni=2.366 zr=516.3 sn=8.412 gd=2.860 ]
      hist[
         cycle{ power=40 burn=284 nlib=8 down=54 }
         cycle{ power=38.6 burn=300 nlib=8 down=28 }
         cycle{ power=25.2 burn=250 nlib=6 down=30 }
      ]
      end
      =shell
         mv \*.assm.f71 assembly_restart.f71
      end
      =origami
         title= 'restart decay'
         asmid= 22
         libs=[ ce14x14 ]
         prefix=origam3
      options{
         stdcomp=yes decayheat=yes relnorm=no restart=yes nz=8
      }
      pz=[ 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 ]
      hist[
         cycle{ down=100000 }
      ]
      end
      =shell
         rm assembly_restart.f71
         rm ${OUTDIR}/\*origam3\*
      end

.. tabularcolumns:: |\Y{0.15}|\Y{0.17}|\Y{0.17}|\Y{0.17}|\Y{0.17}|\Y{0.17}|
.. table:: Calculated actinide inventories by axial zone for sample problem 3
  :class: longtable
  :widths: 15 17 17 17 17 17
  :name: tab-origami-prob3-act-results

  +----------------+--------------+--------------+--------------+--------------+--------------+
  | Nuclide        | Axial Zone 1 | Axial Zone 2 | Axial Zone 3 | Axial Zone 4 | TOTAL        |
  |                |              |              |              |              |              |
  |                | Mass (g)     | Mass (g)     | Mass (g)     | Mass (g)     | Mass (g)     |
  +================+==============+==============+==============+==============+==============+
  | :sup:`234`\ U  | 1.1889E+01   | 1.2133E+01   | 1.4319E+01   | 1.7738E+01   | 1.1216E+02   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`235`\ U  | 9.7454E+02   | 5.9616E+02   | 3.3963E+02   | 1.7955E+02   | 4.1798E+03   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`236`\ U  | 1.0486E+02   | 1.6764E+02   | 2.0378E+02   | 2.1907E+02   | 1.3907E+03   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`238`\ U  | 4.5604E+04   | 4.5202E+04   | 4.4752E+04   | 4.4256E+04   | 3.5963E+05   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`237`\ Np | 9.2242E+00   | 2.5723E+01   | 4.0929E+01   | 5.2246E+01   | 2.5625E+02   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`238`\ Pu | 6.8535E-02   | 3.6104E-01   | 8.8478E-01   | 1.5422E+00   | 5.7132E+00   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`239`\ Pu | 1.7243E+02   | 2.2794E+02   | 2.4262E+02   | 2.4413E+02   | 1.7742E+03   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`240`\ Pu | 3.2192E+01   | 7.5957E+01   | 1.1297E+02   | 1.4095E+02   | 7.2412E+02   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`241`\ Pu | < 0.0001     | < 0.0001     | < 0.0001     | < 0.0001     | < 0.0001     |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`242`\ Pu | 1.4538E+00   | 1.0107E+01   | 2.6379E+01   | 4.7456E+01   | 1.7079E+02   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`241`\ Am | 8.9945E+00   | 2.6564E+01   | 4.0451E+01   | 4.8623E+01   | 2.4927E+02   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`243`\ Am | 9.2577E-02   | 1.3965E+00   | 5.4616E+00   | 1.2516E+01   | 3.8934E+01   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`242`\ Cm | < 0.0001     | < 0.0001     | < 0.0001     | < 0.0001     | < 0.0001     |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`244`\ Cm | < 0.0001     | < 0.0001     | < 0.0001     | < 0.0001     | < 0.0001     |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | :sup:`245`\ Cm | < 0.0001     | < 0.0001     | 5.7288E-02   | 2.3382E-01   | 5.9479E-01   |
  +----------------+--------------+--------------+--------------+--------------+--------------+
  | TOTAL          | 4.6920E+04   | 4.6346E+04   | 4.5780E+04   | 4.5220E+04   | 3.6853E+05   |
  +----------------+--------------+--------------+--------------+--------------+--------------+




Sample problem 4: Simplified 3D multi-pin model
-----------------------------------------------

The fourth example is a simulation of a simplified 3D depletion model.
The ORIGAMI 3D model normally includes all fuel pins within the
assembly, such as a 14×14 array. However to keep this example case
simple and the execution time low, only a 2×2 array of four individual
pins is considered for illustrative purposes. An axial fractional power
distribution is also specified for two axial zones. Therefore the total
number of depletion regions will be eight – two axial for each of the
four pins. Two different ORIGEN libraries are used to obtain cross
sections for the four pins. This is done whenever fuel pins in different
locations in the assembly have significantly different neutron spectra,
such as if some pins are adjacent to a control rod. In this sample
problem, ORIGEN libraries for two different types of assembly designs CE
(Combustion Engineering) 14×14 and 16×16 assembly designs, respectively
are used to demonstrate the use of pin-dependent libraries, although in
reality the ORIGEN libraries normally would be pre-generated for
different pin locations within a single type of assembly configuration.
The values specified in :option:`libmap` indicate which library is to be used
for each pin location. :numref:`ex-origami-prob4` shows the input for this
sample problem.

.. code-block:: scale
  :caption: Input for ORIGAMI Sample Problem 4: a simplified multi-pin, multi-axial model
  :name: ex-origami-prob4

   =origami
    title= 'multi-pin; multi-library pin-deplete model'
    prefix= origam4
    libs=[ ce14x14 ce16x16 ]

    fuelcomp{
       %3.2 w/o
       stdcomp(fuel){ base=uo2 iso[92234=0.028569 92235=3.21 92236=0.014766
                                  92238=96.746665] }
       mix(1){ comps[fuel=100] }
    }

    options{ mtu=0.4 decayheat=yes }
    libmap=[ 1 1
             2 2 ]
    pxy=[ 0.284 0.283
          0.218 0.215 ]
    pz=[ 0.55 0.45 ]
    hist[
      cycle{ power=39.78 burn=284.0 nlib=2 down=54.0 }
    ]
   end


:numref:`tab-origami-prob4-results-pins` shows selected actinide compositions
for the first row of two pins, that is, locations (1,1) and (1,2), for each of the two axial zones. The blended compositions over all fuel pins, for the two
axial zones, are given in :numref:`tab-origami-prob4-axblend`. The output
decay heat file for the assembly is shown in :numref:`tab-origami-prob4-dh`,
as a function of axial zone, summed over all pins. Note that this file has the
prefix "sample4\_"  appended to the standard file name, since *prefix=sample4*
is specified in the input.

.. tabularcolumns:: |p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|
.. table:: Actinide inventories by axial zone for pins (1,1) and (1,2) in sample problem 4
  :class: longtable
  :widths: 14 22 22 22 22
  :name: tab-origami-prob4-results-pins

  ============== ============ ============ ============= ============
  Nuclide        pin (1,1)    pin (1,1)     pin (1,2)    pin (1,2)
                 Axial Zone 1 Axial Zone 2  Axial Zone 1 Axial Zone 2
                 Mass (g)     Mass (g)      Mass (g)     Mass (g)
  ============== ============ ============ ============= ============
  :sup:`234`\ U  1.2115E+01   1.2493E+01    1.2143E+01    1.2516E+01
  :sup:`235`\ U  1.0701E+03   1.1528E+03    1.0762E+03    1.1581E+03
  :sup:`236`\ U  1.0383E+02   8.9286E+01    1.0277E+02    8.8348E+01
  :sup:`237`\ U  1.0664E-03   < 0.0001      1.0428E-03    < 0.0001
  :sup:`238`\ U  4.8003E+04   4.8074E+04    4.8009E+04    4.8078E+04
  :sup:`237`\ Np 4.8000E+00   3.6009E+00    4.7055E+00    3.5303E+00
  :sup:`239`\ Np 5.8742E-07   4.4485E-07    5.7555E-07    4.3692E-07
  :sup:`238`\ Pu 4.7198E-01   2.9453E-01    4.5684E-01    2.8512E-01
  :sup:`239`\ Pu 1.8855E+02   1.6706E+02    1.8705E+02    1.6560E+02
  :sup:`240`\ Pu 3.3235E+01   2.5225E+01    3.2625E+01    2.4736E+01
  :sup:`241`\ Pu 1.3906E+01   9.2953E+00    1.3537E+01    9.0304E+00
  :sup:`242`\ Pu 1.3733E+00   7.3260E-01    1.3161E+00    7.0081E-01
  :sup:`241`\ Am 2.3603E-01   1.5773E-01    2.2978E-01    1.5322E-01
  :sup:`243`\ Am 8.4143E-02   < 0.0001      7.9365E-02    < 0.0001
  TOTAL          4.9432E+04   4.9535E+04    4.9440E+04    4.9541E+04
  ============== ============ ============ ============= ============

.. [#epsilon3] Values < 0.0001 are not shown

.. table:: Blended actinide inventories by axial zone (all pins) for sample problem 4
  :class: longtable
  :name: tab-origami-prob4-axblend

  ============== ============ ============ ==========
  Nuclide        Axial Zone 1 Axial Zone 2 TOTAL
                 Mass (g)     Mass (g)     Mass (g)
  ============== ============ ============ ==========
  :sup:`234`\ U  4.7388E+01   4.9082E+01   9.6469E+01
  :sup:`235`\ U  4.0115E+03   4.3778E+03   8.3894E+03
  :sup:`236`\ U  4.5851E+02   3.9537E+02   8.5387E+02
  :sup:`238`\ U  1.9184E+05   1.9216E+05   3.8399E+05
  :sup:`237`\ Np 2.2821E+01   1.7132E+01   3.9953E+01
  :sup:`238`\ Pu 2.5739E+00   1.6049E+00   4.1789E+00
  :sup:`239`\ Pu 7.8246E+02   6.9963E+02   1.4821E+03
  :sup:`240`\ Pu 1.5436E+02   1.1801E+02   2.7238E+02
  :sup:`241`\ Pu 6.7918E+01   4.6455E+01   1.1437E+02
  :sup:`242`\ Pu 8.1693E+00   4.4411E+00   1.2610E+01
  :sup:`241`\ Am 1.1476E+00   7.8696E-01   1.9346E+00
  :sup:`243`\ Am 6.0150E-01   2.5995E-01   8.6145E-01
  TOTAL          1.9740E+05   1.9787E+05   3.9526E+05
  ============== ============ ============ ==========

.. table:: Sample problem 4: Decay heat by axial zone (Watts)
  :class: longtable
  :name: tab-origami-prob4-dh

  +-------------+
  | 6.96472E+03 |
  |             |
  | 5.72539E+03 |
  +-------------+


Sample problem 5: PWR 3D assembly model
---------------------------------------

This sample problem shows the input for a simulated full 3D pressurized
water reactor (PWR) assembly-depletion model, which corresponds to a
16×16 lattice with 26 axial zones. :numref:`ex-origami-sample-prob4` shows the
ORIGAMI input for this case. The arrays :option:`pxy` and :option:`pz` define the 3D XY-Z
fractional power distribution. Four different pre-processed ORIGEN libraries
are used to describe the pin-averaged ORIGEN cross-sections for the assembly.
The array :option:`libmap` assigns these libraries to the appropriate pin locations.
It can be seen that the :option:`libmap` array contains values of zero at 21 locations.
These correspond to non-depleting (i.e., zero power) locations. The input
includes the information (parameter :option:`pitch`, and array *z=* ) necessary to
generate 3D mesh summary maps for subsequent visualization. In this case, the
axial mesh is not uniform. Since a total of 6110 ORIGEN cases are executed for
the depletable pins, this ORIGAMI calculation was performed in parallel using
MPI. Figure 5.4.3 shows a plot of the axial burnup distribution, summed over
all pins.

.. code-block:: scale
  :name: ex-origami-sample-prob4
  :caption: Input for ORIGAMI Sample Problem 4

    =%origami
    title= 'PWR 3D deplete model'
    prefix= pwr
    options{ pitch= 19.816 }
    fuelcomp{
    uox(fuel){ enrich=3.5 }
       mix(1){ comps[fuel=100] }
    }
    libs=[ lib1 lib2 lib3 lib4]
    libmap=[
       3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
       2 1 1 1 1 4 1 1 1 1 4 1 1 1 1 2
       2 1 1 4 4 0 4 4 1 4 0 4 4 1 1 2
       2 1 4 0 4 4 4 0 4 1 4 4 0 4 1 2
       2 1 4 4 1 4 1 4 1 1 4 1 4 4 1 2
       2 4 0 4 4 0 4 1 1 4 0 4 4 0 4 2
       2 1 4 4 1 4 1 1 1 1 4 1 1 4 1 2
       2 1 4 0 4 1 1 4 1 1 1 1 4 1 1 2
       2 1 1 4 1 1 4 0 4 1 1 4 0 4 1 2
       2 1 4 1 1 4 1 4 1 1 4 1 4 4 1 2
       2 4 0 4 4 0 4 1 1 4 0 4 4 0 4 2
       2 1 4 4 1 4 1 4 1 1 4 1 4 4 1 2
       2 1 4 0 4 4 4 0 4 1 4 4 0 4 1 2
       2 1 1 4 4 0 4 4 1 4 0 4 4 1 1 2
       2 1 1 1 1 4 1 1 1 1 4 1 1 1 1 2
       3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 ]
    pxy=[
       0.99 0.98 0.98 0.99 0.99 0.99 0.99 0.99
       0.99 0.99 0.99 0.99 0.98 0.98 0.97 0.98
       0.99 0.99 0.99 1.00 1.01 1.02 1.00 1.00
       1.00 1.01 1.02 1.00 0.99 0.98 0.98 0.98
       1.00 1.00 1.01 1.03 1.03 0.00 1.03 1.01
       1.03 1.04 0.00 1.03 1.02 1.00 0.99 0.98
       1.01 1.01 1.03 0.00 1.04 1.04 1.02 0.00
       1.03 1.04 1.04 1.04 0.00 1.02 1.00 0.99
       1.01 1.02 1.02 1.05 0.73 1.04 1.02 1.02
       1.03 1.03 1.04 0.72 1.04 1.04 1.01 1.00
       1.02 1.04 0.00 1.05 1.04 0.00 1.03 1.01
       1.01 1.03 0.00 1.03 1.04 0.00 1.02 1.00
       1.02 1.03 1.02 1.05 1.04 1.04 1.02 1.01
       1.01 1.02 1.03 1.02 1.02 1.03 1.01 1.00
       1.01 1.02 1.04 0.00 1.04 1.02 1.02 1.03
       1.01 1.01 1.01 1.02 1.03 1.02 1.00 1.00
       1.00 1.01 1.02 1.03 1.02 1.02 1.03 0.00
       1.02 1.01 1.01 1.03 0.00 1.02 0.99 0.98
       1.00 1.01 1.03 1.02 1.02 1.03 1.03 1.03
       1.01 1.01 1.03 1.02 1.03 1.03 1.00 0.99
       1.01 1.02 0.00 1.04 1.03 0.00 1.03 1.01
       1.01 1.02 0.00 1.03 1.03 0.00 1.01 0.98
       1.00 1.01 1.04 1.04 0.72 1.04 1.03 1.03
       1.01 1.01 1.02 0.71 1.03 1.02 0.99 0.98
       1.00 1.00 1.02 0.00 1.04 1.04 1.04 0.00
       1.02 1.01 1.03 1.03 0.00 1.01 0.98 0.97
       0.99 0.99 1.01 1.03 1.04 0.00 1.04 1.03
       1.01 1.02 0.00 1.02 1.01 0.99 0.97 0.97
       0.99 0.99 0.99 1.00 1.01 1.03 1.01 1.00
       1.00 1.00 1.01 1.00 0.99 0.97 0.97 0.97
       1.00 0.99 1.00 1.00 1.01 1.01 1.01 1.00
       0.99 0.99 0.99 0.99 0.98 0.97 0.97 0.97 ]

    pz=[0.486645842
        0.510544887
        0.641121243
        0.798557507
        0.931372279
        1.063949280
        1.173174524
        1.178015382
        1.241701554
        1.247451593
        1.203231683
        1.228462686
        1.237668911
        1.221002529
        1.191997899
        1.231513011
        1.222065701
        1.172711869
        1.200902470
        1.164812132
        1.083204453
        0.931028309
        0.810656652
        0.700324838
        0.611466339
        0.516416427 ]

    meshz=[ 0.0 2.0 6.0 10.0 16.5 23.0 37.0 57.0 77.0 97.0 16.0
            136.0 156.0 176.0 196.0 216.0 236.0 256.0 276.0 296.0
            316.0 328.5 344.0 352.0 355.5 359.0 366.0 ]
    hist[
       cycle{ power=49.395 burn=385 nlib=3 down=52 }
       cycle{ power=43.772 burn=360 nlib=2 down=7673 }
    ]
    end


.. only:: html

   .. rubric:: References

.. bibliography:: ../zSCALE.bib
   :cited:
   :keyprefix: ORIGAMI-
   :labelprefix: ORIGAMI