crp/OpenMC
1
0
Fork 0
mirror of https://github.com/openmc-dev/openmc.git synced 2026-07-27 21:55:41 -04:00
Code Issues Projects Releases Packages Wiki Activity Actions 5

proofreading changes

Browse source
This commit is contained in:
Adam Nelson 2016-06-15 14:55:46 -04:00
parent f828141b28
commit 6d59516355
2 changed files with 30 additions and 30 deletions
Download patch file Download diff file Expand all files Collapse all files

44
docs/source/methods/cross_sections.rst
View file

@ -76,48 +76,46 @@ The format is described in the :ref:`mgxs_lib_spec`.
The data itself can be prepared via traditional paths or directly from a
continuous-energy OpenMC calculation by use of the Python API as is shown in the
Python API :ref:`_notebook_mgxs_part_iv` example notebook. This multi-group
library consists of library meta-data (such as the energy group structure) and
multiple `xsdata` objects which contains the required microscopic or macroscopic
library consists of meta-data (such as the energy group structure) and multiple
`xsdata` objects which contains the required microscopic or macroscopic
multi-group data.
At a minimum, the library must contain the absorption cross section
(:math:`\sigma_{a,g}`) and a scattering matrix. If the problem is an eigenvalue
problem then all fissionable materials must also contain either fission spectrum
data (:math:`\chi{g'}`) and a fission production cross section
(:math:`\nu\sigma_{f,g}`), or, a fission production matrix cross section
(:math:`\nu\sigma_{f,g\arrow\g'}`). If fission or energy release from fission
tallies are requested by the user, then the library must also contain the
fission cross section (:math:`\sigma_{f,g}`) or the fission energy release
cross section (:math:`\kappa\sigma_{f,g}`).
problem then all fissionable materials must also contain either
a fission production matrix cross section (:math:`\nu\sigma_{f,g\arrow\g'}`), or
both the fission spectrum data (:math:`\chi{g'}`) and a fission production cross
section (:math:`\nu\sigma_{f,g}`), or, . The library must also contain
the fission cross section (:math:`\sigma_{f,g}`) or the fission energy release
cross section (:math:`\kappa\sigma_{f,g}`) if the associated tallies are
required by the model using the library.
After a scattering collision, the outgoing particle experiences a change in both
energy and angle. The probability of a particle resulting in a given outgoing
energy group (`g'`) given a certain incoming energy group (`g`) is provided
by the scattering matrix cross sections themselves. The angular information,
however, can be expressed either via Legendre expansion of the particle's
change-in-angle (:math:`\mu`), a tabular representation of the probability of
a particle experiencing a given :math:`\mu`, or a histogram representation of the
probability of a particle experiencing a given :math:`\mu`. The formats used to
by the scattering matrix data. The angular information can be expressed either
via Legendre expansion of the particle's change-in-angle (:math:`\mu`), a
tabular representation of the probability distribution function of :math:`\mu`,
or a histogram representation of the same PDF. The formats used to
represent these are described in the :ref:`mgxs_lib_spec`.
Unlike the continuous-energy mode, the multi-group mode does not explicitly
track particles produced from scattering multiplication (i.e., :math:`(n,xn)`)
reactions. These are instead accounted for by adjusting the weight of the
particle after the collision such that the correct total weight is maintained.
The information for how to adjust this weight is optionally provided by the
`multiplicity` data which exists as a group-wise matrix. This data represents
the average number of particles emitted from a scattering reaction, given a
scattering reaction has occurred:
The weight adjustment factor is optionally provided by the `multiplicity` data
which is required to be provided in the form of a group-wise matrix.
This data is provided as a group-wise matrix since the probability of producing
multiple particles in a scattering reaction depends on both the incoming energy,
`g`, and the sampled outgoing energy, `g'`. This data represents the average
number of particles emitted from a scattering reaction, given a scattering
reaction has occurred:
.. math::
multiplicity_{g \arrow g'} = \frac{\nu_{scatter}\sigma_{s,g \arrow g'}}{
\sigma_{s,g \arrow g'}}
This data is provided as a group-wise matrix since the probability of producing
multiple particles in a scattering reaction depends on both the incoming energy,
`g`, and the sampled outgoing energy, `g'`.
If this scattering multiplication information is not provided in the library
then no weight adjustment will be performed. This is equivalent to neglecting
any additional particles produced in scattering multiplication reactions.
@ -134,7 +132,7 @@ follows:
\sigma_{a,g} = \sigma_{t,g} - \sum_{g'}{\nu_{scatter}\sigma_{s,g \arrow g'}}
The above method is the same as is typically done with most deterministic methods.
The above method is the same as is usually done with most deterministic solvers.
Note that this method is less accurate than using the scattering multiplication
weight adjustment since simply reducing the absorption cross section does not
include any information about the outgoing energy of the particles produced in

16
docs/source/methods/physics.rst
View file

@ -219,7 +219,7 @@ Multi-Group Scattering
In multi-group mode, a scattering collision requires that the outgoing energy
group of the simulated particle be selected from a probability distribution,
then the change-in-angle selected from a probability distribution according to
the change-in-angle selected from a probability distribution according to
the outgoing energy group, and finally the particle's weight adjusted again
according to the outgoing energy group.
@ -232,17 +232,19 @@ produced from the outgoing group (`g'`) data for the given incoming group (`g`):
CDF = \sum_{g'=0}^{h}\Sigma_{s,g \arrow g'}
If the scattering data is represented as a Legendre expansion, then the
value of :math:`\Sigma_{s,g \arrow g'}` above is simply the 0th order. If the
data is provided as tabular or histogram data, then the value of
:math:`\Sigma_{s,g \arrow g'}` is the sum of all bins of data for a given `g`
and `g'` pair.
value of :math:`\Sigma_{s,g \arrow g'}` above is simply the 0th order for the
given group transfer. If the data is provided as tabular or histogram data, then
the value of :math:`\Sigma_{s,g \arrow g'}` is the sum of all bins of data for a
given `g` and `g'` pair.
Now that the outgoing energy is known the change-in-angle, :math:`\mu` can be
determined. If the data is provided as a Legendre expansion, this is done by
rejection sampling of the probability distribution represented by the Legendre
series. For efficiency, the selected values of the PDF (:math:`f(\mu)`) are
chosen to be between 0 and the maximum value of :math:`f(\mu)` in the domain of
-1 to 1.
-1 to 1. Note that this sampling scheme automatically forces negative values of
the :math:`f(\mu)` probability distribution function to be treated as zero
probabilities.
If the angular data is instead provided as a tabular representation, then the
value of :math:`\mu` is selected as described in the :ref:`angle-tabular`
@ -254,7 +256,7 @@ the selection of the outgoing energy (since the energy group representation is
simply a histogram representation) except the CDF is composed of the angular
bins and not the energy groups. However, since we are interested in a specific
value of :math:`\mu` instead of a group, then an angle selected from a uniform
distribution within from the chosen histogram bin.
distribution within from the chosen angular bin.
The final step in the scattering treatment is to adjust the weight of the
neutron to account for any production of neutrons due to :math:`(n,xn)`