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Improve documentation of MGXS classes

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Paul Romano 2016-06-01 15:40:35 -05:00
parent d21ea5697e
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8
docs/source/_templates/myclassinherit.rst Normal file
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@ -0,0 +1,8 @@
{{ fullname }}
{{ underline }}
.. currentmodule:: {{ module }}
.. autoclass:: {{ objname }}
:members:
:inherited-members:

5
docs/source/pythonapi/index.rst
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@ -271,14 +271,17 @@ Multi-group Cross Sections
.. autosummary::
:toctree: generated
:nosignatures:
:template: myclass.rst
:template: myclassinherit.rst
openmc.mgxs.MGXS
openmc.mgxs.AbsorptionXS
openmc.mgxs.CaptureXS
openmc.mgxs.Chi
openmc.mgxs.FissionXS
openmc.mgxs.KappaFissionXS
openmc.mgxs.MultiplicityMatrixXS
openmc.mgxs.NuFissionXS
openmc.mgxs.NuFissionMatrixXS
openmc.mgxs.NuScatterXS
openmc.mgxs.NuScatterMatrixXS
openmc.mgxs.ScatterXS

3
docs/source/usersguide/input.rst
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@ -1598,7 +1598,8 @@ The ``<tally>`` element accepts the following sub-elements:
|Score | Description |
+======================+===================================================+
|absorption |Total absorption rate. This accounts for all |
| |reactions which do not produce secondary neutrons. |
| |reactions which do not produce secondary neutrons |
| |as well as fission. |
+----------------------+---------------------------------------------------+
|elastic |Elastic scattering reaction rate. |
+----------------------+---------------------------------------------------+

505
openmc/mgxs/mgxs.py
View file

@ -46,9 +46,9 @@ DOMAIN_TYPES = ['cell',
# Supported domain classes
# TODO: Implement Mesh domains
_DOMAINS = [openmc.Cell,
_DOMAINS = (openmc.Cell,
openmc.Universe,
openmc.Material]
openmc.Material)
class MGXS(object):
@ -364,7 +364,7 @@ class MGXS(object):
@domain.setter
def domain(self, domain):
cv.check_type('domain', domain, tuple(_DOMAINS))
cv.check_type('domain', domain, _DOMAINS)
self._domain = domain
# Assign a domain type
@ -1934,11 +1934,30 @@ class MatrixMGXS(MGXS):
class TotalXS(MGXS):
"""A total multi-group cross section.
r"""A total multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group total cross sections for multi-group neutronics calculations. At
a minimum, one needs to set the :attr:`TotalXS.energy_groups` and
:attr:`TotalXS.domain` properties. Tallies for the flux and appropriate
reaction rates over the specified domain are generated automatically via the
:attr:`TotalXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`TotalXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
total cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\sigma_t (r, E) \psi (r, E, \Omega)}{\int_{r \in D} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -1946,7 +1965,7 @@ class TotalXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -1981,7 +2000,9 @@ class TotalXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`TotalXS.tally_keys` property and values
are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2022,11 +2043,39 @@ class TotalXS(MGXS):
class TransportXS(MGXS):
"""A transport-corrected total multi-group cross section.
r"""A transport-corrected total multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`TransportXS.energy_groups` and
:attr:`TransportXS.domain` properties. Tallies for the flux and appropriate
reaction rates over the specified domain are generated automatically via the
:attr:`TransportXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`TransportXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
transport-corrected total cross section is calculated as:
.. math::
\langle \sigma_t \phi \rangle &= \int_{r \in D} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \sigma_t (r, E) \psi
(r, E, \Omega) \\
\langle \sigma_{s1} \phi \rangle &= \int_{r \in D} dr
\int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \int_{4\pi}
d\Omega' \int_0^\infty dE' \int_{-1}^1 d\mu \; \mu \sigma_s
(r, E' \rightarrow E, \Omega' \cdot \Omega)
\phi (r, E', \Omega) \\
\langle \phi \rangle &= \int_{r \in D} dr \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega) \\
\sigma_{tr} &= \frac{\langle \sigma_t \phi \rangle - \langle \sigma_{s1}
\phi \rangle}{\langle \phi \rangle}
Parameters
----------
@ -2034,7 +2083,7 @@ class TransportXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2069,7 +2118,9 @@ class TransportXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`TransportXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2135,12 +2186,26 @@ class TransportXS(MGXS):
class NuTransportXS(TransportXS):
"""A transport-corrected total multi-group cross section which
r"""A transport-corrected total multi-group cross section which
accounts for neutron multiplicity in scattering reactions.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`NuTransportXS.energy_groups` and
:attr:`NuTransportXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`NuTransportXS.tallies` property, which can then
be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`NuTransportXS.xs_tally` property.
The calculation of the transport-corrected cross section is the same as that
for :class:`TransportXS` except that the scattering multiplicity is
accounted for.
Parameters
----------
@ -2148,7 +2213,7 @@ class NuTransportXS(TransportXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2183,7 +2248,9 @@ class NuTransportXS(TransportXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`NuTransportXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2232,11 +2299,34 @@ class NuTransportXS(TransportXS):
class AbsorptionXS(MGXS):
"""An absorption multi-group cross section.
r"""An absorption multi-group cross section.
Absorption is defined as all reactions that do not produce secondary
neutrons (disappearance) plus fission reactions.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group absorption cross sections for multi-group neutronics
calculations. At a minimum, one needs to set the
:attr:`AbsorptionXS.energy_groups` and :attr:`AbsorptionXS.domain`
properties. Tallies for the flux and appropriate reaction rates over the
specified domain are generated automatically via the
:attr:`AbsorptionXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`AbsorptionXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
absorption cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\sigma_a (r, E) \psi (r, E, \Omega)}{\int_{r \in D} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -2244,7 +2334,7 @@ class AbsorptionXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2279,7 +2369,9 @@ class AbsorptionXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`AbsorptionXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2320,16 +2412,37 @@ class AbsorptionXS(MGXS):
class CaptureXS(MGXS):
"""A capture multi-group cross section.
r"""A capture multi-group cross section.
The neutron capture reaction rate is defined as the difference between
OpenMC's 'absorption' and 'fission' reaction rate score types. This includes
not only radiative capture, but all forms of neutron disappearance aside
from fission (e.g., MT > 100).
from fission (i.e., MT > 100).
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group capture cross sections for multi-group neutronics
calculations. At a minimum, one needs to set the
:attr:`CaptureXS.energy_groups` and :attr:`CaptureXS.domain`
properties. Tallies for the flux and appropriate reaction rates over the
specified domain are generated automatically via the
:attr:`CaptureXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`CaptureXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
capture cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\left [ \sigma_a (r, E) \psi (r, E, \Omega) - \sigma_f (r, E) \psi (r, E,
\Omega) \right ]}{\int_{r \in D} dr \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -2337,7 +2450,7 @@ class CaptureXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2372,7 +2485,9 @@ class CaptureXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`CaptureXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2425,11 +2540,31 @@ class CaptureXS(MGXS):
class FissionXS(MGXS):
"""A fission multi-group cross section.
r"""A fission multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group fission cross sections for multi-group neutronics
calculations. At a minimum, one needs to set the
:attr:`FissionXS.energy_groups` and :attr:`FissionXS.domain`
properties. Tallies for the flux and appropriate reaction rates over the
specified domain are generated automatically via the
:attr:`FissionXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`FissionXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
fission cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\sigma_f (r, E) \psi (r, E, \Omega)}{\int_{r \in D} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -2437,7 +2572,7 @@ class FissionXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2472,7 +2607,9 @@ class FissionXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`FissionXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2513,11 +2650,32 @@ class FissionXS(MGXS):
class NuFissionXS(MGXS):
"""A fission production multi-group cross section.
r"""A fission neutron production multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group fission neutron production cross sections for multi-group
neutronics calculations. At a minimum, one needs to set the
:attr:`NuFissionXS.energy_groups` and :attr:`NuFissionXS.domain`
properties. Tallies for the flux and appropriate reaction rates over the
specified domain are generated automatically via the
:attr:`NuFissionXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`NuFissionXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
fission neutron production cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\nu\sigma_f (r, E) \psi (r, E, \Omega)}{\int_{r \in D} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -2525,7 +2683,7 @@ class NuFissionXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2560,7 +2718,9 @@ class NuFissionXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`NuFissionXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2601,11 +2761,37 @@ class NuFissionXS(MGXS):
class KappaFissionXS(MGXS):
"""A recoverable fission energy production rate multi-group cross section.
r"""A recoverable fission energy production rate multi-group cross section.
The recoverable energy per fission, :math:`\kappa`, is defined as the
fission product kinetic energy, prompt and delayed neutron kinetic energies,
prompt and delayed :math:`\gamma`-ray total energies, and the total energy
released by the delayed :math:`\beta` particles. The neutrino energy does
not contribute to this response. The prompt and delayed :math:`\gamma`-rays
are assumed to deposit their energy locally.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`KappaFissionXS.energy_groups` and
:attr:`KappaFissionXS.domain` properties. Tallies for the flux and appropriate
reaction rates over the specified domain are generated automatically via the
:attr:`KappaFissionXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`KappaFissionXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
recoverable fission energy production rate cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\kappa\sigma_f (r, E) \psi (r, E, \Omega)}{\int_{r \in D} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -2613,7 +2799,7 @@ class KappaFissionXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2648,7 +2834,9 @@ class KappaFissionXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`KappaFissionXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2689,11 +2877,34 @@ class KappaFissionXS(MGXS):
class ScatterXS(MGXS):
"""A scatter multi-group cross section.
r"""A scattering multi-group cross section.
The scattering cross section is defined as the difference between the total
and absorption cross sections.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`ScatterXS.energy_groups` and
:attr:`ScatterXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`ScatterXS.tallies` property, which can
then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`ScatterXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
scattering cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\left [ \sigma_t (r, E) \psi (r, E, \Omega) - \sigma_a (r, E) \psi (r, E,
\Omega) \right ]}{\int_{r \in D} dr \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
@ -2701,7 +2912,7 @@ class ScatterXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2736,7 +2947,9 @@ class ScatterXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`ScatterXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2777,11 +2990,35 @@ class ScatterXS(MGXS):
class NuScatterXS(MGXS):
"""A nu-scatter multi-group cross section.
r"""A scattering neutron production multi-group cross section.
The neutron production from scattering is defined as the average number of
neutrons produced from all neutron-producing reactions except for fission.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`NuScatterXS.energy_groups` and
:attr:`NuScatterXS.domain` properties. Tallies for the flux and appropriate
reaction rates over the specified domain are generated automatically via the
:attr:`NuScatterXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`NuScatterXS.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
scattering neutron production cross section is calculated as:
.. math::
\frac{\int_{r \in D} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\sum_i \upsilon_i \sigma_i (r, E) \psi (r, E, \Omega)}{\int_{r \in D} dr
\int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
where :math:`\upsilon_i` is the multiplicity of the :math:`i`-th reaction.
Parameters
----------
@ -2789,7 +3026,7 @@ class NuScatterXS(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2824,7 +3061,9 @@ class NuScatterXS(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`NuScatterXS.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -2869,12 +3108,47 @@ class NuScatterXS(MGXS):
class ScatterMatrixXS(MatrixMGXS):
"""A scattering matrix multi-group cross section for one or more Legendre
r"""A scattering matrix multi-group cross section for one or more Legendre
moments.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`ScatterMatrixXS.energy_groups` and
:attr:`ScatterMatrixXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`ScatterMatrixXS.tallies` property, which can
then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`ScatterMatrixXS.xs_tally` property.
For a spatial domain :math:`D`, incoming energy group
:math:`[E_{g'},E_{g'-1}]`, and outgoing energy group :math:`[E_g,E_{g-1}]`,
the scattering moments are calculated as:
.. math::
\langle \sigma_{s,\ell,g'\rightarrow g} \phi \rangle &= \int_{r \in D} dr
\int_{4\pi} d\Omega' \int_{E_{g'}}^{E_{g'-1}} dE' \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; P_\ell (\Omega \cdot \Omega') \sigma_s (r, E'
\rightarrow E, \Omega' \cdot \Omega) \psi(r, E', \Omega')\\
\langle \phi \rangle &= \int_{r \in D} dr \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega) \\
\sigma_{s,\ell,g'\rightarrow g} &= \frac{\langle
\sigma_{s,\ell,g'\rightarrow g} \phi \rangle}{\langle \phi \rangle}
If the order is zero and a :math:`P_0` transport-correction is applied
(default), the scattering matrix elements are:
.. math::
\sigma_{s,g'\rightarrow g} = \frac{\langle \sigma_{s,0,g'\rightarrow g}
\phi \rangle - \delta_{gg'} \sum_{g''} \langle \sigma_{s,1,g''\rightarrow
g} \phi \rangle}{\langle \phi \rangle}
Parameters
----------
@ -2882,7 +3156,7 @@ class ScatterMatrixXS(MatrixMGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -2895,7 +3169,7 @@ class ScatterMatrixXS(MatrixMGXS):
correction : 'P0' or None
Apply the P0 correction to scattering matrices if set to 'P0'
legendre_order : int
The highest legendre moment in the scattering matrix (default is 0)
The highest Legendre moment in the scattering matrix (default is 0)
name : str, optional
Name of the multi-group cross section
rxn_type : str
@ -2921,7 +3195,9 @@ class ScatterMatrixXS(MatrixMGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`ScatterMatrixXS.tally_keys` property
and values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -3507,7 +3783,21 @@ class NuScatterMatrixXS(ScatterMatrixXS):
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`NuScatterMatrixXS.energy_groups` and
:attr:`NuScatterMatrixXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`NuScatterMatrixXS.tallies` property, which can
then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`NuScatterMatrixXS.xs_tally` property.
The calculation of the scattering-production matrix is the same as that for
:class:`ScatterMatrixXS` except that the scattering multiplicity is
accounted for.
Parameters
----------
@ -3515,7 +3805,7 @@ class NuScatterMatrixXS(ScatterMatrixXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -3554,7 +3844,9 @@ class NuScatterMatrixXS(ScatterMatrixXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`NuScatterMatrixXS.tally_keys` property
and values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -3596,11 +3888,42 @@ class NuScatterMatrixXS(ScatterMatrixXS):
class MultiplicityMatrixXS(MatrixMGXS):
"""The scattering multiplicity matrix.
r"""The scattering multiplicity matrix.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`MultiplicityMatrixXS.energy_groups` and
:attr:`MultiplicityMatrixXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`MultiplicityMatrixXS.tallies` property, which
can then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`MultiplicityMatrixXS.xs_tally`
property.
For a spatial domain :math:`D`, incoming energy group
:math:`[E_{g'},E_{g'-1}]`, and outgoing energy group :math:`[E_g,E_{g-1}]`,
the multiplicity is calculated as:
.. math::
\langle \upsilon \sigma_{s,g'\rightarrow g} \phi \rangle &= \int_{r \in
D} dr \int_{4\pi} d\Omega' \int_{E_{g'}}^{E_{g'-1}} dE' \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \sum_i \upsilon_i \sigma_i (r, E' \rightarrow
E, \Omega' \cdot \Omega) \psi(r, E', \Omega') \\
\langle \sigma_{s,g'\rightarrow g} \phi \rangle &= \int_{r \in
D} dr \int_{4\pi} d\Omega' \int_{E_{g'}}^{E_{g'-1}} dE' \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \sum_i \upsilon_i \sigma_i (r, E' \rightarrow
E, \Omega' \cdot \Omega) \psi(r, E', \Omega') \\
\upsilon_{g'\rightarrow g} &= \frac{\langle \upsilon
\sigma_{s,g'\rightarrow g} \rangle}{\langle \sigma_{s,g'\rightarrow g}
\rangle}
where :math:`\upsilon_i` is the multiplicity for the :math:`i`-th reaction.
Parameters
----------
@ -3608,7 +3931,7 @@ class MultiplicityMatrixXS(MatrixMGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -3643,7 +3966,9 @@ class MultiplicityMatrixXS(MatrixMGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`MultiplicityMatrixXS.tally_keys`
property and values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -3717,11 +4042,35 @@ class MultiplicityMatrixXS(MatrixMGXS):
class NuFissionMatrixXS(MatrixMGXS):
"""A fission production matrix multi-group cross section.
r"""A fission production matrix multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`NuFissionMatrixXS.energy_groups` and
:attr:`NuFissionMatrixXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`NuFissionMatrixXS.tallies` property, which can
then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`NuFissionMatrixXS.xs_tally` property.
For a spatial domain :math:`D`, incoming energy group
:math:`[E_{g'},E_{g'-1}]`, and outgoing energy group :math:`[E_g,E_{g-1}]`,
the fission production is calculated as:
.. math::
\langle \nu\sigma_{f,g'\rightarrow g} \phi \rangle &= \int_{r \in D} dr
\int_{4\pi} d\Omega' \int_{E_{g'}}^{E_{g'-1}} dE' \int_{E_g}^{E_{g-1}} dE
\; \chi(E) \nu\sigma_f (r, E') \psi(r, E', \Omega')\\
\langle \phi \rangle &= \int_{r \in D} dr \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega) \\
\nu\sigma_{f,g'\rightarrow g} &= \frac{\langle \nu\sigma_{f,g'\rightarrow
g} \phi \rangle}{\langle \phi \rangle}
Parameters
----------
@ -3729,7 +4078,7 @@ class NuFissionMatrixXS(MatrixMGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -3764,7 +4113,9 @@ class NuFissionMatrixXS(MatrixMGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`NuFissionMatrixXS.tally_keys`
property and values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
@ -3806,11 +4157,35 @@ class NuFissionMatrixXS(MatrixMGXS):
class Chi(MGXS):
"""The fission spectrum.
r"""The fission spectrum.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group cross sections for multi-group neutronics calculations.
multi-group cross sections for multi-group neutronics calculations. At a
minimum, one needs to set the :attr:`Chi.energy_groups` and
:attr:`Chi.domain` properties. Tallies for the flux and appropriate reaction
rates over the specified domain are generated automatically via the
:attr:`Chi.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`Chi.xs_tally` property.
For a spatial domain :math:`D` and energy group :math:`[E_g,E_{g-1}]`, the
fission spectrum is calculated as:
.. math::
\langle \nu\sigma_{f,\rightarrow g} \phi \rangle &= \int_{r \in D} dr
\int_{4\pi} d\Omega' \int_0^\infty dE' \int_{E_g}^{E_{g-1}} dE \; \chi(E)
\nu\sigma_f (r, E') \psi(r, E', \Omega')\\
\langle \nu\sigma_f \phi \rangle &= \int_{r \in D} dr \int_{4\pi}
d\Omega' \int_0^\infty dE' \int_0^\infty dE \; \chi(E) \nu\sigma_f (r,
E') \psi(r, E', \Omega') \\
\chi_g &= \frac{\langle \nu\sigma_{f,\rightarrow g} \phi \rangle}{\langle
\nu\sigma_f \phi \rangle}
Parameters
----------
@ -3818,7 +4193,7 @@ class Chi(MGXS):
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
@ -3853,7 +4228,9 @@ class Chi(MGXS):
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`Chi.tally_keys` property and values are
instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None