openmc.mgxs.ScatterMatrixXS¶

class
openmc.mgxs.
ScatterMatrixXS
(domain=None, domain_type=None, groups=None, by_nuclide=False, name='', num_polar=1, num_azimuthal=1, nu=False)[source]¶ A scattering matrix multigroup cross section with the cosine of the changeinangle represented as one or more Legendre moments or a histogram.
This class can be used for both OpenMC input generation and tally data postprocessing to compute spatiallyhomogenized and energyintegrated multigroup cross sections for multigroup neutronics calculations. At a minimum, one needs to set the
ScatterMatrixXS.energy_groups
andScatterMatrixXS.domain
properties. Tallies for the flux and appropriate reaction rates over the specified domain are generated automatically via theScatterMatrixXS.tallies
property, which can then be appended to aopenmc.Tallies
instance.For postprocessing, the
MGXS.load_from_statepoint()
will pull in the necessary data to compute multigroup cross sections from aopenmc.StatePoint
instance. The derived multigroup cross section can then be obtained from theScatterMatrixXS.xs_tally
property.For a spatial domain \(V\), incoming energy group \([E_{g'},E_{g'1}]\), and outgoing energy group \([E_g,E_{g1}]\), the Legendre scattering moments are calculated as:
\[\begin{aligned} \langle \sigma_{s,\ell,g'\rightarrow g} \phi \rangle &= \int_{r \in V} dr \int_{4\pi} d\Omega' \int_{E_{g'}}^{E_{g'1}} dE' \int_{4\pi} d\Omega \int_{E_g}^{E_{g1}} dE \; P_\ell (\Omega \cdot \Omega') \sigma_s (r, E' \rightarrow E, \Omega' \cdot \Omega) \psi(r, E', \Omega')\\ \langle \phi \rangle &= \int_{r \in V} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g1}} dE \; \psi (r, E, \Omega) \\ \sigma_{s,\ell,g'\rightarrow g} &= \frac{\langle \sigma_{s,\ell,g'\rightarrow g} \phi \rangle}{\langle \phi \rangle} \end{aligned}\]If the order is zero and a \(P_0\) transportcorrection is applied (default), the scattering matrix elements are:
\[\sigma_{s,g'\rightarrow g} = \frac{\langle \sigma_{s,0,g'\rightarrow g} \phi \rangle  \delta_{gg'} \sum_{g''} \langle \sigma_{s,1,g''\rightarrow g} \phi \rangle}{\langle \phi \rangle}\]To incorporate the effect of neutron multiplication from (n,xn) reactions in the above relation, the nu parameter can be set to True.
An alternative form of the scattering matrix is computed when the formulation property is set to ‘consistent’ rather than the default of ‘simple’. This formulation computes the scattering matrix multigroup cross section as the product of the scatter cross section and grouptogroup scattering probabilities.
Unlike the default ‘simple’ formulation, the ‘consistent’ formulation is computed from the groupwise scattering cross section which uses a tracklength estimator. This ensures that reaction rate balance is exactly preserved with a
TotalXS
computed using a tracklength estimator.For a scattering probability matrix \(P_{s,\ell,g'\rightarrow g}\) and scattering cross section \(\sigma_s (r, E)\) for incoming energy group \([E_{g'},E_{g'1}]\) and outgoing energy group \([E_g,E_{g1}]\), the Legendre scattering moments are calculated as:
\[\sigma_{s,\ell,g'\rightarrow g} = \sigma_s (r, E) \times P_{s,\ell,g'\rightarrow g}\]To incorporate the effect of neutron multiplication from (n,xn) reactions in the ‘consistent’ scattering matrix, the nu parameter can be set to True such that the Legendre scattering moments are calculated as:
\[\sigma_{s,\ell,g'\rightarrow g} = \upsilon_{g'\rightarrow g} \times \sigma_s (r, E) \times P_{s,\ell,g'\rightarrow g}\]Parameters:  domain (openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh) – The domain for spatial homogenization
 domain_type ({'material', 'cell', 'distribcell', 'universe', 'mesh'}) – The domain type for spatial homogenization
 groups (openmc.mgxs.EnergyGroups) – The energy group structure for energy condensation
 by_nuclide (bool) – If true, computes cross sections for each nuclide in domain
 name (str, optional) – Name of the multigroup cross section. Used as a label to identify tallies in OpenMC ‘tallies.xml’ file.
 num_polar (int, optional) – Number of equiwidth polar angle bins for angle discretization; defaults to one bin
 num_azimuthal (int, optional) – Number of equiwidth azimuthal angle bins for angle discretization; defaults to one bin
 nu (bool) – If True, the cross section data will include neutron multiplication; defaults to False
Variables:  formulation ('simple' or 'consistent') – The calculation approach to use (‘simple’ by default). The ‘simple’ formulation simply divides the grouptogroup scattering rates by the groupwise flux, each computed from analog tally estimators. The ‘consistent’ formulation multiplies the groupwise scattering rates by the grouptogroup scatter probability matrix, the former computed from tracklength tallies and the latter computed from analog tallies. The ‘consistent’ formulation is designed to better conserve reaction rate balance with the total and absorption cross sections computed using tracklength tally estimators.
 correction ('P0' or None) – Apply the P0 correction to scattering matrices if set to ‘P0’; this is
used only if
ScatterMatrixXS.scatter_format
is ‘legendre’  scatter_format ({'legendre', or 'histogram'}) – Representation of the angular scattering distribution (default is ‘legendre’)
 legendre_order (int) – The highest Legendre moment in the scattering matrix; this is used if
ScatterMatrixXS.scatter_format
is ‘legendre’. (default is 0)  histogram_bins (int) – The number of equallyspaced bins for the histogram representation of
the angular scattering distribution; this is used if
ScatterMatrixXS.scatter_format
is ‘histogram’. (default is 16)  name (str, optional) – Name of the multigroup cross section
 rxn_type (str) – Reaction type (e.g., ‘total’, ‘nufission’, etc.)
 nu (bool) – If True, the cross section data will include neutron multiplication
 by_nuclide (bool) – If true, computes cross sections for each nuclide in domain
 domain (openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh) – Domain for spatial homogenization
 domain_type ({'material', 'cell', 'distribcell', 'universe', 'mesh'}) – Domain type for spatial homogenization
 energy_groups (openmc.mgxs.EnergyGroups) – Energy group structure for energy condensation
 num_polar (int) – Number of equiwidth polar angle bins for angle discretization
 num_azimuthal (int) – Number of equiwidth azimuthal angle bins for angle discretization
 tally_trigger (openmc.Trigger) – An (optional) tally precision trigger given to each tally used to compute the cross section
 scores (list of str) – The scores in each tally used to compute the multigroup cross section
 filters (list of openmc.Filter) – The filters in each tally used to compute the multigroup cross section
 tally_keys (list of str) – The keys into the tallies dictionary for each tally used to compute the multigroup cross section
 estimator ('analog') – The tally estimator used to compute the multigroup cross section
 tallies (collections.OrderedDict) – OpenMC tallies needed to compute the multigroup cross section. The keys
are strings listed in the
ScatterMatrixXS.tally_keys
property and values are instances ofopenmc.Tally
.  rxn_rate_tally (openmc.Tally) – Derived tally for the reaction rate tally used in the numerator to compute the multigroup cross section. This attribute is None unless the multigroup cross section has been computed.
 xs_tally (openmc.Tally) – Derived tally for the multigroup cross section. This attribute is None unless the multigroup cross section has been computed.
 num_subdomains (int) – The number of subdomains is unity for ‘material’, ‘cell’ and ‘universe’ domain types. This is equal to the number of cell instances for ‘distribcell’ domain types (it is equal to unity prior to loading tally data from a statepoint file).
 num_nuclides (int) – The number of nuclides for which the multigroup cross section is being tracked. This is unity if the by_nuclide attribute is False.
 nuclides (Iterable of str or 'sum') – The optional userspecified nuclides for which to compute cross sections (e.g., ‘U238’, ‘O16’). If by_nuclide is True but nuclides are not specified by the user, all nuclides in the spatial domain are included. This attribute is ‘sum’ if by_nuclide is false.
 sparse (bool) – Whether or not the MGXS’ tallies use SciPy’s LIL sparse matrix format for compressed data storage
 loaded_sp (bool) – Whether or not a statepoint file has been loaded with tally data
 derived (bool) – Whether or not the MGXS is merged from one or more other MGXS
 hdf5_key (str) – The key used to index multigroup cross sections in an HDF5 data store

build_hdf5_store
(filename='mgxs.h5', directory='mgxs', subdomains='all', nuclides='all', xs_type='macro', row_column='inout', append=True, libver='earliest')¶ Export the multigroup cross section data to an HDF5 binary file.
This method constructs an HDF5 file which stores the multigroup cross section data. The data is stored in a hierarchy of HDF5 groups from the domain type, domain id, subdomain id (for distribcell domains), nuclides and cross section type. Two datasets for the mean and standard deviation are stored for each subdomain entry in the HDF5 file.
Note
This requires the h5py Python package.
Parameters:  filename (str) – Filename for the HDF5 file. Defaults to ‘mgxs.h5’.
 directory (str) – Directory for the HDF5 file. Defaults to ‘mgxs’.
 subdomains (Iterable of Integral or 'all') – The subdomain IDs of the cross sections to include in the report. Defaults to ‘all’.
 nuclides (Iterable of str or 'all' or 'sum') – The nuclides of the crosssections to include in the report. This may be a list of nuclide name strings (e.g., [‘U235’, ‘U238’]). The special string ‘all’ will report the cross sections for all nuclides in the spatial domain. The special string ‘sum’ will report the cross sections summed over all nuclides. Defaults to ‘all’.
 xs_type ({'macro', 'micro'}) – Store the macro or micro cross section in units of cm^1 or barns. Defaults to ‘macro’.
 row_column ({'inout', 'outin'}) – Store scattering matrices indexed first by incoming group and second by outgoing group (‘inout’), or vice versa (‘outin’). Defaults to ‘inout’.
 append (bool) – If true, appends to an existing HDF5 file with the same filename directory (if one exists). Defaults to True.
 libver ({'earliest', 'latest'}) – Compatibility mode for the HDF5 file. ‘latest’ will produce files that are less backwards compatible but have performance benefits.
Raises: ValueError
– When this method is called before the multigroup cross section is computed from tally data.

can_merge
(other)¶ Determine if another MGXS can be merged with this one
If results have been loaded from a statepoint, then MGXS are only mergeable along one and only one of enegy groups or nuclides.
Parameters: other (openmc.mgxs.MGXS) – MGXS to check for merging

export_xs_data
(filename='mgxs', directory='mgxs', format='csv', groups='all', xs_type='macro')¶ Export the multigroup cross section data to a file.
This method leverages the functionality in the Pandas library to export the multigroup cross section data in a variety of output file formats for storage and/or postprocessing.
Parameters:  filename (str) – Filename for the exported file. Defaults to ‘mgxs’.
 directory (str) – Directory for the exported file. Defaults to ‘mgxs’.
 format ({'csv', 'excel', 'pickle', 'latex'}) – The format for the exported data file. Defaults to ‘csv’.
 groups (Iterable of Integral or 'all') – Energy groups of interest. Defaults to ‘all’.
 xs_type ({'macro', 'micro'}) – Store the macro or micro cross section in units of cm^1 or barns. Defaults to ‘macro’.

get_condensed_xs
(coarse_groups)¶ Construct an energycondensed version of this cross section.
Parameters: coarse_groups (openmc.mgxs.EnergyGroups) – The coarse energy group structure of interest Returns: A new MGXS condensed to the group structure of interest Return type: MGXS

get_flux
(groups='all', subdomains='all', order_groups='increasing', value='mean', squeeze=True, **kwargs)¶ Returns an array of the fluxes used to weight the MGXS.
This method constructs a 2D NumPy array for the requested weighting flux for one or more subdomains (1st dimension), and energy groups (2nd dimension).
Parameters:  groups (Iterable of Integral or 'all') – Energy groups of interest. Defaults to ‘all’.
 subdomains (Iterable of Integral or 'all') – Subdomain IDs of interest. Defaults to ‘all’.
 order_groups ({'increasing', 'decreasing'}) – Return the cross section indexed according to increasing or decreasing energy groups (decreasing or increasing energies). Defaults to ‘increasing’.
 value ({'mean', 'std_dev', 'rel_err'}) – A string for the type of value to return. Defaults to ‘mean’.
 squeeze (bool) – A boolean representing whether to eliminate the extra dimensions of the multidimensional array to be returned. Defaults to True.
Returns: A NumPy array of the flux indexed in the order each group and subdomain is listed in the parameters.
Return type: Raises: ValueError
– When this method is called before the data is available from tally data, or, when this is used on an MGXS type without a flux score.

get_homogenized_mgxs
(other_mgxs)¶ Construct a homogenized mgxs with other MGXS objects.
Parameters: other_mgxs (openmc.mgxs.MGXS or Iterable of openmc.mgxs.MGXS) – The MGXS to homogenize with this one. Returns: A new homogenized MGXS Return type: openmc.mgxs.MGXS Raises: ValueError
– If the other_mgxs is of a different type.

static
get_mgxs
(mgxs_type, domain=None, domain_type=None, energy_groups=None, by_nuclide=False, name='', num_polar=1, num_azimuthal=1)¶ Return a MGXS subclass object for some energy group structure within some spatial domain for some reaction type.
This is a factory method which can be used to quickly create MGXS subclass objects for various reaction types.
Parameters:  mgxs_type (str or Integral) – The type of multigroup cross section object to return; valid values are members of MGXS_TYPES, or the reaction types that are the keys of REACTION_MT. Note that if a reaction type from REACTION_MT is used, it can be appended with ‘ matrix’ to obtain a multigroup matrix (from incoming to outgoing energy groups) for reactions with a neutron in an outgoing channel.
 domain (openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh) – The domain for spatial homogenization
 domain_type ({'material', 'cell', 'distribcell', 'universe', 'mesh'}) – The domain type for spatial homogenization
 energy_groups (openmc.mgxs.EnergyGroups) – The energy group structure for energy condensation
 by_nuclide (bool) – If true, computes cross sections for each nuclide in domain. Defaults to False
 name (str, optional) – Name of the multigroup cross section. Used as a label to identify tallies in OpenMC ‘tallies.xml’ file. Defaults to the empty string.
 num_polar (Integral, optional) – Number of equiwidth polar angles for angle discretization; defaults to no discretization
 num_azimuthal (Integral, optional) – Number of equiwidth azimuthal angles for angle discretization; defaults to no discretization
Returns: A subclass of the abstract MGXS class for the multigroup cross section type requested by the user
Return type:

get_nuclide_densities
(nuclides='all')¶ Get an array of atomic number densities in units of atom/bcm for all nuclides in the cross section’s spatial domain.
Parameters: nuclides (Iterable of str or 'all' or 'sum') – A list of nuclide name strings (e.g., [‘U235’, ‘U238’]). The special string ‘all’ will return the atom densities for all nuclides in the spatial domain. The special string ‘sum’ will return the atom density summed across all nuclides in the spatial domain. Defaults to ‘all’. Returns: An array of the atomic number densities (atom/bcm) for each of the nuclides in the spatial domain Return type: numpy.ndarray of float Raises: ValueError
– When this method is called before the spatial domain has been set.

get_nuclide_density
(nuclide)¶ Get the atomic number density in units of atoms/bcm for a nuclide in the cross section’s spatial domain.
Parameters: nuclide (str) – A nuclide name string (e.g., ‘U235’) Returns: The atomic number density (atom/bcm) for the nuclide of interest Return type: float

get_nuclides
()¶ Get all nuclides in the cross section’s spatial domain.
Returns: A list of the string names for each nuclide in the spatial domain (e.g., [‘U235’, ‘U238’, ‘O16’]) Return type: list of str Raises: ValueError
– When this method is called before the spatial domain has been set.

get_pandas_dataframe
(groups='all', nuclides='all', xs_type='macro', paths=False)[source]¶ Build a Pandas DataFrame for the MGXS data.
This method leverages
openmc.Tally.get_pandas_dataframe()
, but renames the columns with terminology appropriate for cross section data.Parameters:  groups (Iterable of Integral or 'all') – Energy groups of interest. Defaults to ‘all’.
 nuclides (Iterable of str or 'all' or 'sum') – The nuclides of the crosssections to include in the dataframe. This may be a list of nuclide name strings (e.g., [‘U235’, ‘U238’]). The special string ‘all’ will include the cross sections for all nuclides in the spatial domain. The special string ‘sum’ will include the cross sections summed over all nuclides. Defaults to ‘all’.
 xs_type ({'macro', 'micro'}) – Return macro or micro cross section in units of cm^1 or barns. Defaults to ‘macro’.
 paths (bool, optional) – Construct columns for distribcell tally filters (default is True). The geometric information in the Summary object is embedded into a Multiindex column with a geometric “path” to each distribcell instance.
Returns: A Pandas DataFrame for the cross section data.
Return type: Raises: ValueError
– When this method is called before the multigroup cross section is computed from tally data.

get_slice
(nuclides=[], in_groups=[], out_groups=[], legendre_order='same')[source]¶ Build a sliced ScatterMatrix for the specified nuclides and energy groups.
This method constructs a new MGXS to encapsulate a subset of the data represented by this MGXS. The subset of data to include in the tally slice is determined by the nuclides and energy groups specified in the input parameters.
Parameters:  nuclides (list of str) – A list of nuclide name strings (e.g., [‘U235’, ‘U238’]; default is [])
 in_groups (list of int) – A list of incoming energy group indices starting at 1 for the high energies (e.g., [1, 2, 3]; default is [])
 out_groups (list of int) – A list of outgoing energy group indices starting at 1 for the high energies (e.g., [1, 2, 3]; default is [])
 legendre_order (int or 'same') – The highest Legendre moment in the sliced MGXS. If order is ‘same’ then the sliced MGXS will have the same Legendre moments as the original MGXS (default). If order is an integer less than the original MGXS’ order, then only those Legendre moments up to that order will be included in the sliced MGXS.
Returns: A new MatrixMGXS which encapsulates the subset of data requested for the nuclide(s) and/or energy group(s) requested in the parameters.
Return type:

get_subdomain_avg_xs
(subdomains='all')¶ Construct a subdomainaveraged version of this cross section.
This method is useful for averaging cross sections across distribcell instances. The method performs spatial homogenization to compute the scalar fluxweighted average cross section across the subdomains.
Parameters: subdomains (Iterable of Integral or 'all') – The subdomain IDs to average across. Defaults to ‘all’. Returns: A new MGXS averaged across the subdomains of interest Return type: openmc.mgxs.MGXS Raises: ValueError
– When this method is called before the multigroup cross section is computed from tally data.

get_units
(xs_type='macro')¶ This method returns the units of a MGXS based on a desired xs_type.
Parameters: xs_type ({'macro', 'micro'}) – Return the macro or micro cross section units. Defaults to ‘macro’. Returns: A string representing the units of the MGXS. Return type: str

get_xs
(in_groups='all', out_groups='all', subdomains='all', nuclides='all', moment='all', xs_type='macro', order_groups='increasing', row_column='inout', value='mean', squeeze=True)[source]¶ Returns an array of multigroup cross sections.
This method constructs a 5D NumPy array for the requested multigroup cross section data for one or more subdomains (1st dimension), energy groups in (2nd dimension), energy groups out (3rd dimension), nuclides (4th dimension), and moments/histograms (5th dimension).
Note
The scattering moments are not multiplied by the \((2\ell+1)/2\) prefactor in the expansion of the scattering source into Legendre moments in the neutron transport equation.
Parameters:  in_groups (Iterable of Integral or 'all') – Incoming energy groups of interest. Defaults to ‘all’.
 out_groups (Iterable of Integral or 'all') – Outgoing energy groups of interest. Defaults to ‘all’.
 subdomains (Iterable of Integral or 'all') – Subdomain IDs of interest. Defaults to ‘all’.
 nuclides (Iterable of str or 'all' or 'sum') – A list of nuclide name strings (e.g., [‘U235’, ‘U238’]). The special string ‘all’ will return the cross sections for all nuclides in the spatial domain. The special string ‘sum’ will return the cross section summed over all nuclides. Defaults to ‘all’.
 moment (int or 'all') –
 The scattering matrix moment to return. All moments will be
 returned if the moment is ‘all’ (default); otherwise, a specific moment will be returned.
 xs_type ({'macro', 'micro'}) – Return the macro or micro cross section in units of cm^1 or barns. Defaults to ‘macro’.
 order_groups ({'increasing', 'decreasing'}) – Return the cross section indexed according to increasing or decreasing energy groups (decreasing or increasing energies). Defaults to ‘increasing’.
 row_column ({'inout', 'outin'}) – Return the cross section indexed first by incoming group and second by outgoing group (‘inout’), or vice versa (‘outin’). Defaults to ‘inout’.
 value ({'mean', 'std_dev', 'rel_err'}) – A string for the type of value to return. Defaults to ‘mean’.
 squeeze (bool) – A boolean representing whether to eliminate the extra dimensions of the multidimensional array to be returned. Defaults to True.
Returns: A NumPy array of the multigroup cross section indexed in the order each group and subdomain is listed in the parameters.
Return type: Raises: ValueError
– When this method is called before the multigroup cross section is computed from tally data.

load_from_statepoint
(statepoint)[source]¶ Extracts tallies in an OpenMC StatePoint with the data needed to compute multigroup cross sections.
This method is needed to compute cross section data from tallies in an OpenMC StatePoint object.
Note
The statepoint must be linked with an OpenMC Summary object.
Parameters: statepoint (openmc.StatePoint) – An OpenMC StatePoint object with tally data Raises: ValueError
– When this method is called with a statepoint that has not been linked with a summary object.

merge
(other)¶ Merge another MGXS with this one
MGXS are only mergeable if their energy groups and nuclides are either identical or mutually exclusive. If results have been loaded from a statepoint, then MGXS are only mergeable along one and only one of energy groups or nuclides.
Parameters: other (openmc.mgxs.MGXS) – MGXS to merge with this one Returns: merged_mgxs – Merged MGXS Return type: openmc.mgxs.MGXS

print_xs
(subdomains='all', nuclides='all', xs_type='macro', moment=0)[source]¶ Prints a string representation for the multigroup cross section.
Parameters:  subdomains (Iterable of Integral or 'all') – The subdomain IDs of the cross sections to include in the report. Defaults to ‘all’.
 nuclides (Iterable of str or 'all' or 'sum') – The nuclides of the crosssections to include in the report. This may be a list of nuclide name strings (e.g., [‘U235’, ‘U238’]). The special string ‘all’ will report the cross sections for all nuclides in the spatial domain. The special string ‘sum’ will report the cross sections summed over all nuclides. Defaults to ‘all’.
 xs_type ({'macro', 'micro'}) – Return the macro or micro cross section in units of cm^1 or barns. Defaults to ‘macro’.
 moment (int) – The scattering moment to print (default is 0)