4. Tallies Specification – tallies.xml

The tallies.xml file allows the user to tell the code what results he/she is interested in, e.g. the fission rate in a given cell or the current across a given surface. There are two pieces of information that determine what quantities should be scored. First, one needs to specify what region of phase space should count towards the tally and secondly, the actual quantity to be scored also needs to be specified. The first set of parameters we call filters since they effectively serve to filter events, allowing some to score and preventing others from scoring to the tally.

The structure of tallies in OpenMC is flexible in that any combination of filters can be used for a tally. The following types of filter are available: cell, universe, material, surface, birth region, pre-collision energy, post-collision energy, and an arbitrary structured mesh.

The five valid elements in the tallies.xml file are <tally>, <filter>, <mesh>, <derivative>, and <assume_separate>.

4.1. <tally> Element

The <tally> element accepts the following sub-elements:

name:

An optional string name to identify the tally in summary output files.

Default: “”

filters:

A space-separated list of the IDs of filter elements.

nuclides:

If specified, the scores listed will be for particular nuclides, not the summation of reactions from all nuclides. The format for nuclides should be [Atomic symbol]-[Mass number], e.g. “U-235”. The reaction rate for all nuclides can be obtained with “total”. For example, to obtain the reaction rates for U-235, Pu-239, and all nuclides in a material, this element should be:

<nuclides>U-235 Pu-239 total</nuclides>

Default: total

estimator:

The estimator element is used to force the use of either analog, collision, or tracklength tally estimation. analog is generally the least efficient though it can be used with every score type. tracklength is generally the most efficient, but neither tracklength nor collision can be used to score a tally that requires post-collision information. For example, a scattering tally with outgoing energy filters cannot be used with tracklength or collision because the code will not know the outgoing energy distribution.

Default: tracklength but will revert to analog if necessary.

scores:

A space-separated list of the desired responses to be accumulated. A full list of valid scores can be found in the user’s guide.

trigger:

Precision trigger applied to all filter bins and nuclides for this tally. It must specify the trigger’s type, threshold and scores to which it will be applied. It has the following attributes/sub-elements:

type:

The type of the trigger. Accepted options are “variance”, “std_dev”, and “rel_err”.

variance:Variance of the batch mean \(\sigma^2\)
std_dev:Standard deviation of the batch mean \(\sigma\)
rel_err:Relative error of the batch mean \(\frac{\sigma}{\mu}\)

Default: None

threshold:

The precision trigger’s convergence criterion for tallied values.

Default: None

scores:

The score(s) in this tally to which the trigger should be applied.

Note

The scores in trigger must have been defined in scores in tally. An optional “all” may be used to select all scores in this tally.

Default: “all”

derivative:

The id of a derivative element. This derivative will be applied to all scores in the tally. Differential tallies are currently only implemented for collision and analog estimators.

Default: None

4.2. <filter> Element

Filters can be used to modify tally behavior. Most tallies (e.g. cell, energy, and material) restrict the tally so that only particles within certain regions of phase space contribute to the tally. Others (e.g. delayedgroup and energyfunction) can apply some other function to the scored values. The filter element has the following attributes/sub-elements:

type:The type of the filter. Accepted options are “cell”, “cellfrom”, “cellborn”, “surface”, “material”, “universe”, “energy”, “energyout”, “mu”, “polar”, “azimuthal”, “mesh”, “distribcell”, “delayedgroup”, “energyfunction”, and “particle”.
bins:A description of the bins for each type of filter can be found in Filter Types.
energy:energyfunction filters multiply tally scores by an arbitrary function. The function is described by a piecewise linear-linear set of (energy, y) values. This entry specifies the energy values. The function will be evaluated as zero outside of the bounds of this energy grid. (Only used for energyfunction filters)
y:energyfunction filters multiply tally scores by an arbitrary function. The function is described by a piecewise linear-linear set of (energy, y) values. This entry specifies the y values. (Only used for energyfunction filters)

4.2.1. Filter Types

For each filter type, the following table describes what the bins attribute should be set to:

cell:

A list of unique IDs for cells in which the tally should be accumulated.

surface:

This filter allows the tally to be scored when crossing a surface. A list of surface IDs should be given. By default, net currents are tallied, and to tally a partial current from one cell to another, this should be used in combination with a cell or cell_from filter that defines the other cell. This filter should not be used in combination with a meshfilter.

cellfrom:

This filter allows the tally to be scored when crossing a surface and the particle came from a specified cell. A list of cell IDs should be given. To tally a partial current from a cell to another, this filter should be used in combination with a cell filter, to define the other cell. This filter should not be used in combination with a meshfilter.

cellborn:

This filter allows the tally to be scored to only when particles were originally born in a specified cell. A list of cell IDs should be given.

material:

A list of unique IDs for materials in which the tally should be accumulated.

universe:

A list of unique IDs for universes in which the tally should be accumulated.

energy:

In continuous-energy mode, this filter should be provided as a monotonically increasing list of bounding pre-collision energies for a number of groups. For example, if this filter is specified as

<filter type="energy" bins="0.0 1.0e6 20.0e6" />

then two energy bins will be created, one with energies between 0 and 1 MeV and the other with energies between 1 and 20 MeV.

In multi-group mode the bins provided must match group edges defined in the multi-group library.

energyout:

In continuous-energy mode, this filter should be provided as a monotonically increasing list of bounding post-collision energies for a number of groups. For example, if this filter is specified as

<filter type="energyout" bins="0.0 1.0e6 20.0e6" />

then two post-collision energy bins will be created, one with energies between 0 and 1 MeV and the other with energies between 1 and 20 MeV.

In multi-group mode the bins provided must match group edges defined in the multi-group library.

mu:

A monotonically increasing list of bounding post-collision cosines of the change in a particle’s angle (i.e., \(\mu = \hat{\Omega} \cdot \hat{\Omega}'\)), which represents a portion of the possible values of \([-1,1]\). For example, spanning all of \([-1,1]\) with five equi-width bins can be specified as:

<filter type="mu" bins="-1.0 -0.6 -0.2 0.2 0.6 1.0" />

Alternatively, if only one value is provided as a bin, OpenMC will interpret this to mean the complete range of \([-1,1]\) should be automatically subdivided in to the provided value for the bin. That is, the above example of five equi-width bins spanning \([-1,1]\) can be instead written as:

<filter type="mu" bins="5" />
polar:

A monotonically increasing list of bounding particle polar angles which represents a portion of the possible values of \([0,\pi]\). For example, spanning all of \([0,\pi]\) with five equi-width bins can be specified as:

<filter type="polar" bins="0.0 0.6283 1.2566 1.8850 2.5132 3.1416"/>

Alternatively, if only one value is provided as a bin, OpenMC will interpret this to mean the complete range of \([0,\pi]\) should be automatically subdivided in to the provided value for the bin. That is, the above example of five equi-width bins spanning \([0,\pi]\) can be instead written as:

<filter type="polar" bins="5" />
azimuthal:

A monotonically increasing list of bounding particle azimuthal angles which represents a portion of the possible values of \([-\pi,\pi)\). For example, spanning all of \([-\pi,\pi)\) with two equi-width bins can be specified as:

<filter type="azimuthal" bins="0.0 3.1416 6.2832" />

Alternatively, if only one value is provided as a bin, OpenMC will interpret this to mean the complete range of \([-\pi,\pi)\) should be automatically subdivided in to the provided value for the bin. That is, the above example of five equi-width bins spanning \([-\pi,\pi)\) can be instead written as:

<filter type="azimuthal" bins="2" />
mesh:

The unique ID of a mesh to be tallied over.

distribcell:

The single cell which should be tallied uniquely for all instances.

Note

The distribcell filter will take a single cell ID and will tally each unique occurrence of that cell separately. This filter will not accept more than one cell ID. It is not recommended to combine this filter with a cell or mesh filter.

delayedgroup:

A list of delayed neutron precursor groups for which the tally should be accumulated. For instance, to tally to all 6 delayed groups in the ENDF/B-VII.1 library the filter is specified as:

<filter type="delayedgroup" bins="1 2 3 4 5 6" />
energyfunction:

energyfunction filters do not use the bins entry. Instead they use energy and y.

particle:

A list of integers indicating the type of particles to tally (‘neutron’ = 1, ‘photon’ = 2, ‘electron’ = 3, ‘positron’ = 4).

4.3. <mesh> Element

If a mesh is desired as a filter for a tally, it must be specified in a separate element with the tag name <mesh>. This element has the following attributes/sub-elements:

type:The type of mesh. This can be either “regular”, “rectilinear”, or “unstructured”.
dimension:The number of mesh cells in each direction. (For regular mesh only.)
lower_left:The lower-left corner of the structured mesh. If only two coordinates are given, it is assumed that the mesh is an x-y mesh. (For regular mesh only.)
upper_right:The upper-right corner of the structured mesh. If only two coordinates are given, it is assumed that the mesh is an x-y mesh. (For regular mesh only.)
width:The width of mesh cells in each direction. (For regular mesh only.)
x_grid:The mesh divisions along the x-axis. (For rectilinear mesh only.)
y_grid:The mesh divisions along the y-axis. (For rectilinear mesh only.)
z_grid:The mesh divisions along the z-axis. (For rectilinear mesh only.)
library:The mesh library used to represent an unstructured mesh. This can be either “moab” or “libmesh”. (For unstructured mesh only.)
filename:The name of the mesh file to be loaded at runtime. (For unstructured mesh only.)

Note

One of <upper_right> or <width> must be specified, but not both (even if they are consistent with one another).

4.4. <derivative> Element

OpenMC can take the first-order derivative of many tallies with respect to material perturbations. It works by propagating a derivative through the transport equation. Essentially, OpenMC keeps track of how each particle’s weight would change as materials are perturbed, and then accounts for that weight change in the tallies. Note that this assumes material perturbations are small enough not to change the distribution of fission sites. This element has the following attributes/sub-elements:

id:A unique integer that can be used to identify the derivative.
variable:The independent variable of the derivative. Accepted options are “density”, “nuclide_density”, and “temperature”. A “density” derivative will give the derivative with respect to the density of the material in [g / cm^3]. A “nuclide_density” derivative will give the derivative with respect to the density of a particular nuclide in units of [atom / b / cm]. A “temperature” derivative is with respect to a material temperature in units of [K]. The temperature derivative requires windowed multipole to be turned on. Note also that the temperature derivative only accounts for resolved resonance Doppler broadening. It does not account for thermal expansion, S(a, b) scattering, resonance scattering, or unresolved Doppler broadening.
material:The perturbed material. (Necessary for all derivative types)
nuclide:The perturbed nuclide. (Necessary only for “nuclide_density”)

4.5. <assume_separate> Element

In cases where the user needs to specify many different tallies each of which are spatially separate, this tag can be used to cut down on some of the tally overhead. The effect of assuming all tallies are spatially separate is that once one tally is scored to, the same event is assumed not to score to any other tallies. This element should be followed by “true” or “false”.

Warning

If used incorrectly, the assumption that all tallies are spatially separate can lead to incorrect results.

Default: false