8. Specifying Tallies¶

In order to obtain estimates of physical quantities in your simulation, you need to create one or more tallies using the openmc.Tally class. As explained in detail in the theory manual, tallies provide estimates of a scoring function times the flux integrated over some region of phase space, as in:

\[X = \underbrace{\int d\mathbf{r} \int d\mathbf{\Omega} \int dE}_{\text{filters}} \underbrace{f(\mathbf{r}, \mathbf{\Omega}, E)}_{\text{scores}} \psi (\mathbf{r}, \mathbf{\Omega}, E)\]

Thus, to specify a tally, we need to specify what regions of phase space should be included when deciding whether to score an event as well as what the scoring function (\(f\) in the above equation) should be used. The regions of phase space are generally called filters and the scoring functions are simply called scores.

The only cases when filters do not correspond directly with the regions of phase space are when expansion functions are applied in the integrand, such as for Legendre expansions of the scattering kernel.

8.1. Filters¶

To specify the regions of phase space, one must create a openmc.Filter. Since openmc.Filter is an abstract class, you actually need to instantiate one of its sub-classes (for a full listing, see Constructing Tallies). For example, to indicate that events that occur in a given cell should score to the tally, we would create a openmc.CellFilter:

cell_filter = openmc.CellFilter([fuel.id, moderator.id, reflector.id])

Another commonly used filter is openmc.EnergyFilter, which specifies multiple energy bins over which events should be scored. Thus, if we wanted to tally events where the incident particle has an energy in the ranges [0 eV, 4 eV] and [4 eV, 1 MeV], we would do the following:

energy_filter = openmc.EnergyFilter([0.0, 4.0, 1.0e6])

Energies are specified in eV and need to be monotonically increasing.

Caution

An energy bin between zero and the lowest energy specified is not included by default as it is in MCNP.

Once you have created a filter, it should be assigned to a openmc.Tally instance through the Tally.filters attribute:

tally.filters.append(cell_filter)
tally.filters.append(energy_filter)

# This is equivalent
tally.filters = [cell_filter, energy_filter]

Note

You are actually not required to assign any filters to a tally. If you create a tally with no filters, all events will score to the tally. This can be useful if you want to know, for example, a reaction rate over your entire model.

8.2. Scores¶

To specify the scoring functions, a list of strings needs to be given to the Tally.scores attribute. You can score the flux (‘flux’), or a reaction rate (‘total’, ‘fission’, etc.). For example, to tally the elastic scattering rate and the fission neutron production, you’d assign:

tally.scores = ['elastic', 'nu-fission']

With no further specification, you will get the total elastic scattering rate and the total fission neutron production. If you want reaction rates for a particular nuclide or set of nuclides, you can set the Tally.nuclides attribute to a list of strings indicating which nuclides. The nuclide names should follow the same naming convention as that used for material specification. If we wanted the reaction rates only for U235 and U238 (separately), we’d set:

tally.nuclides = ['U235', 'U238']

You can also list ‘all’ as a nuclide which will give you a separate reaction rate for every nuclide in the model.

The following tables show all valid scores:

**Flux scores: units are particle-cm per source particle.**¶
Score	Description
flux	Total flux.

**Reaction scores: units are reactions per source particle.**¶
Score	Description
absorption	Total absorption rate. For incident neutrons, this accounts for all reactions that do not produce secondary neutrons as well as fission. For incident photons, this includes photoelectric and pair production.
elastic	Elastic scattering reaction rate.
fission	Total fission reaction rate.
scatter	Total scattering rate.
total	Total reaction rate.
(n,2nd)	(n,2nd) reaction rate.
(n,2n)	(n,2n) reaction rate.
(n,3n)	(n,3n) reaction rate.
(n,na)	(n,n\(\alpha\)) reaction rate.
(n,n3a)	(n,n3\(\alpha\)) reaction rate.
(n,2na)	(n,2n\(\alpha\)) reaction rate.
(n,3na)	(n,3n\(\alpha\)) reaction rate.
(n,np)	(n,np) reaction rate.
(n,n2a)	(n,n2\(\alpha\)) reaction rate.
(n,2n2a)	(n,2n2\(\alpha\)) reaction rate.
(n,nd)	(n,nd) reaction rate.
(n,nt)	(n,nt) reaction rate.
(n,n3He)	(n,n³He) reaction rate.
(n,nd2a)	(n,nd2\(\alpha\)) reaction rate.
(n,nt2a)	(n,nt2\(\alpha\)) reaction rate.
(n,4n)	(n,4n) reaction rate.
(n,2np)	(n,2np) reaction rate.
(n,3np)	(n,3np) reaction rate.
(n,n2p)	(n,n2p) reaction rate.
(n,nX)	Level inelastic scattering reaction rate. The X indicates what which inelastic level, e.g., (n,n3) is third-level inelastic scattering.
(n,nc)	Continuum level inelastic scattering reaction rate.
(n,gamma)	Radiative capture reaction rate.
(n,p)	(n,p) reaction rate.
(n,d)	(n,d) reaction rate.
(n,t)	(n,t) reaction rate.
(n,3He)	(n,³He) reaction rate.
(n,a)	(n,\(\alpha\)) reaction rate.
(n,2a)	(n,2\(\alpha\)) reaction rate.
(n,3a)	(n,3\(\alpha\)) reaction rate.
(n,2p)	(n,2p) reaction rate.
(n,pa)	(n,p\(\alpha\)) reaction rate.
(n,t2a)	(n,t2\(\alpha\)) reaction rate.
(n,d2a)	(n,d2\(\alpha\)) reaction rate.
(n,pd)	(n,pd) reaction rate.
(n,pt)	(n,pt) reaction rate.
(n,da)	(n,d\(\alpha\)) reaction rate.
coherent-scatter	Coherent (Rayleigh) scattering reaction rate.
incoherent-scatter	Incoherent (Compton) scattering reaction rate.
photoelectric	Photoelectric absorption reaction rate.
pair-production	Pair production reaction rate.
Arbitrary integer	An arbitrary integer is interpreted to mean the reaction rate for a reaction with a given ENDF MT number.

**Particle production scores: units are particles produced per source particles.**¶
Score	Description
delayed-nu-fission	Total production of delayed neutrons due to fission.
prompt-nu-fission	Total production of prompt neutrons due to fission.
nu-fission	Total production of neutrons due to fission.
nu-scatter	This score is similar in functionality to the `scatter` score except the total production of neutrons due to scattering is scored vice simply the scattering rate. This accounts for multiplicity from (n,2n), (n,3n), and (n,4n) reactions.
H1-production	Total production of H1.
H2-production	Total production of H2 (deuterium).
H3-production	Total production of H3 (tritium).
He3-production	Total production of He3.
He4-production	Total production of He4 (alpha particles).

**Miscellaneous scores: units are indicated for each.**¶
Score	Description
current	Used in combination with a meshsurface filter: Partial currents on the boundaries of each cell in a mesh. It may not be used in conjunction with any other score. Only energy and mesh filters may be used. Used in combination with a surface filter: Net currents on any surface previously defined in the geometry. It may be used along with any other filter, except meshsurface filters. Surfaces can alternatively be defined with cell from and cell filters thereby resulting in tallying partial currents. Units are particles per source particle.
events	Number of scoring events. Units are events per source particle.
inverse-velocity	The flux-weighted inverse velocity where the velocity is in units of centimeters per second.
heating	Total nuclear heating in units of eV per source particle. For neutrons, this corresponds to MT=301 produced by NJOY’s HEATR module while for photons, this is tallied from direct photon energy deposition. See Heating and Energy Deposition.
heating-local	Total nuclear heating in units of eV per source particle assuming energy from secondary photons is deposited locally. Note that this score should only be used for incident neutrons. See Heating and Energy Deposition.
kappa-fission	The recoverable energy production rate due to fission. The recoverable energy is defined as the fission product kinetic energy, prompt and delayed neutron kinetic energies, prompt and delayed \(\gamma\)-ray total energies, and the total energy released by the delayed \(\beta\) particles. The neutrino energy does not contribute to this response. The prompt and delayed \(\gamma\)-rays are assumed to deposit their energy locally. Units are eV per source particle.
fission-q-prompt	The prompt fission energy production rate. This energy comes in the form of fission fragment nuclei, prompt neutrons, and prompt \(\gamma\)-rays. This value depends on the incident energy and it requires that the nuclear data library contains the optional fission energy release data. Energy is assumed to be deposited locally. Units are eV per source particle.
fission-q-recoverable	The recoverable fission energy production rate. This energy comes in the form of fission fragment nuclei, prompt and delayed neutrons, prompt and delayed \(\gamma\)-rays, and delayed \(\beta\)-rays. This tally differs from the kappa-fission tally in that it is dependent on incident neutron energy and it requires that the nuclear data library contains the optional fission energy release data. Energy is assumed to be deposited locally. Units are eV per source paticle.
decay-rate	The delayed-nu-fission-weighted decay rate where the decay rate is in units of inverse seconds.
damage-energy	Damage energy production in units of eV per source particle. This corresponds to MT=444 produced by NJOY’s HEATR module.

8.3. Normalization of Tally Results¶

As described in Scores, all tally scores are normalized per source particle simulated. However, for analysis of a given system, we usually want tally scores in a more natural unit. For example, neutron flux is often reported in units of particles/cm²-s. For a fixed source simulation, it is usually straightforward to convert units if the source rate is known. For example, if the system being modeled includes a source that is emitting 10⁴ neutrons per second, the tally results just need to be multipled by 10⁴. This can either be done manually or using the openmc.Source.strength attribute.

For a \(k\)-eigenvalue calculation, normalizing tally results is not as simple because the source rate is not actually known. Instead, we typically know the system power, \(P\), which represents how much energy is deposited per unit time. Most of this energy originates from fission, but a small percentage also results from other reactions (e.g., photons emitted from \((n,\gamma)\) reactions). The most rigorous method to normalize tally results is to run a coupled neutron-photon calculation and tally the heating score over the entire system. This score provides the heating rate in units of [eV/source], which we’ll denote \(H\). Then, calculate the heating rate in J/source as

\[H' = 1.602\times10^{-19} \left [ \frac{\text{J}}{\text{eV}} \right ] \cdot H \left [\frac{\text{eV}}{\text{source}} \right ].\]

Dividing the power by the observed heating rate then gives us a normalization factor that can be applied to other tallies:

\[f = \frac{P}{H'} = \frac{[\text{J}/\text{s}]}{[\text{J}/\text{source}]} = \left [ \frac{\text{source}}{\text{s}} \right ].\]

Multiplying by the normalization factor and dividing by volume, we can then get the flux in typical units:

\[\phi' = \frac{f\phi}{V} = \frac{[\text{source}/\text{s}][\text{particle-cm}/\text{source}]} {[\text{cm}^3]} = \left [\frac{\text{particle}}{\text{cm}^2\cdot\text{s}} \right ]\]

There are several slight variations on this procedure:

Run a neutron-only calculation and estimate the total heating using the heating-local score (this requires that your nuclear data has local heating data available, such as in the official data library at https://openmc.org. See Heating and Energy Deposition for more information.)
Run a neutron-only calculation and use the kappa-fission or fission-q-recoverable scores along with an estimate of the extra heating due to neutron capture reactions.
Calculate the overall fission rate and then used a fixed Q value to estimate the heating rate.

Note that the only difference between these and the above procedures is in how \(H'\) is estimated.