6. Criticality Calculations

Monte Carlo criticality calculations use the fission source iteration method, that is, the fission sources generated in the current generation are used as the initial sources for the next generation. The user needs to specify the basic parameters for source iteration in the input file, including the initial effective multiplication factor (keff), the number of neutrons per generation, and the number of neutron generations, as well as the initial fission source distribution.

In the criticality calculation module, users can also select the type and parameters of the random number generator, as well as the parallel mode of parallel critical calculation.

6.1. Source Iteration Parameters

PowerIter [Keff0 = <keff0>] [Population = <N Mi Mt>] [Batchnum = <Mb>]

where,

  • PowerIter is the keyword for the source iteration input card.
  • Keff0 is an input option that sets the initial effective multiplication coefficient, and the default value is keff0 = 1. The program requires the user to enter the initial effective multiplication coefficient 0.1 < keff0 < 10.
  • Population is an input option that sets the number of neutrons per generation N, the number of inactive generations (Mi）, and the total number of generations(Mt). Accordingly, the number of active generations for Monte Carlo critical calculations is Ma = Mt – Mi, and the total number of active neutrons is M = N × Ma.
  • Batchnum is used to reduce the tally merging operations in parallel critical calculations, compressing Ma active generations into Mb groups and merging data every Ma / Mb active generations. The default value is Mb = Ma.

6.2. UFS Mesh Parameters

UfsMesh [UfsType = <type>] [Scope = <params>] [Bound = <params>] [AutoCutWgt = <Mt>]

where,

  • UfsMesh is the keyword for the UFS Mesh input card.
  • UfsType sets the UFS method type. UfsType = 0 (default value) means the UFS method is not used, UfsType = 1 means using the uniform fission source method, UfsType = 2 means using the biased fission source method (since the biased fission source method directly uses the maximum number of neutrons in the mesh divided by the number of neutrons in the corresponding mesh, the uniform result obtained is not obvious, so this method is not recommended)
  • Scope specifies the number of mesh cells in the x, y, and z directions. In particular, a parameter of “-1” means there is only one layer of infinite mesh cell in that direction.
  • Bound specifies the number of mesh cells in the x, y, and z directions. For example, “Bound = x_min x_max y_min y_max z_min z_max”. If there is only one layer of mesh cell in a certain direction, the corresponding parameters in the Bound have no practical meaning.
  • AutoCutWgt specifies whether to use automatic change of neutron cutoff weight. If Mt = 0, the program sets the neutron cutoff weight to 0.01. If Mt = 1, the program automatically changes the neutron cutoff weight. It is recommended to use Mt = 1. When UfsType = 2, it is recommended to use Mt = 1, otherwise a warning will be reported.

6.3. Initial fission source

InitSrc [<type> = {params}]

where,

  • InitSrc is the keyword for the initial fission source input card.

  • type is the keyword of the fission source type, and params is the corresponding parameter. The initial fission source distribution supported by RMC includes three types: point source, uniform source and universal source; see 表6.2 for further details. In addition to the initial sources mentioned above, the program also supports user input of “HDF5 = 1”, which allows for reading fission source parameters from the “convergent_source.h5” file to accelerate source convergence.

    注解

    This method is typically applied during coupled calculations. By reading the converged fission source output from the previous iteration step as the initial source for the next iteration step, it can reduce the number of source iterations and speed up source convergence.

表6.2 Distribution of initial fission sources supported by RMC
Keyword Description Parameter
Point Isolated point source x1 y1 z1 x2 y2 z2 …
Slab A rectangular uniform source parallel to the coordinate axis xmin xmax ymin ymax zmin zmax
Sph Spherical uniform source x y z R
Cyl/x Cylindrical uniform source parallel to the x-axis y z R xmin xmax
Cyl/y Cylindrical uniform source parallel to the y-axis x z R ymin ymax
Cyl/z Cylindrical uniform source parallel to the z-axis x y R zmin zmax
ExternalSource Universal Source x
HDF5 HDF5 Convergent Fission Source 1

6.4. External Source Subroutines

When a description of a general source requires a higher degree of flexibility in terms of description, an external source subroutine can be used. The input card for this section is:

SOURCESUB [SOURCE = <source>] [PTMOD = <PTMod>]

For details, see the section External Source Subroutine for Fixed Source Calculation. Note that this card must be defined after the InitSrc input option, and it can only be used with the general source ExternalSource is in use.

6.5. Random Number Generator

RMC contains three different types of random number generators. For general users, it is recommended to use the default random number generator type and parameters. Advanced users may need to use specific random number parameters, for example, use different random number seeds for the same case to obtain independent calculation results. RMC provides input card for custom random number generators:

RNG [Type = <type>] [Seed = <seed>] [Stride = <stride>]

where,

  • RNG is the keyword for the random number generator input card.
  • Type specifies the type of random number generator. Type = 1 is a 48-bit multiplicative linear congruential random number generator, Type = 2 (default) is a 64-bit multiplicative linear congruential random number generator, Type = 3 is a 64-bit hybrid linear congruential random number generator, and Type = 5 is a 128-bit random number generator.
  • Seed specifies the initialization seed of the random number generator, which can be any positive odd number. The default value is Seed = 1.
  • Stride is used to set the length of the random number of each neutron history when parallel computing is performed. It is only recommended for advanced users. The default value is Stride = 10000.

6.6. Truncation Conditions

CutOff [MaxLost=<maxLost>]
       [MinWeight=<minWeightN minWeightP>]
       [MaxWeight=<maxWeightP>]

where,

  • CutOff is the keyword for the truncation condition input card.
  • MaxLost specifies the maximum number of particles that the program allows to be lost. The default value is 10.
  • MinWeight specifies the lower limit of the weight in the transport process. minWeightN specifies the lower limit of the weight of neutrons, with the default value as 0.25, and minWeightP specifies the lower limit of the weight of photons, with the default value as 0.6. After the weight window variance reduction function is turned on, the input here is invalid
  • MaxWeightP specifies the upper limit of the weight of photons in the transport process. The default value is 1.4.

6.7. Parallel Criticality Calculation Mode

In parallel critical calculations, and considering load balancing, it is necessary to collect and redistribute the fission source neutrons on each process. Traditional Monte Carlo programs generally use the master-slave mode, which has low collection and distribution efficiency. RMC uses the peer-to-peer mode (slave-slave) to improve parallel efficiency. The input option for selecting the parallel critical calculation mode is:

ParallelBank <flag>

where,

  • ParallelBank is the keyword for the Parallel Criticality Calculation Mode input card.
  • flag specifies the parallel mode. flag = 0 represents master-slave mode, while flag = 1 (default) represents peer-to-peer mode.

6.8. Fission Matrix Method for Solving Critical Adjoint Flux

MGAdjFisMatrix [Energy=<enenrgy>]  [Scope=<scope>] [Bound=<bound>]

where,

  • MGAdjFisMatrix is the keyword for the input card for the fission matrix method to solve the critical adjoint flux.
  • Energy specifies energy cutoff points for the adjoint flux.
  • Scope specifies the number of mesh cells in the x, y, and z directions. In particular, a parameter of “-1” means there is only one layer of infinite mesh cell in that direction (Note: in the Scope tab of the Universe Repeated Geometry, a parameter of 1 means there is only one layer of infinite mesh cell in that direction).
  • Bound specifies the boundary range of the mesh in the x, y, and z directions, in the form of “Bound = x_min x_max y_min y_max z_min z_max”. If there is only one layer of mesh cell in a certain direction, the corresponding parameters in the Bound have no practical meaning.

In addition, when using the fission matrix to solve the critical adjoint flux, it is necessary to write the fission matrix of the same geometric mesh in the source convergence module.

6.9. Output counting results generation by generation

Outputcyc [num]

The Outputcyc option specifies to enable and set the number of generations of tally results output in critical calculations, and [num] defines the number of generations the tally results are output each time. If you need to perform statistical tests on the counting results output for each generation, you will also need to turn on the statistical test switch in the Tally input option.

6.10. Criticality calculation module input example

CRITICALITY
PowerIter Population = 5000 30 100 // keff0 = 1.0
InitSrc point = 0.0 0.0 0.0
                0.5 0.5 0.0
               -0.5 -0.5 0.0
RNG type = 3 seed = 12345 stride = 10000
ParallelBank 1

In the critical calculation module above, the PowerIter input card specifies that the number of particles per generation is 5000, 30 generations are skipped, and a total of 100 generations are simulated; the initial effective proliferation coefficient is the default value, that is, 1.0. InitSrc specifies that the type of the initial source is a point source, and the positions are (0, 0, 0), (0.5, 0.5, 0) and (-0.5, -0.5, 0). Fission sources will be randomly generated at these three positions. RNG specifies that the random number type is a 64-bit mixed linear congruential random number generator, the initial random number seed is 12345, and the random number length assigned to each particle is 10000. ParallelBank indicates that the peer-to-peer mode is used to collect and distribute fission sources in parallel computing.