32. Stochastic Neutron Dynamics (Enterprise Version Only)

RMC supports stochastic neutron dynamics calculation and simulation functions such as neutron static system ignition probability, dynamic system survival probability and neutron pulse initiation time, and lastly, RMC also supports the direct simulation method for neutron dynamics calculation function.

When simulating stochastic neutron dynamics, the neutron chain is used as a unit. According to the defined time step size, the evolution characteristics of the neutron chain over time are simulated, the standard of neutron chain self-sustaining is set, and the ignition probability of statistical neutrons or the pulse initiation time of the supercritical system is calculated.

32.1. Stochastic Neutron Dynamics Input Option

KINETICS
Particle  FissionChain=<fission_chain_number>  TimeStep=<time_step>
          StochasticMode=<calculation_mode_option>
          [MaxPopulation=<maximum_population>]  [Batch=<batch_number>]
          [Lambda=<sponta_fission_rate>]  [Nu=<average_neutron_number>]
          [TerminateTime=<terminate_time>]  [TerminateFisRate=Terminate_fission_rate]
          [ExpFisRate=<exponential_fission_rate>]  [TargetFisRate=<target_fission_rate>]
          [InitSourceNum=<initial_neutron_number>] [PrecursorMode=<precursor_mode_option>]
          [DecayTimeStep=<decay_timestep>] [CaptureMode=<capture_mode_option>]
          [UseComb=<use_comb_method_option>] [ControlNum=<comb_control_number>]
          [FissMultiplicity=<fission_multiplicity>] [SpontaFiss=<spontaneous_fission>]
          [InitCriSrc=<initial_critical_source>] [GeoMatTimeStep=<geo_mat_time_step>]
          [PosStartTime=<start_time>] [PosEndTime=<end_time>]
TimeStep  Time=<t0 t1 t2 ... tn>  Step=<s1 s2 ... sn>
RNG       [Type = <type>] [Seed = <seed>] [Stride = <stride>]
FissMult  zaid=<nuclide_ID>  method=<number> data=<number> shift=<number>

where,

  • KINETICS is the keyword for random neutron dynamics. Particle defines the parameters related to the neutron chain, TimeStep defines the parameters related to the variable time step, RNG defines the random number. The usage method of RNG is the same as the random number definition input option in the criticality calculation module, hence it will not be repeated here. FissMult defines the detailed neutron fission multiplicity parameter settings, which is the same as the usage method of the FissMult card in the fixed source calculation mode, so it will not be repeated here. The following introduces the usage of the Particle and TimeStep input options.

32.1.1. Particle Input Option

The Particle input option specifies the relevant parameters of the neutron chain in the stochastic neutron dynamics simulation.

  • FissionChain specifies the number of simulated neutron chains, which must be a positive integer.
  • TimeStep is the time step interval during the subchain simulation, in seconds.
  • StochasticMode is the random neutron dynamics calculation mode option. 0 represents the pulse initiation time calculation or direct simulation neutron dynamics calculation mode, 1 indicates the POI calculation mode, 2 indicates that the neutron library tracking method is used to calculate POS, 3 indicates that the single neutron tracking method is used to calculate POS, and the default value is 0.
  • MaxPopulation specifies the maximum number of neutrons in the neutron chain simulation. When the number of prompt neutrons in the neutron chain exceeds this number, the neutron chain is considered self-sustaining and the simulation of the neutron chain is stopped.
  • Batch defines the number of groups. This card is used when using group statistics to calculate the uncertainty of the ignition probability. By default, there is no grouping, that is, the number of groups is 1.
  • Lambda defines the fission intensity of the spontaneous fission source, in units of /s.
  • Nu defines the average fission neutron number of a spontaneous fission source.
  • TerminateTime defines the termination time of the subchain simulation, in seconds.
  • TerminateFisRate defines the fission reaction rate at which the neutron chain simulation terminates, in units of /s.
  • ExpFisRate defines the fission reaction rate at which exponential growth begins during neutron chain simulation. If this fission rate is exceeded, the neutron chain is considered to have entered a significant exponential growth phase.
  • TargetFisRate defines the extrapolated target fission reaction rate during neutron chain simulation. In a static supercritical system, the time when the neutron chain fission rate reaches TargetFisRate can be extrapolated based on the defined ExpFisRate and TargetFisRate exponents.
  • InitSourceNum defines the initial neutron source number, used in the direct simulation neutron dynamics calculation mode.
  • PrecursorMode defines the delayed neutron precursor decay mode. 0 is direct simulation of the precursor (commonly used in pulse initiation time calculation mode), 1 is forced decay of the precursor (commonly used in direct simulation neutron dynamics calculation mode), and the default is 0.
  • DecayTimeStep is the time step for the forced decay of the delayed neutron precursor nucleus (i.e. forced decay once every this time step). The default value is 1ms and is only valid in the forced decay mode of the precursor nucleus.
  • CaptureMode handles two modes of radiation capture reaction, 0 is direct simulation absorption and killing particles, 1 is latent capture, with the default value being 0.
  • UseComb indicates whether to enable the comb method, with the value of 0 meaning off, 1 meaning on, and the default value being 0.
  • ControlNum is the number of particles adjusted by the comb method. It is only valid after the comb method is turned on. The default value is 10000.
  • FissMultiplicity defines if fission multiplicity is enabled, with 0 indicating off, 1 indicating on, and the default is 1.
  • SpontaFiss defines if spontaneous fission is enabled, with 0 indicating off, 1 indicating on, and the default is 1.
  • InitCriSrc defines if there is an initial critical source (firstly, calculate the source using quasi-static S mode, and generate a source file with the suffix “.KineticsInitSource”), where the value of 0 means no initial critical source is used, the value of 1 means an initial critical source is used, with the default value being 0. If it exists, the initial source distribution is determined by the given file, which is often used in the direct simulation neutron dynamics calculation mode.
  • GeoMatTimeStep defines the time step for geometry and material changes (applied in POS).
  • PosStartTime defines the start time of POS calculation.
  • PosEndTime defines the end time of POS calculation.

32.1.2. TimeStep Input Option

The TimeStep input option specifies the parameters related to the dynamic time step in stochastic neutron dynamics simulations for dynamic systems (geometry or materials that vary with time).

  • Time specifies the time interval boundary in seconds.
  • TimeStep represents the time step length within each time interval. The number is one less than the number of time interval boundaries. The unit used here is seconds.

32.2. Stochastic Neutron Dynamics Module Input Example

  • Neutron Static System Ignition Probability Calculation Example
KINETICS
Particle  StochasticMode=1 FissionChain=1000 TimeStep=1e-9  MaxPopulation=1000 Batch=10

This example defines the calculation parameters for the ignition probability of a neutron static system, with the calculation mode used here as POI. 1000 neutron chains are simulated and divided into 10 groups for simulation and statistics. The simulation time step size is 1 nanosecond (ns). The upper limit of the number of prompt neutrons in each neutron chain is 1000.

  • Neutron Dynamic System Survival Probability (Neutron Bank Tracking Method) Calculation Example
KINETICS
particle  FissionChain = 100000 TimeStep=10e-8  MaxPopulation=100000000 batch=20 PosStartTime=990e-8 PosEndTime=1000e-8 ControlNum=100000 GeoMatTimeStep=10e-8 StochasticMode=2

This example defines the calculation parameters for calculating the survival probability of a dynamic system using the neutron bank tracking method. The calculation mode is POS, 100,000 neutron chains are simulated, and they are divided into 20 groups for simulation and statistics. The simulation time step size is 10 sh, the upper limit of the number of prompt neutrons in each neutron chain is 100,000,000, the start time of POS calculation is 990 sh, the end time is 1000 sh, the comb method threshold is 100,000 (the comb method is enabled when the number of particles exceeds this value, and the comb method is disabled when it is lower than this value), and the geometric material change time step is 10 sh.

  • Neutron Dynamic System Survival Probability (Single Neutron Tracking Method) Calculation Example
KINETICS
particle  FissionChain = 100000 TimeStep=10e-8  MaxPopulation=100000000 batch=20 PosStartTime=990e-8 PosEndTime=1000e-8 GeoMatTimeStep=10e-8 StochasticMode=3

This example defines the calculation parameters for calculating the survival probability of a dynamic system using the single neutron tracking method. The calculation mode is POS, 100,000 neutron chains are simulated, and they are divided into 20 groups for simulation and statistics. The simulation time step size is 10 sh, and the upper limit of the number of prompt neutrons in each neutron chain is 100,000,000. The start time of POS calculation is 990sh, the end time is 1000sh, and the time step of geometric material change is 10sh.

  • Neutron Pulse Initiation Time Calculation Example
KINETICS
Particle  StochasticMode=0 fissionchain=2  TimeStep=0.1  MaxPopulation=100000  lambda=200
          Nu=1  TerminateTime=300  TerminateFisRate=2.0e9  ExpFisRate=1e9
          TargetFisRate=2.7e11
TimeStep  Time=0 10  300  Step=0.1 0.5

This example defines the calculation parameters of the neutron pulse initiation time (all unset parameters are set to their default values). The calculation mode is pulse initiation time calculation. Two neutron chains are simulated with a time step of 0.1s. The maximum number of prompt neutrons for each neutron chain is 100,000. If it exceeds 100,000, the neutron pulse initiation is considered successful. The spontaneous fission source strength is 200 times/s. The average number of fission neutrons released by each spontaneous fission is 1. The cutoff time for each neutron chain simulation is 300s. If it exceeds 300s, the simulation of the neutron chain is terminated. The cutoff fission rate of each neutron chain is 2.0e9/s. If it exceeds this fission rate, the simulation of the neutron chain is automatically stopped. The fission reaction rate at which each neutron chain starts to grow exponentially is 1e9/s. If it exceeds this fission rate, the neutron chain is considered to have entered a significant exponential growth stage. The extrapolated target fission reaction rate during neutron chain simulation is 2.7e11/s. This example also defines a dynamic time step. At this time, the time step defined in the Particle card is invalid. Between 0 and 10s, the time step is 0.1s, and between 10s and 300s, the time step is 0.5s.

  • Example 1 of using the Direct Simulation Method for Neutron Dynamics Calculation
Kinetics
particle  StochasticMode=0 UseComb=1 ControlNum=1000 InitSourceNum=1000 PrecursorMode=1  CaptureMode=1
          SpontaFiss=0 FissMultiplicity=0  FissionChain =10  TimeStep=0.000001
          MaxPopulation=1e12 TerminateTime=0.00001

This example defines the calculation parameters of direct simulation neutron dynamics. The calculation mode is direct simulation neutron dynamics. The comb method is used. The number of particles controlled by the comb method is 1000, the number of initial source neutrons is 1000, the delayed neutron decay mode is forced decay, the radiation capture mode is latent capture, spontaneous fission is turned off, fission multiplicity is turned off, 10 neutron chains are simulated, which is equivalent to dividing them into 10 groups for simulation and statistics. The time step size during simulation is 0.000001s, the upper limit of the number of neutrons in each neutron chain is 1e12, and the simulation end time is set to 0.00001s.

  • Example 2 of using the Direct Simulation Method for Neutron Dynamics Calculation
Kinetics
particle  StochasticMode=0 UseComb=1 ControlNum=100 InitCriSrc=1 PrecursorMode=1  CaptureMode=0
          SpontaFiss=0 FissMultiplicity=0 FissionChain = 4 TimeStep=1e-7 MaxPopulation=1e12 TerminateTime=1e-6

Tally
CellTally 1 type = 1 cell = 1 time =0 1.0e-07 2.0e-07 3.0e-07 4.0e-07 5.0e-07 6.0e-07 7.0e-07 8.0e-07 9.0e-07 1.0e-06
CellTally 2 type = 2 cell = 1 time =0 1.0e-07 2.0e-07 3.0e-07 4.0e-07 5.0e-07 6.0e-07 7.0e-07 8.0e-07 9.0e-07 1.0e-06
CellTally 3 type = 3 cell = 1 time =0 1.0e-07 2.0e-07 3.0e-07 4.0e-07 5.0e-07 6.0e-07 7.0e-07 8.0e-07 9.0e-07 1.0e-06

This example defines the calculation parameters of direct simulation neutron dynamics. The calculation mode is the direct simulation method for neutron dynamics. The comb method is used. The number of particles controlled by the comb method is 100. The initial critical source distribution is adopted (a source file with the suffix “.KineticsInitSource” is required and to be placed in the same directory as the executable file). The delayed neutron decay mode is forced decay, the radiation capture mode is direct simulation absorption, spontaneous fission is turned off, fission multiplicity is turned off, and 4 neutron chains are simulated, which is equivalent to dividing into 4 groups for simulation and statistics. The time step size during simulation is 1e-7s, the upper limit of the number of neutrons in each neutron chain is 1e12, and the simulation termination time is set to 1e-6s. Three counters are set for flux, power, and fission reaction rate, and time binning is set.