17. Criticality Search (Enterprise Version Only)¶
RMC supports criticality search in both criticality and burnup modes, including searches for nuclide density in materials and surface position in geometry, where material nuclide density search is based on material density perturbation.
17.1. Material Search Module Input Card¶
CriticalitySearch
Materialsearch target=<param> error=<param> max=<maximum> perb=<differentialoperator id>
Differentialoperator <id> [cell=<cell_vector>] [material=<mat id>] [nuclide=<nuc>] [variable=<param>]
[estimator=<param>] [sourceperb=<param>] [batchcycle=<param>] [outputbycycle=<param>]
[crosssection=<param>] [response=<param>]
Where:
- CriticalitySearch is the keyword for the criticality search module.
- materialsearch is material search input card. Since this is a single-parameter search, this card can be used only once.
- target is the target value of Keff for the search.
- error is the search threshold. The search is considered complete when target-error < keff+-keff_std < target+error.
- max is the maximum number of search iterations. After a criticality calculation is completed, the program will perform parameter search calculations. The parameters obtained from the search will then be used for another criticality calculation, followed by another round of parameter search, and so on, until convergence criteria are met. This parameter is set to prevent the program from falling into an infinite loop in extreme cases where it fails to converge. It should be noted that the tally counting will be turned off until the parameters meet the convergence criteria. If the user has enabled the tally function, the tally will be re-enabled and another criticality calculation (active generations only) will be performed after the parameters converge. Therefore, if max = 1 and tally is not enabled, the calculation process will be: criticality calculation → parameter search → criticality calculation. If max = 1 and tally is enabled, the process will be: criticality calculation → parameter search → criticality calculation → active generation criticality calculation. Notably, if max = 0 is specified, the program will only perform one criticality calculation and one search, with no tally counting.
- perb is the ID of the differential operator method used for the search, corresponding to the differentialoperator input card. Note that the corresponding differentialoperator must match, and the variable in the input card must be set to 1.
- differentialoperator is the differential operator input card, the usage of which can be found in the material perturbation module instructions.
17.2. Material Search Module Input Example¶
The following example demonstrates a search on the density of nuclide ZAID 92235 in material 1 of cell 3, with a target value of 1.23, a threshold of 0.02, a maximum of 5 iterations, using a collision estimator for the differential operator method, and including source perturbation. The batch cycle is set to 5, and only the last cycle outputs.
CRITICALITYSEARCH
Materialsearch target=1.23 error=0.02 max=5 perb=1
DifferentialOperator 1 cell = 3
material = 1
nuclide = 92235
variable = 1
estimator = 0
order = 2
sourceperb = 1
batchcycle = 5
outputbycycle = 0
response = 1
17.3. Material Search Output File¶
The material search information is stored in the .critisearch file, which contains the first- and second-order perturbation coefficients for various differential operator methods, along with their relative standard deviations. During criticality iteration, the current keff and its standard deviation are provided, along with the atomic density of the searched nuclide before and after iteration, separated by an arrow (–>). For the first- and second-order perturbation coefficients for various differential operator methods, users can directly check the .Result.h5 file.
Cycle Perb First_Ave First_Re Second_Ave Second_Re
50 1 2.49773E-02 4.85185E+00 -4.22016E-02 8.69707E+00
Iter Nuc keff Atom Density Gram Density
0 92235.71c 1.218068 +- 0.012354 9.10578E-04 --> 1.34558E-03 -3.55398E-01 --> -5.25179E-01
Cycle Perb First_Ave First_Re Second_Ave Second_Re
50 1 2.73379E-01 5.61727E-01 -8.78828E-01 6.68638E-01
Iter Nuc keff Atom Density Gram Density
1 92235.71c 1.301338 +- 0.014911 1.34558E-03 --> 9.94452E-04 -5.25179E-01 --> -3.88134E-01
Cycle Perb First_Ave First_Re Second_Ave Second_Re
50 1 1.66851E-01 4.64208E-01 -4.77677E-01 6.47156E-01
Iter Nuc keff Atom Density Gram Density
2 92235.71c 1.253746 +- 0.011225 9.94452E-04 --> 8.52920E-04 -3.88134E-01 --> -3.32894E-01
Cycle Perb First_Ave First_Re Second_Ave Second_Re
50 1 1.80428E-01 4.79098E-01 -2.63040E-01 1.30613E+00
Iter Nuc keff Atom Density Gram Density
3 92235.71c 1.196194 +- 0.011493 8.52920E-04 --> 1.01273E-03 -3.32894E-01 --> -3.95267E-01
Cycle Perb First_Ave First_Re Second_Ave Second_Re
50 1 1.35776E-01 1.13751E+00 -5.65172E-01 4.01294E-01
Iter Nuc keff Atom Density Gram Density
4 92235.71c 1.275107 +- 0.012141 1.01273E-03 --> 6.76280E-04 -3.95267E-01 --> -2.63952E-01
Cycle Perb First_Ave First_Re Second_Ave Second_Re
50 1 2.11684E-01 2.94337E-01 -3.85332E-01 6.42138E-01
17.4. Geometry Search Module Input Card¶
CriticalitySearch
Geometrysearch surface=<surf id> target=<param> error=<param> max=<maximum> method=<param> adaptive=<param>
leftbound=<param> rightbound=<param> adjointtally=<param>
where,
- CriticalitySearch is the keyword for the criticality search module.
- geometrysearch is the input card for geometry search. Since it is a single-parameter search, this card can only be used once.
- surface is the identifier for the search surface.
- target is the target keff value for the search.
- error is the threshold for the search. The search is considered complete when target-error < keff±keff_std < target+error.
- max is the maximum number of iterations, used to prevent an infinite loop in extreme cases where convergence cannot be achieved.
- method is the numerical iteration method for the search. 0 is Newton’s method using geometric perturbation coefficients calculated by the mesh. 1 is the bisection method. 2 is the false position method. 3 is Ridder’s method.
- adaptive is whether to adaptively adjust the number of active generations. 0 is to not use adaptive adjustment. 1 is to use adaptive adjustment.
- leftbound is the initial left boundary for the search surface position. The search will stop if it goes below this value.
- rightbound is the initial right boundary for the search surface position. The search will stop if it exceeds this value. The target value should be estimated to lie between the left and right boundaries.
- adjointtally is the tally number corresponding to the geometric perturbation coefficient used in Newton’s method, calculated by the iterated fission probability method.
17.5. Geometry Search Module Input and Output Example¶
The results of the geometry search are in the .critisearch file, including keff and standard deviation for each iteration. The “Parameter” is the search surface position for the next iteration, and “Cycle” is the total number of cycles used in the current iteration.
In the following example, the position of surface 1 is searched between 5 cm and 10 cm, with a target keff between 0.99 and 1.01, using the Ridder method with adaptive cycle adjustment. The final surface position is 8.74888 cm, and keff is 1.001257 ± 0.001635.
Geometrysearch
surface=1
target=1
error=0.01
method=3
adaptive=1
leftbound=5
right=10
Final Keff: 1.001257 Standard Deviation: 0.001635
Iter SurfId keff Parameter Cycle
0 1 0.602600 +- 0.000280 1.00000E+01 300
Iter SurfId keff Parameter Cycle
1 1 1.115286 +- 0.000489 7.50000E+00 300
Iter SurfId keff Parameter Cycle
2 1 0.876570 +- 0.001635 8.74888E+00 110