Fission Matrix Capability for MCNP Monte Carlo
- Los Alamos National Laboratory
In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poor neutron communication between regions are also slow to converge. The fission matrix method, implemented into MCNP[1], addresses these problems. When Monte Carlo random walk from a source is executed, the fission kernel is stochastically applied to the source. Random numbers are used for: distances to collision, reaction types, scattering physics, fission reactions, etc. This method is used because the fission kernel is a complex, 7-dimensional operator that is not explicitly known. Deterministic methods use approximations/discretization in energy, space, and direction to the kernel. Consequently, they are faster. Monte Carlo directly simulates the physics, which necessitates the use of random sampling. Because of this statistical noise, common convergence acceleration methods used in deterministic methods do not work. In the fission matrix method, we are using the random walk information not only to build the next-iteration fission source, but also a spatially-averaged fission kernel. Just like in deterministic methods, this involves approximation and discretization. The approximation is the tallying of the spatially-discretized fission kernel with an incorrect fission source. We address this by making the spatial mesh fine enough that this error is negligible. As a consequence of discretization we get a spatially low-order kernel, the fundamental eigenvector of which should converge faster than that of continuous kernel. We can then redistribute the fission bank to match the fundamental fission matrix eigenvector, effectively eliminating all higher modes. For all computations here biasing is not used, with the intention of comparing the unaltered, conventional Monte Carlo process with the fission matrix results. The source convergence of standard Monte Carlo criticality calculations are, to some extent, always subject to the characteristics of the problem. This method seeks to partially eliminate this problem-dependence by directly calculating the spatial coupling. The primary cost of this, which has prevented widespread use since its inception [2,3,4], is the extra storage required. To account for the coupling of all N spatial regions to every other region requires storing N{sup 2} values. For realistic problems, where a fine resolution is required for the suppression of discretization error, the storage becomes inordinate. Two factors lead to a renewed interest here: the larger memory available on modern computers and the development of a better storage scheme based on physical intuition. When the distance between source and fission events is short compared with the size of the entire system, saving memory by accounting for only local coupling introduces little extra error. We can gain other information from directly tallying the fission kernel: higher eigenmodes and eigenvalues. Conventional Monte Carlo cannot calculate this data - here we have a way to get new information for multiplying systems. In Ref. [5], higher mode eigenfunctions are analyzed for a three-region 1-dimensional problem and 2-dimensional homogenous problem. We analyze higher modes for more realistic problems. There is also the question of practical use of this information; here we examine a way of using eigenmode information to address the negative confidence interval bias due to inter-cycle correlation. We apply this method mainly to four problems: 2D pressurized water reactor (PWR) [6], 3D Kord Smith Challenge [7], OECD - Nuclear Energy Agency (NEA) source convergence benchmark fuel storage vault [8], and Advanced Test Reactor (ATR) [9]. We see excellent source convergence acceleration for the most difficult problems: the 3D Kord Smith Challenge and fuel storage vault. Additionally, we examine higher eigenmode results for all these problems. Using part of the eigenvalue spectrum for a one-group 1D problem, we find confidence interval correction factors that are improvements over existing corrections [10].
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- DOE/LANL
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1050495
- Report Number(s):
- LA-UR-12-24533; TRN: US1204707
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
22 GENERAL STUDIES OF NUCLEAR REACTORS
97 MATHEMATICAL METHODS AND COMPUTING
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ABSORPTION
ACCELERATION
ALGEBRA
APPROXIMATIONS
BENCHMARKS
COMMUNICATIONS
COMPUTERS
CONVERGENCE
CRITICALITY
EIGENFUNCTIONS
EIGENVALUES
EIGENVECTORS
FISSION
KERNELS
MULTIPLICATION FACTORS
NEA
NEUTRONS
OECD
PHYSICS
PWR TYPE REACTORS
RESOLUTION
SAMPLING
SCATTERING
STORAGE
TEST REACTORS