A new importance biasing scheme for deep-penetration Monte Carlo

• Published in: Annals of nuclear energy Vol. 9; no. 7; pp. 359 - 368
• Main Author: Dwivedi, S.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1982
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/0306-4549(82)90038-X

For neutron- or radiation-transport problems the transport kernel consists of two parts, viz. the space-transition part and the collision part. Importance biasing of the space-transition part is referred to as the exponential biasing scheme. An ideal biasing scheme should, in principle, be used for both factors of the transport kernel to obtain zero variance. By using analytical expression for the importance function, the biasing schemes were derived for both these factors, for a simple 1-D, one-energy group deep-penetration problem. The angular biasing scheme, thus obtained, is new and very simple to implement in Monte Carlo codes. Only one parameter is required for biasing both factors of the transport kernel, which can be analytically evaluated for homogeneous slabs. For heterogeneous slabs, the biasing parameter is obtained by a homogenization procedure. Monte Carlo calculations were performed for 20-mean-free-path thick slabs with different Σ s Σ t values using this scheme. It was observed that the variance could be reduced by approx. two orders of magnitude over the well-known exponential biasing scheme.