On the Markov Chain Analysis of Source Iteration Monte Carlo Procedures for Criticality Problems: I

Monte Carlo techniques for the calculation of the effective multiplication factor K_eff of a nuclear reactor are discussed. A source iteration procedure based on a fixed number of fission points per generation is rigorously analyzed in the framework of the Markov chain corresponding to that procedure. It is shown that the estimated eigenvalue converges asymptotically to the correct eigenvalue of the transport equation and the bias in K_eff is bounded by an expression of the form C·N^1/2, where N is the number of fission points in each generation and C is a constant depending on the bulk properties of the reactor.