Monte-Carlo eigenvalue calculation

Abstract

A Monte Carlo algorithm to efficiently calculate static alpha eigenvalues, N = ne^αt, for supercritical systems has been developed and tested. A direct Monte Carlo approach to calculating a static alpha is to simply follow the buildup in time of neutrons in a supercritical system and evaluate the logarithmic derivative of the neutron population with respect to time. This procedure is expensive, and the solution is very noisy and almost useless for a system near critical. The modified approach is to convert the time-dependent problem to a static α-eigenvalue problem and regress a on solutions of a k-eigenvalue problem. In practice, this procedure is much more efficient than the direct calcuation, and produces much more accurate results. Because the Monte Carlo codes are intrinsically three-dimensional and use elaborate continuous-energy cross sections, this technique is now used as a standard for evaluating other calculational techniques in odd geometries or with group cross sections.

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