A KINETIC-THEORY FOR NONANALOG MONTE-CARLO PARTICLE-TRANSPORT ALGORITHMS - EXPONENTIAL TRANSFORM WITH ANGULAR BIASING IN PLANAR-GEOMETRY ANISOTROPICALLY SCATTERING MEDIA

We show that Monte Carlo simulations of neutral particle transport in planar-geometry anisotropically scattering media, using the exponentia l transform with angular biasing as a Variance reduction device, are g overned by a new ''Boltzmann Monte Carlo'' (BMC) equation, which inclu des particle weight as an extra independent variable, The weight momen ts of the solution of the BMC equation determine the moments of the sc ore and the mean number of collisions per history in the nonanalog Mon te Carlo simulations. Therefore, the solution of the BMC equation pred icts the variance of the score and the figure of merit In the simulati on. Also, by (i) using an angular biasing function that is closely rel ated to the ''asymptotic'' solution of the linear Boltzmann equation a nd (ii) requiring isotropic weight changes at collisions, we derive a new angular biasing scheme. Using the BMC equation, we propose a unive rsal ''safe'' upper Limit of the transform parameter, valid fur any ty pe of exponential transform. In numerical calculations, we demonstrate that the behavior of the Monte Carlo simulations and the performance predicted by deterministically solving the BMC equation agree well, an d that the new angular biasing scheme is always advantageous. (C) 1998 Academic Press.