Transport in random media with space-time noise

Abstract

Transport of particles in media whose cross sections are random functions of space and time is considered. The linear transport equation, in the presence of this space-time noise, is viewed as a Boltzmann-Langevin equation, the solution of which generates a stochastic process, the angular flux, for different realizations of the cross section. A Gaussian model of fluctuations is adopted with a prescribed mean, variance and correlation function. For white noise in time, but with otherwise arbitrary spatial correlation, an exactly closed equation for the ensemble averaged angular flux is obtained and seen to be identical to the transport equation but with renormalised cross sections. Similar exact closures are demonstrated for the second moment and the two-point space-angle correlation of the angular flux. Standard methods may be adapted to solve these averaged transport equations which are valid in the small correlation time limit.