TRANSVERSE DIFFUSION OF A COLLIMATED PARTICLE-BEAM

We consider the problem of describing the steady-state spreading of a collimated particle beam as it penetrates a background material. The e xact description for this problem is taken as the linear transport equ ation with full six-dimensional phase space dependence. In the limit o f very forward peaked scattering with small energy transfer, the Fokke r-Planck scattering description is used. To obtain a simplified model of beam transport, we assume that the beam in question has weak spatia l gradients in the plane perpendicular to the beam direction, and that the beam nearly maintains its collimated integrity as it passes throu gh the material. These assumptions lead to a hierarchy of advection-di ffusion-like approximations for the spatial distribution of the partic le density per unit energy. In the simple case of monoenergetic transp ort in a purely scattering homogeneous material, these equations are e asily solved via Laplace and Fourier transformations to obtain explici t analytical results. Comparisons with benchmark Monte Carlo calculati ons give an indication of the accuracy of this treatment of beam sprea ding.