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 exact description for this problem is taken as the linear transport equation with full six-dimensional phase space dependence. In the limit of very forward peaked scattering with small energy transfer, the Fokker-Planck scattering description is used. To obtain a simplified model of beam transport, we assume that the beam in question has weak spatial gradients in the plane perpendicular to the beam direction, and that the beam nearly maintains its collimated integrity as it passes through the material. These assumptions lead to a hierarchy of advection-diffusion-like approximations for the spatial distribution of the particle density per unit energy. In the simple case of monoenergetic transport in a purely scattering homogeneous material, these equations are easily solved via Laplace and Fourier transformations to obtain explicit analytical results. Comparisons with benchmark Monte Carlo calculations give an indication of the accuracy of this treatment of beam spreading.