Abstract
Abstract A model is presented for the transport of energetic charged particles in a medium whose density is a continuous random function of position. Using the straight-ahead continuous slowing down approximation and assuming Gaussian statistics for the density fluctuations, exact solutions for the ensemble-averaged flux and dose are obtained. It is demonstrated that the ensemble-averaged flux satisfies an exact closed equation of the Fokker-Planck type in energy. The effect of fluctuations is to introduce straggling in space and energy, resulting in the dose profile extending well beyond the ion range for a corresponding deterministic medium. Very reasonable results are obtained for a fluctuation amplitude on the order of the mean density, in spite of the negative densities admitted by the Gaussian process. However, for very large fluctuations, the Gaussian model leads to a considerable overestimate of the dose near the surface.
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