Abstract
A nonlinear formulation of the displacement cascade is described using the Boltzmann equation with a stochastic collision kernel. For the special case of the very hard sphere model the resulting exact solution is used to assess the limitations of the linear theory for calculating sputtered atom spectra and yields. Significant differences are found in the two cases, amounting to factors of 2 in some energy regions. The extension of the method to more realistic kernels is outlined.