An analytical solution for the distribution of neutral particles in a Maxwellian plasma using the method of singular eigenfunctions

The method of singular eigenfunctions is used to obtain a solution to the problem of penetration of neutrals into a dense plasma with a realistic Maxwellian ion distribution. A general solution is obtained and explicit results given for models of the reflection processes at the wall. These include the neutral density distribution, the emergent neutral velocity distribution and the neutral particle and energy fluxes to the wall. The analytic results indicate the validity of the diffusion approximation and provide a boundary condition for such a treatment. (author)