The effect of a velocity-dependent charge-exchange kernel on neutral-atom transport in a half-space plasma: exact solution

A symmetric factorization of the velocity-dependent charge-exchange kernel (the so-called separable-kernel model) is used in the Boltzmann equation for neutral atoms to obtain an exact solution for a half-space plasma by the Wiener-Hopf method. This work generalizes earlier work employing constant, velocity-independent charge-exchange interactions to the case of an arbitrary velocity dependence of the Maxwellian averaged charge-exchange reaction rate. The effects of velocity dependence on the speed-angle distribution of escaping neutrals and the total charge-exchange rate in the half-space are shown to be significant. It is also shown how the Wiener-Hopf method can be applied to such problems with a realistic Maxwellian plasma background, without first approximating the ion distribution.