Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

The general equations describing the quasi-linear diffusion of charged particles from resonant interactions with a spectrum of electrostatic waves are given, assuming the wave and particle distributions to be azimuthally symmetric. Such diffusion is, in general, two-dimensional and is similar to magnetized diffusion. The connection between the two types of diffusion is presented. In order to apply the general quasi-linear diffusion coefficients in pitch angle and speed, a specific particle-distribution model is assumed. An expression for the unmagnetized dielectric function is derived and evaluated for the assumed particle distribution model. It is found that slow-mode ion-sound waves are unstable for the range of plasma parameters considered. A qualitative interpretation of unmagnetized diffusion is presented. The diffusion coefficients are then evaluated for resonant ion interactions with ion-sound waves. The results illustrate how resonant ion diffusion rates vary with pitch angle and speed, and how the diffusion rates depend upon the distribution of wave energy in k-space. The results of this study have relevance for ion beam heating in the plasma-sheet boundary layer and upstream of the earth's bow shock. (author)