Acceleration and heating in quasi-linear diffusion

Quasi-linear diffusion of charged particles due to a stationary and homogeneous spectrum of electrostatic field fluctuations is investigated via a Fokker-Planck approach. The energy of a given distribution of test particles is found to be conserved whenever the wave spectrum is isotropic and none of the spectral components of the field has a phase speed that equals the speed of any test particle. Quite generally, the energy is monotonically increasing for isotropic spectra. An interesting quantum mechanical interpretation of these results is given, and the special case of beam evolution in an isotropic spectrum of non-dispersive waves is studied in some detail. Conditions for isotropization of directed electron and ion beams from Coulomb collisions and collective oscillations are discussed in the context of the quasi-linear description. Some promising results from a beam-plasma experiment are quoted.