Stochastic Acceleration of Electrons by Plasma Waves. III. Waves Propagating Perpendicular to the Magnetic Field

Open Access
Publisher Website
Google Scholar
Abstract
In this paper we consider the interaction of particles with turbulent plasma waves propagating perpendicular to the ordered magnetic field. Our investigation of the dispersion relation for waves propagating at an arbitrary angle θ with respect to the magnetic field lines indicates that the qualitative behavior of the acceleration characteristics at all angles θ≠0 are similar to that of the θ=π/2 case. We use the perpendicular case as a representative example because it leads to a much simpler analysis. Therefore, the results presented here and the results of our earlier papers dealing with the θ=0 case will give a somewhat complete picture of stochastic acceleration for all waves. Unlike the θ=0 case, where only the fundamental mode of each wave contributes, for general value of θ, and in particular for the perpendicular case, many harmonics enter into the equation, making the analysis more complicated. We develop a recipe for evaluation of the contributions of all harmonics and derive an analytic expression for the asymptotic behavior at nonrelativistic energies. We use the formalism of our previous papers and find that all Fokker-Planck coefficients for the perpendicular waves are of the same order of magnitude, so the ratio of the pitch angle to momentum (or energy) diffusion rates is of order unity at all energies and pitch angles. This is unlike the parallel case, where this ratio varies from being much less than 1 at low energies to much greater than 1 at relativistic energies. As a result, the simplifications of the transport equation arising from these inequalities are no longer applicable. On the other hand, we find that when the transport equation for the θ=π/2 case is expressed in terms of diffusion in the parallel and perpendicular components of the momentum, only diffusion in the perpendicular component is present. This again yields a one-dimensional diffusion equation and implies that the parallel momentum does not change. Consequently, we expect a rapid anisotropization of the pitch angle distribution (into a pancake-like distribution) for particles accelerated by perpendicular waves. From comparison of the acceleration rate of the thermal particles with the decay rate of the waves in hot plasmas, we find that a substantial fraction of the background plasma electrons can be accelerated through this process for reasonable values of the energy density and spectrum of turbulence.