Charged-Particle Resonance Conditions and Transport Coefficients in Slab-Mode Waves

Abstract

Transport of charged particles in cold plasma is considered. The full dispersion relation for slab-mode waves is employed, and the quasi-linear particle scattering is discussed. Previous results of the dispersive-wave model on the ion mean free path are recalled and further developed. For small cross-helicities, the model predicts ion mean free paths that are not affected by the steepening of the turbulence spectrum at high wavenumbers, if the dissipation-range spectral index is q<6. Large cross-helicities, |H_c|~1, of the left-hand polarized waves, however, imply an approximately constant mean free path of the nonrelativistic protons, which may account for the long-standing flatness problem of the mean free path of solar flare particles. The mean free path in a mixture of slab-mode and isotropic fast-mode waves is also shown to agree with observations only in the case of |H_c|~1, contradicting a previously published result. Finally, it is shown that, owing to an interplay of resonances with whistlers and proton-cyclotron waves, electron bulk speeds can be considerably larger than the Alfvén speed. This implies limitations on diffusive acceleration of electrons at low Mach number shocks below ultrarelativistic energies.