Charged-particle resonance conditions and transport coefficients in slab-mode waves

Transport of charged particles in cold plasma is considered. The full dispe rsion relation for slab-mode waves is employed, and the quasi-linear partic le scattering is discussed. Previous results of the dispersive-wave model o n the ion mean free path are recalled and further developed. For small cros s-helicities, the model predicts ion mean free paths that are not affected by the steepening of the turbulence spectrum at high wavenumbers, if the di ssipation-range spectral index is q < 6. Large cross-helicities, /H-c/ <sim ilar to> 1, of the left-hand polarized waves, however, imply an approximate ly constant mean free path of the nonrelativistic protons, which may accoun t for the long-standing flatness problem of the mean free path of solar fla re particles. The mean free path in a mixture of slab-mode and isotropic fa st-mode waves is also shown to agree with observations only in the case of /H-c/ similar to 1, contradicting a previously published result. Finally, i t is shown that, owing to an interplay of resonances with whistlers and pro ton-cyclotron waves, electron bulk speeds can be considerably larger than t he Alfven speed. This implies limitations on diffusive acceleration of elec trons at low Mach number shocks below ultrarelativistic energies.