Stochastic gyroresonant electron acceleration in a low-beta plasma. I - Interaction with parallel transverse cold plasma waves

The gyroresonance of electrons with parallel transverse cold plasma waves is considered, and the Fokker-Planck equation describing the evolution of the electron distribution function in the presence of a spectrum of turbulence is derived. A new resonance which produces a divergence in the Fokker-Planck coefficients is identified; it results when the electron is in gyroresonance with a wave that has a group velocity equal to the velocity of the electron along the magnetic field. Under the assumption of a power-law spectral density, the Fokker-Planck coefficients are calculated numerically, and their complicated momentum and pitch-angle dependence, as well as the influence of various approximations to the dispersion relation, gyroresonance condition, and spectral density are discussed. It is found that there is no resonance gap at any pitch angle as long as the full gyroresonance condition is used and waves propagating on both directions are present.