Higher-order gyroresonant acceleration of electrons by superluminous (AKR) wave-modes

We consider gyroresonant acceleration of electrons by the superluminous (R-X, L-O, L-X) wave modes that are generated as AKR in the Earth's magnetosphere. This work is an extension of our previous study in which we considered the case α>1, where α=|Ωe|2/ωpe2, with the restriction that the cyclotron harmonic N=1. Here, we consider both regimes α>1 and α⩽1, and allow higher-order harmonics N>1. For the case α>1, we find that (a) the R-X mode can accelerate electrons more effectively at higher harmonics in that acceleration to higher energies (∼MeV) is not limited to small wave angles, as is the case for N=1, (b) the L-O mode can produce significant acceleration of electrons from ∼10keV to ∼MeV energies at higher harmonics over a broad range of magnetosphere and wave normal angles, as is the case for N=1, (c) the L-X mode is less effective for electron acceleration at higher harmonics, with typical minimum resonant energies (∼MeV) being higher than those for N=1. For the case α⩽1, we find that electron gyroresonance with the superluminous wave modes can only occur at the higher harmonics, e.g., typically N⩾4 for the R-X mode, and N⩾3 for L-O and L-X modes. Significant acceleration of electrons from ∼1keV to ∼MeV by each of the superluminous wave modes can occur for higher harmonic resonances over a wide range of wave normal angles.