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 Earthʹs magnetosphere. This work is an extension of our previous study in which we considered the case α > 1 , where α = | Ω e | 2 / ω pe 2 , 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 ∼ 10 keV 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 ∼ 1 keV to ∼ MeV by each of the superluminous wave modes can occur for higher harmonic resonances over a wide range of wave normal angles.