Relativistic diffusion coefficients for superluminous (auroral kilometric radiation) wave modes in space plasmas

We have constructed expressions of the relativistic diffusion coefficients in both pitch angle and momentum resulting from gyroresonant interactions between electrons and superluminous (R-X, L-O, L-X) wave modes that are generated as auroral kilometric radiation (AKR) in the Earth's magnetosphere. Detailed analysis is made of wave resonant frequencies for each given harmonic n, electron energy, wave normal angles for two typical regions of the magnetosphere: the higher-density region eta=vertical bar Omega(e)vertical bar(2)/omega(2)(pe)<1 (e.g., near the geostationary orbit) and the lower-density region eta>1 (e.g., at the high latitude of the radiation belts), where vertical bar Omega(e)vertical bar and omega(pe) are the electron gyrofrequency and the plasma frequency. The resonant frequency range in the higher-density region is found to be generally smaller than that in the lower-density region, and the efficient electron gyroresonance with the superluminous wave modes occurs mainly at the higher harmonics, e.g., vertical bar n vertical bar >= 3. In contrast to the subluminous waves, e.g., chorus which has easily up to three resonant frequencies, only one or two resonant frequencies were found for superluminous waves at each combination of wave and particle parameters of interest. Numerical calculations for diffusion coefficients of the momentum D-pp, the pitch angle D-alpha alpha, and the mixed D-p alpha are performed specifically for the two typical regions above. It is found that the momentum diffusion generally dominates over the pitch angle diffusion, namely, D-pp>vertical bar D-p alpha vertical bar>D-alpha alpha for the pitch angle a above a critical angle alpha(c), whereas D-alpha alpha generally dominates below the critical angle alpha(c). Specifically, D-pp/D-alpha alpha can exceed 10 for alpha>alpha(c)approximate to 7.5 degrees and eta=0.2, while for alpha>alpha(c)approximate to 30 degrees and eta=20. This is a new result in contrast to the case of subluminous waves (e.g., whistler mode waves) in which basically D-alpha alpha>vertical bar D-p alpha vertical bar>D-pp. We have also presented some estimates regarding what wave amplitudes are required to produce particular acceleration timescales and found that the required wave amplitudes in the lower-density region are much lower than those in the higher-density region. The results suggest that superluminous wave modes may contribute significantly to both the stochastic acceleration of trapped electrons (with larger pitch angle) and the loss process of untrapped electrons (with smaller pitch angles) during magnetic storms if those waves are found to be present in the radiation belts of the Earth, but this needs to be further investigated.