Relativistic dispersion, the cyclotron maser instability, and auroral kilometric radiation
It is demonstrated that relativistic effects can significantly modify the wave dispersion in auroral kilometric radiation (AKR), even for only mildly relativistic electrons, when the ratio of the square of the electron plasma frequeny omega(pe) to the square of the electron cyclotron frequency Omega(e) is much less than one, which is frequently the case in the AKR source region. The k-parallel dispersion relation for waves in a relativistic Maxwellian plasma is considered for the case of omega(pe) much less than Omega(e). The results of Shkarovsky (1966) are used to evaluate the relativistic corrections to the R-X mode cutoff. The general relativistic dispersion tensor is applied to evaluate the dispersion relation for a delta function ring distribution in p-perpendicular, again assuming omega(pe) much less than Omega(e). The effect of finite velocity spread is studied by analyzing the Dory-Guest-Harris distribution in the semirelativistic approximation. The results of computer simulations for ring and shell distributions are presented.