Instability of electromagnetic R-mode waves in a relativistic plasma

Abstract

An explicit mathematical formalism is developed to evaluate the growth rate of field-aligned electromagnetic R-mode waves in a relativistic plasma. The methodology is valid for weak wave growth or damping when the resonant relativistic electrons comprise a small portion of the total plasma population. Numerical results are obtained for realistic plasma parameters using three distinct distribution functions for the relativistic electron population. Wave growth rates obtained by numerical integration along the resonant relativistic ellipse are shown to be substantially smaller than calculations performed under the nonrelativistic approximation. The relativistic corrections are primarily due to a reduction in the resonant electron anisotropy. Changes from the standard nonrelativistic treatment are noticeable at relatively small electron thermal energies (a few keV), and they become very significant for thermal energies above 100 keV, especially in low density regions where the plasma frequency is comparable to or lower than the electron gyrofrequency. The results have applications to wave instability in the outer radiation belts of the Earth, the inner Jovian magnetosphere, and other space plasmas where relativistic electrons are present.