INSTABILITY OF ELECTROMAGNETIC R-MODE WAVES IN A RELATIVISTIC PLASMA

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 to tal plasma population. Numerical results are obtained for realistic pl asma parameters using three distinct distribution functions for the re lativistic electron population. Wave growth rates obtained by numerica l integration along the resonant relativistic ellipse are shown to be substantially smaller than calculations performed under the nonrelativ istic approximation. The relativistic corrections are primarily due to a reduction in the resonant electron anisotropy. Changes from the sta ndard nonrelativistic treatment are noticeable at relatively small ele ctron thermal energies (a few keV), and they become very significant f or thermal energies above 100 keV, especially in low density regions w here the plasma frequency is comparable to or lower than the electron gyrofrequency. The results have applications to wave instability in th e outer radiation belts of the Earth, the inner Jovian magnetosphere, and other space plasmas where relativistic electrons are present. (C) 1998 American Institute of Physics. [S1070-664X(98)01307-X]