ION-CYCLOTRON MODES IN WEAKLY RELATIVISTIC PLASMAS

We derive a dispersion relation for the perpendicular propagation of ion-cyclotron waves around the ion gyrofrequency OMEGA+, in a weakly relativistic, anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius r(L+) (k(perpendicular-to) r(L+) < 1), propagate in a plasma characterized by large ion plasma frequencies (omega(p+)2 much greater than OMEGA+2). Using an ordering parameter epsilon, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency omega < OMEGA+ and a high-frequency (HF) mode with omega > OMEGA+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.