ION-CYCLOTRON MODES IN WEAKLY RELATIVISTIC PLASMAS

We derive a dispersion relation for the perpendicular propagation of i on-cyclotron waves around the ion gyrofrequency OMEGA+, in a weakly re lativistic, anisotropic Maxwellian plasma. These waves, with wavelengt h greater than the ion Larmor radius r(L+) (k(perpendicular-to) r(L+) < 1), propagate in a plasma characterized by large ion plasma frequenc ies (omega(p+)2 much greater than OMEGA+2). Using an ordering paramete r epsilon, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensiti vely on them. The solutions of the former dispersion relation yield tw o 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 yiel ds a new LF mode in addition to the modes supported by the non-relativ istic dispersion relation. The two LF modes can coalesce to make the p lasma unstable. These results are also verified numerically using a st andard root solver.