Theories of relativistic ion cyclotron instabilities

A perturbation theory and a kinetic theory are developed to investigate the novel physics of relativistic ion cyclotron instabilities. The existence o f the instabilities is determined by the normalized mass deficits per nucle on of fast and slow ions (delta m(f) and delta m(s), respectively), and by their Lorentz factors (gamma(f) and gamma(s), respectively); while the ion bunching is caused by the relativistic variation of ion mass. If delta m(f) - delta m(s) - gamma(f) + gamma(s) > 0, only a quadratic instability can o ccur at high cyclotron harmonics of the fast ion in the lower-hybrid freque ncy regime and above; the threshold on the harmonic number is determined by the dielectric constant of the slow ion. The peak growth rate is higher at the harmonics just above the threshold. If it is negative, both a cubic in stability (or instead a coupled quadratic instability if the resonant slow ion cyclotron harmonic is the first harmonic) and the high harmonic quadrat ic instability can be driven. The cubic instability is due to the harmonic interaction of fast and slow ion cyclotron motions with the wave frequency in between. This introduces a novel instability concept, namely, a two-stre aming process in gyrospace. Thus, the cubic instability is also called a tw o-gyro-stream instability even without beams in real space in contrast to c onventional two-stream instability. Both theories show that, as compared to the conventional axial phase bunching mechanism, the importance of the inc lusion of the relativistic mass variation effect (and the gyro-bunching mec hanism) depends on the phase velocity of the wave along the external magnet ic field, and is not related to the Lorentz factors (or kinetic energies); that is, if omega/k(z) > c (e.g., k(z) = 0), the relativistic gyro-bunching mechanism always dominates. While the importance of this study in fundamen tal plasma physics is emphasized here, some issues (e.g., nonlinear saturat ion, wave polarization, and nonuniform magnetic field) related to its appli cation are also discussed. (C) 2000 American Institute of Physics. [S1070-6 64X(00)05502-6].