Ion cyclotron harmonic wave generation by ring protons in space plasmas

Abstract

Spacecraft such as the Active Magnetospheric Particle Tracer Explorers, Giotto and the Combined Release and Radiation Effects Spacecraft have shown that suprathermal protons with ringlike or shell‐like distributions in velocity space exist in many space plasmas. Examples include the radiation belts, the auroral zones, the bow shock, and the solar wind. Ring proton distributions may excite obliquely propagating fast Alfvén waves at harmonics of the ion cyclotron frequency. In this paper we carry out an analytical study of this instability, restricting our attention to strictly perpendicular propagation. In the case of a monoenergetic proton ring in a cold plasma, we show that cyclotron harmonics can have a higher growth rate than parallel‐propagating ion cyclotron waves, depending on the ratio of the proton ring speed to the Alfvén speed. Analytical stability boundaries in parameter space are determined, indicating that the threshold for the growth of cyclotron harmonics depends critically on the ion plasma beta, βi. If βi ≪1, for example in the radiation belts or the auroral zones, the concentration of ring protons required for instability is very low. If, on the other hand, βi ∼ 1, for example in the bow shock or the solar wind, instability will only occur if the ring protons constitute a large fraction of the total ion density. In the bow shock case, the required concentrations may indeed occur. Growth rates are also calculated for the case of a ring proton distribution with a Gaussian spread of velocities, and it is shown that the instability persists even if the velocity dispersion is comparable to the ring speed itself. Our analysis is consistent with the observed excitation of perpendicular‐propagating ion cyclotron harmonics in the vicinity of the Earth's plasmapause.