Proton velocity ring‐driven instabilities and their dependence on the ring speed: Linear theory

Abstract

AbstractLinear dispersion theory is used to study the Alfvén‐cyclotron, mirror and ion Bernstein instabilities driven by a tenuous (1%) warm proton ring velocity distribution with a ring speed, vr, varying between 2vA and 10vA, where vA is the Alfvén speed. Relatively cool background protons and electrons are assumed. The modeled ring velocity distributions are unstable to both the Alfvén‐cyclotron and ion Bernstein instabilities whose maximum growth rates are roughly a linear function of the ring speed. The mirror mode, which has real frequency ωr=0, becomes the fastest growing mode for sufficiently large vr/vA. The mirror and Bernstein instabilities have maximum growth at propagation oblique to the background magnetic field and become more field‐aligned with an increasing ring speed. Considering its largest growth rate, the mirror mode, in addition to the Alfvén‐cyclotron mode, can cause pitch angle diffusion of the ring protons when the ring speed becomes sufficiently large. Moreover, because the parallel phase speed, v∥ph, becomes sufficiently small relative to vr, the low‐frequency Bernstein waves can also aid the pitch angle scattering of the ring protons for large vr. Potential implications of including these two instabilities at oblique propagation on heliospheric pickup ion dynamics are discussed.