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

Linear dispersion theory is used to study the Alfven-cyclotron, mirror and ion Bernstein instabilities driven by a tenuous (1%) warm proton ring velocity distribution with a ring speed, v(r), varying between 2v(A) and 10v(A), where v(A) is the Alfven speed. Relatively cool background protons and electrons are assumed. The modeled ring velocity distributions are unstable to both the Alfven-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 omega(r)=0, becomes the fastest growing mode for sufficiently large v(r)/v(A). 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 Alfven-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(vertical bar ph), becomes sufficiently small relative to v(r), the low-frequency Bernstein waves can also aid the pitch angle scattering of the ring protons for large v(r). Potential implications of including these two instabilities at oblique propagation on heliospheric pickup ion dynamics are discussed.