Ion Bernstein instability dependence on the proton‐to‐electron mass ratio: Linear dispersion theory

Abstract

AbstractFast magnetosonic waves, which have as their source ion Bernstein instabilities driven by tenuous ring‐like proton velocity distributions, are frequently observed in the inner magnetosphere. One major difficulty in the simulation of these waves is that they are excited in a wide frequency range with discrete harmonic nature and require time‐consuming computations. To overcome this difficulty, recent simulation studies assumed a reduced proton‐to‐electron mass ratio, mp/me, and a reduced light‐to‐Alfvén speed ratio, c/vA, to reduce the number of unstable modes and, therefore, computational costs. Although these studies argued that the physics of wave‐particle interactions would essentially remain the same, detailed investigation of the effect of this reduced system on the excited waves has not been done. In this study, we investigate how the complex frequency, ω = ωr+iγ, of the ion Bernstein modes varies with mp/me for a sufficiently large c/vA (such that ) using linear dispersion theory assuming two different types of energetic proton velocity distributions, namely, ring and shell. The results show that low‐ and high‐frequency harmonic modes respond differently to the change of mp/me. For the low harmonic modes (i.e., ωr∼Ωp), both ωr/Ωp and γ/Ωp are roughly independent of mp/me, where Ωp is the proton cyclotron frequency. For the high harmonic modes (i.e., , where ωlh is the lower hybrid frequency), γ/ωlh (at fixed ωr/ωlh) stays independent of mp/me when the parallel wave number, k∥, is sufficiently large and becomes inversely proportional to (mp/me)1/4 when k∥ goes to zero. On the other hand, the frequency range of the unstable modes normalized to ωlh remains independent of mp/me, regardless of k∥.