Ion Bernstein instability dependence on the proton-to-electron mass ratio: Linear dispersion theory
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Fast 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, m(p)/m(e), and a reduced light-to-Alfven speed ratio, c/v(A), 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, = (r)+i, of the ion Bernstein modes varies with m(p)/m(e) for a sufficiently large c/v(A) (such that pe2</mml:msubsup>/e2</mml:msubsup>(me/mp)(c/vA)2 >> 1) 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 m(p)/m(e). For the low harmonic modes (i.e., (r)approximate to(p)), both (r)/(p) and /(p) are roughly independent of m(p)/m(e), where (p) is the proton cyclotron frequency. For the high harmonic modes (i.e., p<<<mml:msub>r less than or similar to<mml:msub>lh, where (lh) is the lower hybrid frequency), /(lh) (at fixed (r)/(lh)) stays independent of m(p)/m(e) when the parallel wave number, k(vertical bar), is sufficiently large and becomes inversely proportional to (m(p)/m(e))(1/4) when k(vertical bar) goes to zero. On the other hand, the frequency range of the unstable modes normalized to (lh) remains independent of m(p)/m(e), regardless of k(vertical bar).