# Scalings of Alfven-cyclotron and ion Bernstein instabilities on temperature anisotropy of a ring-like velocity distribution in the inner magnetosphere

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A ring-like proton velocity distribution with f(p)(v)/v>0 and which is sufficiently anisotropic can excite two distinct types of growing modes in the inner magnetosphere: ion Bernstein instabilities with multiple ion cyclotron harmonics and quasi-perpendicular propagation and an Alfven-cyclotron instability at frequencies below the proton cyclotron frequency and quasi-parallel propagation. Recent particle-in-cell simulations have demonstrated that even if the maximum linear growth rate of the latter instability is smaller than the corresponding growth of the former instability, the saturation levels of the fluctuating magnetic fields can be greater for the Alfven-cyclotron instability than for the ion Bernstein instabilities. In this study, linear dispersion theory and two-dimensional particle-in-cell simulations are used to examine scalings of the linear growth rate and saturation level of the two types of growing modes as functions of the temperature anisotropy T/T-parallel to for a general ring-like proton distribution with a fixed ring speed of 2v(A), where v(A) is the Alfven speed. For the proton distribution parameters chosen, the maximum linear theory growth rate of the Alfven-cyclotron waves is smaller than that of the fastest-growing Bernstein mode for the wide range of anisotropies (1T/T-parallel to <= 7) considered here. Yet the corresponding particle-in-cell simulations yield a higher saturation level of the fluctuating magnetic fields for the Alfven-cyclotron instability than for the Bernstein modes as long as T perpendicular to/T-parallel to greater than or similar to. Since fast magnetosonic waves with ion Bernstein instability properties observed in the magnetosphere are often not accompanied by electromagnetic ion cyclotron waves, the results of the present study indicate that the ring-like proton distributions responsible for the excitation of these fast magnetosonic waves should not be very anisotropic.