# Fast magnetosonic waves driven by shell velocity distributions

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Using linear dispersion theory and particle-in-cell simulations, we explore the ion Bernstein instability driven by the shell-type ion velocity distribution which is related to the excitation of fast magnetosonic waves in the terrestrial magnetosphere. We first demonstrate a novel idea to construct the shell velocity distribution out of multiple Maxwellian ring-beam velocity distributions. Applying this technique, we find that the convergence of the linear theory instability can be achieved with only a moderate number of ring-beam components. In order to prove that such an approximation is legitimate and the linear theory instabilities evaluated are indeed valid, we use the exact shell distribution to carry out a number of one dimensional particle-in-cell simulations corresponding to multiple wave propagation angles adjacent to the direction at which the most unstable waves are expected to grow. The agreement between the linear dispersion analysis and the simulation results is generally very good: enhanced waves are organized along the linear theory dispersion curves in the frequency-wave number space, and relative wave amplitudes are ordered as the linear theory growth rates very well. However, the simulations show a few extra branches that are not expected from the linear dispersion analysis. A close examination of these extra branches suggests that they are not simulation artifacts and particularly related to the ring/shell-type distributions with large ring/shell speed (v>approximate to 1.5 v(A), where v(A) is the Alfven speed). In addition, our results show that substantial wave growth can occur at nonintegral harmonics of the proton cyclotron frequency at wave normal angles substantially far away from the perpendicular direction, which may provide an alternative explanation of the off-harmonic peaks of some fast magnetosonic waves observed in space.