Effects of Background Heavy Ions on Fast Magnetosonic Waves Excited by Proton-shell Velocity Distributions

Fast Magnetosonic (MS) waves are frequently observed in the Earth’s inner magnetosphere and play a vital role in the acceleration of radiation belt electrons and the perpendicular heating of magnetospheric ions. They are generally believed to be generated via the proton Bernstein instability driven by proton velocity distributions with a positive gradient along the velocity component perpendicular to the background magnetic field. However, the effects of cool background heavy ions, such as helium ions and oxygen ions, on the instability remain insufficiently explored. The present study employs linear kinetic plasma theory to investigate how the concentrations of cool background helium and oxygen ions affect the growth rate, wave number, and unstable harmonic range of the proton Bernstein instability driven by proton-shell velocity distributions. The results show that increasing the concentrations of these heavy ions shifts the unstable waves toward larger wave numbers (corresponding to shorter wavelengths), reduces their overall growth rate, and moves the unstable harmonic range toward lower frequencies. These modulations of the proton Bernstein instability are more pronounced with the increase of the oxygen ion concentration than with that of the helium ion concentration. The reasons for these modulations are also discussed. First, the unstable waves approximately follow the cold plasma dispersion relation of MS waves which moves to larger wave numbers with the addition of heavy ions, leading to the wave number increase of the unstable waves. This also explains the overall growth rate reduction, because the most unstable waves tend to occur with wave numbers determined by the first peak of the squared Bessel function of the first kind involved in the growth rate calculation. This peak becomes farther away from the MS wave dispersion relation when the heavy ion concentrations increase. Finally, the heavy ion concentration increase comes with the background proton concentration decrease. Fewer background protons mean less damping on the lower harmonic modes, producing the shift of the unstable harmonic range toward lower frequencies. These findings improve the physical understanding of the excitation of not only MS waves in the Earth’s magnetosphere but also similar waves in heavy-ion-rich magnetospheres of other planets.