Magnetosonic Waves Excited by Maxwellian Ring Protons in Space Plasma Environment

A comprehensive theoretical model for a homogeneous plasma system of hot, tenuous Maxwellian ring-distributed protons and the cold background of Maxwellian ions and electrons is used to study the resonant instabilities of magnetosonic (MS) waves. The perpendicular velocity integrals associated with the Maxwellian ring distribution have no analytical solution, hence, are solved numerically, while the parallel velocity integrals are solved analytically by invoking series expansion of the plasma dispersion function. For the plasma parameters relevant to Earth’s inner magnetosphere, the theoretical model generates MS waves with frequencies from 5 times the local proton cyclotron frequency to above the lower hybrid frequency for a propagation angle of 89.5°. Hydrogen (H ^+ ) band electromagnetic ion cyclotron waves are also excited by the Maxwellian ring protons for the same set of plasma parameters. A detailed analysis reveals that a sufficiently large ring velocity, as well as a smaller perpendicular and parallel thermal velocity, can enhance the MS wave growth. The study also explores the role of background plasma parameters in modulating the waves. The present theoretical model reproduces the harmonics of the MS waves observed by the Van Allen Probes in the Earth’s inner magnetosphere. Further, the model can generate MS waves in other plasma environments, e.g., Mars, where the presence of ring protons has been established by MAVEN in connection with the MS wave observations.