A Comprehensive Theoretical Model for the Generation of Magnetosonic Waves in Terrestrial and Planetary Plasma Environments

Magnetosonic (MS) waves are low frequency, compressional electromagnetic oscillations commonly observed in Earth’s inner magnetosphere and Martian upper ionosphere, propagating nearly perpendicular to the background magnetic field. These waves typically have frequencies between the local proton gyrofrequency and the local lower hybrid frequency, exhibiting linear polarization. MS waves are known to accelerate and pitch angle scatter relativistic killer electrons in Earth’s radiation belts [1]. In the Martian ionosphere, they contribute to heating heavier oxygen ions and facilitate their escape [2]. Concurrent wave and particle data from various satellite missions within Earth’s magnetosphere suggest that MS waves arise from the ring-like velocity distribution of energetic protons with a positive perpendicular slope [1].

A comprehensive theoretical model comprising of hot, tenuous Maxwellian ring-distributed energetic protons and the cold background of Maxwellian protons, heavier ions (O⁺ and O₂⁺), and electrons is developed using kinetic theory to study the generation of magnetosonic waves in a homogenous collisionless plasma system. The derivation of the dispersion relation, and consequently the growth rate expression, requires solving both parallel and perpendicular velocity integrals. The perpendicular integrals associated with the Maxwellian ring distribution lack analytical solutions and are therefore computed numerically. In contrast, the parallel integrals are solved analytically using series expansion of the plasma dispersion function, with approximations applied depending on whether the particle species is cold or energetic. The model is validated using plasma parameters pertinent to Earth’s inner magnetosphere and the Martian upper ionosphere. Results reveal that the model generates sharp MS wave harmonics within the range of the local proton cyclotron frequency to the local lower hybrid frequency at highly oblique propagation angles.

The developed theoretical model is used to study the linear growth rate of MS wave instability in Earth’s inner magnetosphere and Martian upper ionosphere. A parametric comparison study is done on the energy of the ring proton population optimum for the wave generation. The influence of the ambient magnetic field and cold background plasma on the growth and damping of MS waves in terrestrial and Martian environments will be discussed.

References

[1] R. B. Horne et al., Geophys. Res. Lett. 34, L17107 (2007)

[2] J. Wang et al., Geophys. Res. Lett. 50, L102911 (2023)