Analytical Approach to Two-Dimensional Full Reflections of Fast Magnetosonic Waves Due To Mesoscale Density Boundaries

Propagation of fast magnetosonic (MS) waves in the equatorial plane has attracted a growing attention in recent studies. Although computer simulations including ray tracing, PIC, and full wave simulations have been utilized to study the propagation of MS waves, analytical approach is needed to investigate the physics insight. In this letter, we first derive the wave equations describing the two-dimensional propagation of MS waves under the assumption that the mesoscale density inhomogeneity is only along one dimensional. After investigating the essential role of the potential function in the wave equation for the full reflection of MS waves, we find that full reflection can occur when the minimum potential is significantly negative. Finally, we have discussed the effects of incidence angles and wave frequencies on the full reflection. Our results show that MS waves with an incidence angle or wave frequency greater than the critical value would be fully reflected. Fast magnetosonic (MS) waves have been found to play an important role in the dynamics of radiation belt electrons, especially the butterfly distribution in pitch angles. To make contribution to particle scattering, MS waves should arrive in the regions where particle exists. Previous studies have made efforts on the radial propagation, and found that a significantly larger density gradient is needed to result in an efficient reflection of MS waves. Such a large density gradient is seldom observed in the inner magnetosphere. However, satellites have often observed that MS waves quickly stop at the front of a mesoscale density boundary, which is hardly explained via radial propagation theory. Instead, two-dimensional propagation model for MS waves in the equatorial plane is needed. Here we provide an analytical model to describe such a propagation, which can be used to interpret the satellite observations successfully. Wave equations have been simplified to clearly describe the two-dimensional propagation of magnetosonic (MS) waves emerging mesoscale density boundariesTwo-dimensional full reflection of MS waves has been found to be determined by the potential functionTheoretical results on the two-dimensional full reflection of MS waves have been verified with observations and full wave simulations