Reflection Coefficient for Two-Dimensional Propagation of Fast Magnetosonic Waves Emerging One-Dimensional Mesoscale Density Boundaries

In recent studies, two-dimensional propagation model of fast magnetosonic (MS) waves has been proposed to interpret the satellite observations of MS waves knocking into a density boundary. Although the theoretical model is able to capture the main properties of the two-dimensional propagation of MS waves, quantitative description about the MS wave behaviors has not been given yet. Here, with the assumption of a parabolic function for the potential function near its minimum, we solve the wave equation only with a potential function to obtain the reflection coefficients. It is found that the wave equation with a potential function can describe the full reflection and full transmission of MS waves rather well. Furthermore, the first-order derivative term in the wave equation is utilized to modify the reflection coefficient when the minimum of the potential function is near zero. Our result is helpful for further understanding the two-dimensional propagation of MS waves. Fast magnetosonic (MS) waves have been demonstrated to play an important role in the dynamical evolution of radiation belt electrons. As ray tracing simulations have shown that MS waves propagate around the magnetic equator, wave equation of the two-dimensional propagation model is given to describe the behaviors of MS waves. In the wave equation, the potential function is the key factor to determine the wave behaviors (full reflections, full transmissions, or partial reflections). However, the first-order derivative term in the wave equation should take effects, especially when the potential function is near zero. Here the reflection coefficients in the both cases where the first-order derivative term is included or not have been given. Our results are also compared to the full wave simulation results. It is suggested that the first-order derivative term is important to give a reasonable result when partial reflections occur. Otherwise, the potential function can describe the wave behavior rather well. Analytical expression of reflection coefficient for two-dimensional propagation of MS waves emerging density boundaries has been given We find that the behavior near the minimum potential function can be described by a Weber differential equation Correction near the minimum potential function has been provided to give a more reliable physical solution