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

Abstract

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.

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

“…Journal of Geophysical Research: Space Physics 10.1029/2023JA032376 second term is often smaller than the third term in the wave equation (see Appendix A in Yu et al, 2023), in the following we firstly solve Equation 1 only with the potential function U(x) . The first-order derivative term is considered to modify the reflection coefficient in those circumstances where U mini is near zero.…”

“…Here we adopt the same coordinate system as used by Yu et al. (2023). That is, the z axis is set along the background magnetic field, and x axis is directed parallelly with the density gradient, while y axis is set to complete a right‐handed coordinate frame.…”

“…As adopted in previous studies (Wu et al., 2023; Yu et al., 2023), a smooth density boundary is assumed between two density platforms to model the density boundary. In such a case, MS waves propagate from a low‐density region to a high‐density region or vice versa.…”

“…To solve the reflection coefficient, we should obtain the relation between E 1+ , E 1− , and E 2 . Since the second term is often smaller than the third term in the wave equation (see Appendix in Yu et al., 2023), in the following we firstly solve Equation only with the potential function $$U\left(\overline{x}\right)$$. The first‐order derivative term is considered to modify the reflection coefficient in those circumstances where U mini is near zero.…”

“…With an analytical approach, Yu et al. (2023) proposed the wave equation describing the wave behaviors of MS wave propagation and found that the filtering effect can be well captured by the potential function in the wave equation which they have given. However, quantitative description has not been given yet.…”