Giant overreflection of magnetohydrodynamic waves from inhomogeneous plasmas with nonuniform shear flows

Abstract

We study theoretically mode conversion and resonant overreflection of magnetohydrodynamic waves in an inhomogeneous plane-stratified plasma in the presence of a nonuniform shear flow, using precise numerical calculations of the reflection and transmission coefficients and the field distributions based on the invariant imbedding method. The cases where the flow velocity and the external magnetic field are directed perpendicularly to the inhomogeneity direction and both the flow velocity and the plasma density vary arbitrarily along it are considered. When there is a shear flow, the wave frequency is modulated locally by the Doppler shift and resonant amplification and overreflection occur where the modulated frequency is negative and its absolute value matches the local Alfv\'en or slow frequency. For many different types of the density and flow velocity profiles, we find that, especially when the parameters are such that the incident waves are totally reflected, there arises a giant overreflection where the reflectance is much larger than 10 in a fairly broad range of the incident angles, the frequency, and the plasma $\beta$ and its maximum attains values larger than $10^5$. In a finite $\beta$ plasma, both incident fast and slow magnetosonic waves are found to cause strong overreflection and there appear multiple positions exhibiting both Alfv\'en and slow resonances inside the plasma. We explain the mechanism of overreflection in terms of the formation of inhomogeneous and open cavities close to the resonances and the strong enhancement of the wave energy due to the occurrence of semi-bound states there. We give discussions of the observational consequences in magnetized terrestrial and solar plasmas.