Non-Reflective Magnetohydrodynamic Waves in an Inhomogeneous Plasma

Abstract

The existence of traveling waves in a strongly inhomogeneous magnetized plasma is studied. It is shown that under certain conditions for characteristics of the medium, the waves do not reflect from inhomogeneities, although their amplitude and phase vary in space. Such non-reflective waves are found mathematically as solutions of wave equations with constant coefficients, to which the original equations with variable coefficients are reduced after a certain transformation. The existence of non-reflective waves in various plasma configurations is established.

Traveling Waves in Shallow Seas of Variable Depths

“…In fact, the system in Equations ( 18) and ( 19) representing the integral-differential equations for c and A are not analyzed here in detail because of our focusing on the wave Equation (17). We indicate here only an important particular solution to this system, which can be obtained by setting A = 1.…”

“…A few examples are constructed for surface gravity waves in water layers of variable depths [6,7], waves in inhomogeneous flow [8,9], internal waves in a stratified fluid [10], and waves in the atmosphere of the Earth and the Sun [11,12]. Some rigorous solutions demonstrating traveling wave features are known for acoustic waves [13,14], electromagnetic waves and plasma waves [15][16][17].…”

Reflectionless wave propagation on shallow water with variable bathymetry and current

“…The problem of reflectionless wave propagation in inhomogeneous media has a long history. It was studied for monochromatic waves in plasma physics (Ginzburg 1970;Petrukhin, Pelinovsky & Didenkulova 2020), acoustics (Brekhovskih 1980), solids (Clements & Rogers 1974), fluids (Magaard 1962;Vlasenko 1987), etc. A more general analysis of reflectionless propagation of water waves of different shapes was presented in the above-cited papers by Didenkulova, Pelinovsky, Dobrokhotov et al for particular configurations of bottom profile.…”