Rayleigh–Taylor instability of a magnetic tangential discontinuity in the presence of oscillating gravitational acceleration

Abstract

We study the magnetic Rayleigh–Taylor (MRT) instability of a magnetohydrodynamic interface in an infinitely conducting incompressible plasma in the presence of oscillating gravity acceleration. We show that the evolution of the interface shape is described by the Mathieu equation. Written in the dimensionless form this equation contains two parameters, a and q. The parameter q can be considered as the dimensionless wavenumber. The two parameters are related by a = Kq2, where K, in turn, depends on the ratio of densities at the two sides of the interface, ζ, the parameter s determining the relative magnitude of the gravity acceleration, the magnetic shear angle α, and the angle ϕ determining the direction of the perturbation wave vector. We calculate the dependence of the instability increment on q at fixed K, and the dependence on K of the maximum value of the increment with respect to q. We apply the theoretical results to the stability of a part of the heliopause near its apex point. Using the typical values of plasma and magnetic field parameters near the heliopause we obtain that the instability growth time is comparable with the solar cycle period.