Magnetohydrodynamic instability of a high magnetic shear layer with a finite curvature radius

Abstract

This article deals with the magnetohydrodynamic instability of a thin layer which is characterized by a high magnetic shear, a constant curvature radius, and a plasma velocity shear. The magnetic field and the plasma parameters are considered to be piecewise constant inside the layer and in the regions adjacent to the layer. The plasma parameters and the magnetic field are assumed to obey the ideal incompressible magnetohydrodynamics. Fourier analysis is used to calculate small perturbations of the magnetic field and plasma parameters near the layer in linear approximation. The instability growth rate is obtained as a function of different parameters: the magnetic shear angle, the velocity direction angle, the tangential plasma velocity, the layer thickness, the wave number, and the curvature radius. The resulting instability is a mixture of interchange and Kelvin–Helmholtz instabilities on a surface with nonzero curvature. For a fixed velocity shear and curvature radius, the instability growth has a maximum in the case of antiparallel magnetic fields (maximal magnetic shear). This growth rate is an increasing function of the tangential velocity component perpendicular to the magnetic field, and a decreasing function of the velocity component along the magnetic field. The instability is stronger for smaller curvature radius.