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.

Interchange instability of a curved current layerconvecting in the magnetosheath from the bow shock towards themagnetopause

“…For a nonlocal analysis with smooth profiles, it is rather complicated to take into account a shear angle. However, effects of a finite shear angle have been studied previously by Arshukova et al (2002) for the particular case of a uniform layer with enhanced plasma pressure which is separated by two tangential discontinuities. The interchange instability growth rate was obtained by Arshukova et al (2002) as a function of the magnetic shear angle.…”

“…For our instability analysis, we use the profiles of the magnetic field and plasma parameters which are obtained from the MHD model of a nonsteady solar wind flow around the magnetosphere (Erkaev et al, 2002) modeled as a paraboloid of revolution. This model is similar to that applied previously to a steady solar wind flow around the Earth's magnetosphere , or the nonsteady flow around a magnetic cloud .…”

“…In the context of the Earth's magnetospheric boundary (magnetopause), the interchange instability was analyzed for a tangential discontinuity by Alexeev and Maltsev (1990), and also by Rezenov and Maltsev (1994). The MHD instabilities of structured plasma layers with piecewise constant parameters were studied by Arshukova et al (2002).…”

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

“…Then, Kelvin's circulation theorem, which ensures the conservation of the circulation, does not hold in MHD flows. Thus, the previous works on the theoretical analysis have been limited to either the linear stability theory (Gerwin, 1967, Chen and Hasegawa, 1974, Arshukova et al, 2002, Ilin et al, 2003, Cao et al, 2008 or the weakly nonlinear analysis (Hunter and Thoo, 2011). However, it is found that when the magnetic field does not initially possess the normal component to the interface, the concept of vortex sheet model can be extended naturally to the currentvortex sheet model in MHD flows including the nonlinear regime.…”

Geophysical and Atmospheric Evolution of Habitable Planets

“…This magnetic tension forms specific types of plasma flow stream lines near the ionopause, which are orthogonal to the magnetic field lines. This process favors the appearance of Kelvin-Helmholtz and interchange instabilities that can detach ionospheric plasma in the form of detached ion clouds from a planet (Biernat et al, 1999;Arshukova et al, 2002).…”