Nonideal magnetohydrodynamic Kelvin–Helmholtz instability driven by the shear in the ion diamagnetic drift velocity in a high-β plasma

Abstract

A two-dimensional nonideal magnetohydrodynamic eigenmode equation for the most dangerous perturbation (k∥=0) is derived for a high-β plasma by making use of the generalized Ohm’s law and becomes identical to the equation describing the two-dimensional hydrodynamic stability. When the pressure is nonuniform, the density is uniform, and there is no unperturbed electric field or gravity, a Kelvin–Helmholtz instability, which is driven by the shear in the ion diamagnetic drift velocity, is found. When the unperturbed ion pressure is proportional to the unperturbed total pressure, a necessary condition for the instability is that d3B0/dx3 must change sign at least once between x=x1 and x=x2, where x is the direction of the nonuniformity perpendicular to the unperturbed magnetic field B0(x) and x=x1 and x2 are points where the x component of the velocity perturbation vanishes. An unstable B0(x) profile and the dispersion relation are obtained for a polygonal ion diamagnetic drift velocity profile.

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear

“…2(a)], in the latter case (monotonic q) it is stable. In contrast, higher-m modes such as (6, 3) and (12,6) have similar growth rates in both cases, so for these the coupling between the resonances does not seem to play a crucial role.…”

Nonideal high‐β magnetohydrodynamic Kelvin‐Helmholtz instability driven by the shear in the ion diamagnetic drift velocity at the subsolar magnetopause

“…They have observed that the rapid development of a short wavelength, lower hybrid drift instability in the current sheet is followed by the slow development of long wavelength current sheet kinking. They calculated the growth rate and the wave number of the kink modes for the realistic mass ratio and found an excellent agreement between those obtained by simulation results and those calculated analytically for the present new K‐H instability driven by the shear in the ion diamagnetic drift velocity [ Miura , 2001]. Therefore even in collisionless plasmas, where the present fluid analysis is not strictly applicable, the existence of the present new K‐H instability is indicated.…”

“…Since a temporal growth of the instability is considered, k is real and ω is complex. When the density is nonuniform, the eigenmode equation for the x component of the velocity perturbation δv x becomes [ Miura , 2001] where V 0 (x) is given by in the present simplified model. In general, V 0 (x) is given by the sum of the E × B drift and the ion diamagnetic drift as given by .…”

“…Since a temporal growth of the instability is considered, k is real and w is complex. When the density is nonuniform, the eigenmode equation for the x component of the velocity perturbation dv x becomes [Miura, 2001]…”

“…Therefore the flank magnetopause is subject to the ideal magnetohydrodynamic (MHD) Kelvin‐Helmholtz (K‐H) instability driven by the shear in the E × B drift velocity, which was studied by Chandrasekhar [1961] using the frozen‐in assumption ( E + v × B = 0 ). A new K‐H instability driven by the shear in the ion diamagnetic drift velocity, which is a nonideal MHD drift in a high‐β plasma, was recently found [ Miura , 2001]. This new instability is peculiar to the high‐β MHD because the ion diamagnetic drift, which is an artifact of gyration, is not entirely the motion of guiding centers but is due to the magnetization and the ∇B drift averaged over a thermal distribution of velocities for a straight field line geometry.…”