Hydromagnetic equilibrium and instabilities in the convectively driven near‐Earth plasma sheet

Abstract

Recent particle simulations have suggested that the convectively driven near‐Earth plasma sheet can develop a structure in which a thin current sheet is embedded within the much thicker plasma sheet and that finite‐ky modes with the character of kink and interchange modes can be excited in this system. Here the ideal magnetohydrodynamic (MHD) equations are used to investigate the equilibrium and linear stability properties of such a system. It is shown that the embedded current sheet configuration satisfies the conditions of pressure balance and represents an approximate two‐dimensional (x,z) MHD equilibrium state. The stability analysis, in which the boundary conditions are imposed in terms of MHD characteristic waves, indicates that two types of pressure‐driven modes are unstable. One mode is associated with the presence of a tailward gradient in the equatorial magnetic field profile. As the wavelength of this mode is made shorter, the mode becomes localized on the field lines crossing the region of increasing field and has the character of an interchange/ballooning mode. A second mode is associated with the existence of a magnetic island and is localized within the island; it has a structure similar to that of the classical kink mode for a plasma column. While the MHD growth rates continue to increase at short wavelengths, at longer wavelengths determined by the ion gyroradius (kyρi ≲ 1, where ρi is computed in the local equatorial field) they are comparable to those for the dominant nonlinear modes observed in the kinetic simulations.