Excitation of a magnetospheric MHD cavity by Kelvin-Helmholtz instability

The Kelvin-Helmholtz instability is investigated analytically by using a one-dimensional nonuniform model of the Earth’s magnetosphere and the adjacent solar wind region. Its properties are shown to be essentially governed by the presence of an MHD cavity that arises in the magnetosphere because of the non-uniformity of the latter and also because of the jump in the parameters of the medium at the magnetopause (the outer boundary of the magnetosphere). System oscillations constitute a discrete spectrum of eigenmodes, which are determined by the wave vector k t along the tangential discontinuity and also by the mode number n = 0, 1, 2, …, playing the role of the wavenumber along a coordinate normal to the magnetopause. Analytic expressions are obtained for the frequency and instability growth rate of each eigenmode and for the functions describing its spatial structure. All these quantities depend parametrically on the solar wind velocity V W , or more precisely, on the Doppler frequency shift ω W = k t · V W . For each eigenmode, there is a lower instability threshold depending on the parameter ω W and a sharp maximum in the growth rate at the eigenfrequency of the magnetospheric cavity. For ω W values below the threshold, the properties of an eigenmode are highly sensitive to the type of solar wind nonuniformity. Three cases are considered: a uniform solar wind and solar winds in which the speed of sound increases or decreases away from the magnetopause.