Hybrid Kelvin-Helmholtz/Rayleigh-Taylor instability in the plasma sheet

Abstract

[1] This paper is to generalize the previous linear analysis of the hybrid Kelvin-Helmholtz/Rayleigh-Taylor (KH/RT) instability in a system of the magnetosphere-ionosphere (M-I) coupling, which is valid in the long-wavelength limit of Lky ≪ 2, where ky is the azimuthal wave number and L stands for the scale length of a latitudinal profile in azimuthal velocity or energy density. For the first time, the linear growth rate profile of a hybrid wave can be revealed in an essentially overall range of ky. When the gradient of the energy density is directed inward (toward inner magnetic shells), the hybrid growth rate is positive (meaning growth) in a certain range of ky: 0 < Lky < m. As the inertial relaxation rate v approaches zero, the growth rate curve is close to the KH “spectrum” with m = 2, where v ≡ ΣP/Cm, the ratio between the inertial capacitance of the magnetospheric plasma and the height-integrated Pedersen conductivity in the ionosphere. Without a velocity shear in the background flow, the spectrum much broadens, namely, the RT spectrum appears. The hybrid growth rate is shown to have a spectrum intermediate between the two ones of the corresponding KH and RT “root” instabilities. It is also found that the electrostatic KH instability is completely suppressed when the KH growth rate, estimated excluding the M-I coupling, is less than v, which is a straightforward extension of that previous work. On the basis of the evaluation of Cm in the Tsyganenko model, electrostatic waves (with wavelengths greater than a few tens of kilometers at the ionospheric height) are unlikely to grow by the KH instability alone in the nighttime plasma sheet. Instead, hybrid waves can grow at the places where the particle energy density has an inward gradient. This fact may account for the frequent appearance of periodic auroral luminosity in a high-latitude part of the nighttime oval as well as the formation of omega bands typically in the recovery phase of a substorm.