Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

Abstract : Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.