Effect of pressure anisotropy and flow velocity on Kelvin–Helmholtz instability of anisotropic magnetized plasma using generalized polytrope laws

Abstract

The effect of pressure anisotropy and flow velocity on the Kelvin–Helmholtz (KH) instability of two magnetized anisotropic pressure plasmas flowing relative to each other is investigated using generalized polytrope laws. The anisotropic pressure with the generalized polytrope laws is considered with three-dimensional perturbations in the description of plasma using relevant magnetohydrodynamic (MHD) set of equations. The magnetic field is assumed in the x-direction and parallel to the direction of the flow of plasma streams. A complete polytrope model is given for the considered system in terms of pressure components, magnetic field, and density of the fluids to discuss the condition of KH instability, stability, and overstability. The problem is solved using the normal mode analysis and the general dispersion relation is obtained by applying the appropriate boundary conditions. The case of nonvanishing wavenumber transverse to the direction of the stream is obtained, which represents the stationery configuration without excitation of KH instability. The longitudinal mode of propagation is discussed with conditions of KH instability, stability, and overstability for collisionless (anisotropic) double-adiabatic Chew-Goldberger-Low (CGL) and collisional (isotropic) MHD media, depending on various values of polytrope indices. The effects of pressure anisotropy, different flow velocities, and magnetic field are also discussed on the growth rate of KH instability. We observe that the presence of flow velocity and pressure anisotropy of the plasmas has a destabilizing influence on the growth rate of the system. The growth rate is found larger for MHD set of equations in comparison to the CGL set of equations. The presence of magnetic field has a stabilizing role on the growth rate of the considered system.