Kelvin-Helmholtz instability of anisotropic magnetized plasma using generalized polytrope laws

The problem of Kelvin-Helmholtz (K-H) instability of two superposed compressible magnetized anisotropic pressure plasmas is investigated using generalized polytrope laws. The relevant magnetohydrodynamic (MHD) equations of the problem have been modified using generalized polytrope laws in terms of polytropic indices. The general dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The conditions for K-H stability, instability and overstability are obtained for MHD and Chew-Goldberger and Low (CGL) set of equations. It is found that the conditions of K-H stability, instability and overstability depend on polytropic indices and magnetic field. We find that in general overstability is not possible unless the new conditions in terms of polytropic indices are not satisfied. The weak magnetic field changes the criteria of K-H instability. The effect of pressure anisotropy is studied on the growth rate of K-H instability. We conclude that increase in pressure anisotropy causes increase in the region of K-H instability.