Kelvin-Helmholtz instabilities of high-velocity magnetized shear layers with generalized polytrope laws

The linear stability of zero and finite width, arbitrarily compressible, an d magnetized velocity shear layers with isotropic or anisotropic pressure i s investigated. Such flows, modeled by the magnetohydrodynamic equations wi th generalized polytrope laws for the pressure parallel and perpendicular t o the magnetic field, are relevant in various astrophysical, geophysical an d space plasma configurations. The conditions for instability of shear laye rs of zero width are derived. For layers of finite width, shooting numerica l schemes are employed to satisfy the Sommerfeld radiation conditions of ou tgoing, spatially damping modes in a frame comoving with the plasma flow. T he resulting eigenvalues for the angular frequency and linear growth rate a re mapped out for different regions of the wave number/Mach number space. F or polytrope indices corresponding to the double adiabatic and magnetohydro dynamic equations, the results reduce to those obtained earlier using these models.