Kelvin--Helmholtz instability in a high-β collisionless plasma

The stability of an inhomogeneous plasma, of arbitrary β, flowing along a straight magnetic field is studied. Both the velocity flow and the plasma density are spatially varying in a direction perpendicular to the field. For drift-type waves, very elongated along the magnetic field direction, an Alfvén wave branch and a magnetosonic branch turn out to be decoupled. It is found that both branches may be driven unstable by the velocity shear. Stability conditions are worked out, quantitatively discussed, and compared in terms of β and of the magnitude of the shear.