Kelvin-Helmholtz instability of a compressible plasma in a magnetic field

The Kelvin-Helmholtz instability of a compressible plasma in a uniform magnetic field with respect to disturbances propagating along the flow is considered. First, the case with the magnetic field parallel to the direction of streaming is considered. The result given by Sen 4] that the compressibility effects destabilize an otherwise neutrally stable system even in the hydrodynamic limit is apparently erroneous. Re-examination of the dispersion relation in the limit of small compressibility effects shows that the latter reduce the growth rate of an otherwise unstable disturbance. Attention is also drawn to errors in the calculations of Fejer 2] in the limit of small compressibility effects. Next, the case with the magnetic field transverse to the direction of streaming is considered. It is found that the transverse magnetic field does influence the stability of the system when the compressibility effects are present, contrary to the result given by Chandrasekhar 1] for the case of an incompressible plasma. However, interestingly enough, the compressibility effects are effectively reduced if a transverse magnetic field is present! It is further shown that the transverse magnetic field reduces the stability of the system.