Abstract
The longitudinal oscillations of a cylindrical plasma jet which moves with the lines of force of an externally impressed magnetic field (aligned to the jet) is investigated under the usual normal mode technique. A generalized dispersion relation is derived using the appropriate boundary conditions. Formal criteria for the cylindrical vortex sheet to be stable are obtained for long and short wavelength perturbations. Certain special cases in which the conditions for stability can be simplified, are discussed in detail. It is found that the cylindrical current-vortex sheet is stable to supersonic disturbances (whose wavelengths are assumed to be large) for strong magnetic interaction and equal uniform density distribution in the stationary configuration, in either of the media. For the incompressible case, the stability conditions are rederived and it is shown that the magnetic field stabilises the current-vortex sheet, irrespective of the strength of the magnetic field.
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