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A spatial stability analysis of the Kelvin-Helmholtz instability in an expanding axially magnetized slab jet is presented. The results are then compared with numerical simulations to see if the perturbation theory correctly describes global instabilities. Provided the jet is highly super-Alfvenic and highly supersonic then the dispersion relation describing the propagation and growth of a perturbation admits the same type of solutions as those found for purely fluid jets. However, in the region where the jet is only slightly super-Alfvenic or slightly supersonic, the expansion of the jet causes the solution to split into a growing and damped pair. This splitting occurs for both sonic and Alfvenic disturbances which propagate along the flow direction. At high frequencies, the growing solutions of the fundamental sinusoidal mode correspond to sound waves and Alfven waves propagating in the flow direction, while the damped solutions correspond to sound waves and Alfven waves propagating against the flow. Those solutions which are damped at high frequencies become growing as the frequency is decreased. The opposite is true for growing solutions at high frequencies. When the jet is sub-Alfvenic, at least one solution of the fundamental mode is not stabilized. However, the simulations suggest that any instabilities that arise when the jet is sub- or trans-Alfvenic will be damped out as the jet becomes fully super-Alfvenic. Therefore, for sub-Alfvenic jets it may be necessary to consider the effects of expansion on the stability of the jet.
This work was supported by NSF grant AST-8919180 and EPSCoR grant EHR-9108761.
