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Hydromagnetic Stability of a Streaming Cylindrical Incompressible Plasma

Zabusky, N. J. (1960) Hydromagnetic Stability of a Streaming Cylindrical Incompressible Plasma. Physics of Fluids, 3 (2). pp. 278-288. ISSN 0031-9171.

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A dispersion relation is derived and analyzed for the case where the equilibrium velocity of an incompressible, nonresistive, cylindrical plasma has a spiral motion along magnetic field lines. The symmetric hydromagnetic equations are used to derive the plasma hydromagnetic pressure. The dispersion relation is found by matching plasma and outer-region hydromagnetic pressures across a sharp-moving interface. The zeros of the dispersion relation are obtained by a sequence of mappings between three complex planes. The presence of flow introduces overstable modes. For m = 0 the time-divergences are removed by flow. For m = 1 the divergences are enhanced by flow such that the growth rates and oscillation frequencies increase linearly with the flow velocity. The smaller is the wavelength of the disturbance in the z direction, the larger are the overstable eigenvalues.

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Additional Information:©1960 The American Institute of Physics. Received September 21, 1959; revised November 19, 1959. The author would like to thank Professors L. Davis, Jr., and M.S. Plesset for their advice during the conduct of this investigation. The Hughes Aircraft Company (1955-57) and the Standard Oil Company of California (1958-59) supported the author through their generous graduate fellowship programs. This paper was written at the Bell Telephone Laboratories during the summer of 1959. Submitted in partial fulfillment of the requirements for the degree Doctor of Philosophy in the Department of Physics, California Institute of Technology. Preliminary accounts of this problem and two additional ones were presented at the San Diego meeting of the American Physical Society, Division of Fluid Dynamics, November 1958.
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Record Number:CaltechAUTHORS:ZABpof60
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Deposited On:12 Jun 2008
Last Modified:03 Oct 2019 00:13

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