Zabusky, Norman J. (1959) Hydromagnetic stability of a streaming cylindrical plasma. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02272006-080626
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Dispersion relations for hydromagnetic stability were found for three related problems in which the effects of plasma motion were considered. The hydromagnetic differential equations and boundary conditions were linearized in an analysis which assumes small amplitude perturbations about an equilibrium configuration. This configuration consists of a dissipationless plasma flowing in an infinite cylinder with internal and external longitudinal and azimuthal magnetic field components.
Problem 1 is an extension of earlier work and includes electromagnetic radiation and compressibility effects. Problems 2 and 3 assume that the plasma is bound by a non-conducting compressible medium in addition to the magnetic fields. The equilibrium magnetic and velocity field vary as [...], [...] where [...]. In problem 2 incompressibility is assumed, while in 3 the assumption of compressibility is made where [...] sonic speed of the plasma. This allows a matrix-perturbation expansion about the incompressible solution. The effects of the moving boundary were included. It was found convenient to use the hydromagnetic pressure [...] as the basic dependent variable and to use the hydromagnetic equations in symmetric form. The equations were extended to a quasi-symmetrical form for treating the compressible medium.
An analytical-numerical study was made in which the dispersion relation for incompressible flow was treated as a function of a complex variable. In each of ten different physical situations the flow parameter, [...], was varied over the range [...] and the following conclusions were reached:
1. The oscillation frequencies are symmetrically distributed about the origin with [...] = 0. When [...] > 0 the mode frequencies are all shifted toward the negative and vary monotonically with [...].
2. The growth rates are larger for large wave number disturbances.
3. The oscillation frequency for complex modes increases with increasing [...].
4. Increasing the flow ([...]) removes sausage instabilities and enhances (the magnitude of) kink instabilities.
5. Adding a strong longitudinal magnetic field intensifies the sausage instabilities by increasing the magnitude of their growth rate and requiring a larger flow to remove them. Kink instabilities are removed.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 January 1959|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||02 Mar 2006|
|Last Modified:||26 Dec 2012 02:32|
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