Citation
Zabusky, Norman J. (1959) Hydromagnetic stability of a streaming cylindrical plasma. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd02272006080626
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
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 nonconducting 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 matrixperturbation 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 quasisymmetrical form for treating the compressible medium.
An analyticalnumerical 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 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1959 
Record Number:  CaltechETD:etd02272006080626 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd02272006080626 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  780 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  02 Mar 2006 
Last Modified:  26 Dec 2012 02:32 
Thesis Files

PDF (Zabusky_nj_1959.pdf)
 Final Version
See Usage Policy. 9Mb 
Repository Staff Only: item control page