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Seungjin Kim

Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School


First Advisor

George H. Duffey


In plasma physics, the Debye shielding distance is a measure of the distance over which the electron density can deviate appreciably from its value in the bulk of the plasma. Since it is a function of the electron temperature and the bulk electron density, it is a parameter for a given plasma. On introducing a probe of a given shape, the potential is caused to vary in the neighborhood in a determinable way. Generally, the distribution of potential is considered for a planar probe; less often, for a spherical one. We have been interested in comparing these results with results obtained for cylindrical and elliptic symmetries. Thus, we have employed rectangular, spherical, cylindrical, and elliptic coordinates in our investigations. The resulting potential distributions have been compared for particular cases. Analytical solutions were obtained for planar and spherical symmetries, and for the first solution of cylin­drical symmetry. To obtain the second solution of cylindrical symmetry, and to solve the differential equation for the potential in elliptic coordinates, however, we employed the Runge-Kutta numerical procedure. The distribution in spherical coordinates showed the most rapidly-decreasing potential over the given distances, while that in planar coordinates showed the slowest rate of decrease. Thus, in spherical coordinates, the potential is shielded out most effectively.

Library of Congress Subject Headings

Plasma probes
Electron distribution
Plasma (Ionized gases)
Potential theory (Mathematics)



Number of Pages



South Dakota State University