Vibrations of a Confined Cylindrical Plasma about a Gaussian Equilibrium Density Distribution †
- 1 January 1963
- journal article
- electronics section
- Published by Taylor & Francis in Journal of Electronics and Control
- Vol. 14 (1) , 1-20
- https://doi.org/10.1080/00207216308937470
Abstract
A fully ionized, bounded, cylindrical plasma with a. gaussian equilibrium density distribution is assumed, liquations of conservation of energy and of pressure change are obtained. An equation of radial vibrations is obtained without linearization. Analytic solutions for standing waves to this equation are found in terms of the confluent hypergeomotric function. The fundamental frequencies for radial standing waves are found to beC/πσ√2 for ion sound waves and C e/πσ√2 for electronic sound waves. C is the well-known plasma ion sound speed, C e is (γRT)1/2 evaluated for the electron gas. σ is the standard deviation of the density distribution. Conditions for the plasma to bo ‘ stablo ’ (i.e. to remain at rest.) are found,Keywords
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