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Variational calculations for resonance oscillationsof inhomogeneous plasmas

Published online by Cambridge University Press:  13 March 2009

Y-K.M. Peng  and
F. W. Crawford
Y-K.M. Peng
Affiliation:
Institute for Plasma Research, Stanford University
F. W. Crawford
Affiliation:
Institute for Plasma Research, Stanford University
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Extract

In this paper, the electrostatic resonance properties of an inhomogeneous plasma column are treated by the Rayleigh–Ritz method. In contrast to Parker, Nickel & Gould (1964), who carried out an exact computation, we use a description of the RF equation of motion and pressure term that allows us to express the system of equations in Euler–Lagrange form. The Rayleigh–Ritz procedure is then applied to the corresponding Lagrangian, to obtain approximate resonance frequences and eigenfunctions. An appropriate set of trial co-ordinate functions is defined, which leads to frequency and eigenfunction estimates in excellent agreement with the work of Parker et al. (1964).

Type
Articles
Information
Journal of Plasma Physics , Volume 13 , Issue 2 , April 1975 , pp. 283 - 298
Copyright
Copyright © Cambridge University Press 1975

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References

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