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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

REFERENCES

Baldwin, D. E. 1969 Phys. Fluids, 12, 279.CrossRefGoogle Scholar
Ballieu, R., Messiaen, A. M. & Vandenplas, P. E. 1972 J. Plasma Phys. 8, 113.CrossRefGoogle Scholar
Barston, E. M. 1963 Phys. Fluids, 6, 828.CrossRefGoogle Scholar
Barston, E. M. 1965 Phys. Rev. 139, A 394.CrossRefGoogle Scholar
Briggs, R. J. & Paik, S. F. 1968 Int. J. Electron. 23, 163.CrossRefGoogle Scholar
Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics, vol. 1. Interscience.Google Scholar
Crawford, F. W. & Kino, G. S. 1963a C. R. Hebd. Seano. Acad. Sci., Paris, 256, 1939.Google Scholar
Crawford, F. W. & Kino, G. S. 1963b C. R. Hebd. Seanc. Acad. Sci., Paris, 256, 2798.Google Scholar
Crawford, F. W., Kino, G. S. & Cannara, A. B. 1963 J. Appl. Phys. 34, 3168.CrossRefGoogle Scholar
Crawford, F. W. 1964 J. Appl. Phys. 35, 1365.CrossRefGoogle Scholar
Crawford, F. W. 1965 Int. J. Electron. 19, 217.CrossRefGoogle Scholar
Dorman, G. 1969. J. Plasma Phys. 3, 387.CrossRefGoogle Scholar
Fox, L. 1962 Numerical Solution of Ordinary and Partial Differential Equations. Addison- Wesley.Google Scholar
Harker, K. J., Kino, G. S. & Eitelbach, D. L. 1968 Phys. Fluids, 11, 425.CrossRefGoogle Scholar
Messiaen, A. M. & Vandenplas, P. E. 1962 Physica, 28, 537.CrossRefGoogle Scholar
Mikhlin, S. G. 1964 Variational Methods in Mathematical Physics. Pergamon.Google Scholar
Mikhlin, S. G. 1965 The Problem of the Minimum of a Quadratic Functional. Holden-Day.Google Scholar
Mikhlin, S. G. 1971 The Numerical Performance of the Variational Method. WoltersNoordhoff.Google Scholar
Miura, R. M. & Barston, E. M. 1971 J. Plasma Phys. 6, 271.CrossRefGoogle Scholar
Newcomb, W. A. 1962 Nuclear Fusion, Suppl. 2, 451.Google Scholar
Parbhakar, K. J. & Gregory, B. C. 1971 Can. J. Phys. 49, 2578.CrossRefGoogle Scholar
Parker, J. V. 1963 Phys. Fluids, 6, 1657.CrossRefGoogle Scholar
Peratt, A. K. & Kuehl, H. H. 1972 Phys. Fluids, 15, 1117.CrossRefGoogle Scholar
Parker, J. V., Nickel, J. C. & Gould, R. W. 1964 Phys. Fluids, 7, 1489.CrossRefGoogle Scholar
Self, S. A. 1963 Phys. Fluids, 6, 1762.CrossRefGoogle Scholar
Sturrock, P. A. 1958 Ann. Phys. 4, 306.CrossRefGoogle Scholar
Vandenplas, P. E. 1968 Electron Waves and Resonances in Bounded Plasmas. Wiley.Google Scholar
Vandenplas, P. E. & Messiaen, A. M. 1964 Plasma Phys. 6, 459.Google Scholar
Vandenplas, P. E. & Messiaen, A. M. 1965 Nuclear Fusion, 5, 47.CrossRefGoogle Scholar