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Energy absorption in cold inhomogeneous plasmas: the Herlofson paradox†

Published online by Cambridge University Press:  13 March 2009

F. W. Crawford  and
K. J. Harker
F. W. Crawford
Affiliation:
Institute for Plasma Research, Stanford University
K. J. Harker
Affiliation:
Institute for Plasma Research, Stanford University
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Abstract

The Herlofson paradox is exemplified by a capacitor containing cold, collisionless, inhomogeneous plasma as the dielectric: its response to a sinusoidal driving signal can exhibit continuous energy absorption, even though the system is lossless. The underlying mechanism has been explained generally by Barston in terms of the transient response of the system. In this paper, we confirm Barston 's conclusions by examining in detail several analytically tractable cases of delta-function and sinusoidal excitation, and consider the effects of collisions and non-zero electron temperature in determining the steady state fields and dissipation. Energy absorption without dissipation in plasmas is analogous to that occurring after application of a signal to a network of lossless resonant circuits. This analogy is pursued, and extended to cover Landau damping in a warm homogeneous plasma, in which the resonating elements are the electron streams making up the velocity distribution. Some of the practical consequences of resonant absorption are discussed, together with a number of paradoxical plasma phenomena which can also be elucidated by considering a superposition of normal modes rather than a single Fourier component.

Type
Research Article
Information
Journal of Plasma Physics , Volume 8 , Issue 3 , December 1972 , pp. 261 - 286
Copyright
Copyright © Cambridge University Press 1972

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References

REFERENCES

M., Abramovitz & Stegun, I. A. (eds.) 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Baldwin, D. E. 1969 Phys. Fluids, 12, 279.Google Scholar
Baldwin, D. E., Henderson, D. M. & Hirschfield, J. L. 1968 Phys. Rev. Letters, 20, 314.CrossRefGoogle Scholar
Baldwin, D. E. & Ignat, D. W. 1969 Phys. Fluids, 12, 697.CrossRefGoogle Scholar
Baldwin, D. E. & Rowlands, G. 1966 Phys. Fluids, 9, 2444.CrossRefGoogle Scholar
Barston, E. M. 1964 Ann. Phys. (N.Y.) 29, 282.CrossRefGoogle Scholar
Bers, A. & Schneider, H. M. 1968 MIT Rep. 89, 123–130; 91, 118–132.Google Scholar
Briggs, R. J. & Paik, S. F. 1968 Int. J. Electron. 23, 163.CrossRefGoogle Scholar
Buneman, O. 1961 J. Appl. Phys. 32, 1783.CrossRefGoogle Scholar
Etievant, C. 1971 Proc. 10th Int. Conf. on Phenomena in Ionized Gases, Oxford, p. 259. Donald Parsons.Google Scholar
Fisher, R. K. & Gould, R. W. 1971 Phys. Fluids, 14, 857.CrossRefGoogle Scholar
Gil'denburg, V. B. 1964 Sov. Phys. JETP, 18, 1359.Google Scholar
Gould, R. W. & Blum, F. A. 1967 Proc. 8th Int. Conf. on Phenomena in Ionized Gases, Vienna, p. 405. Springer.Google Scholar
Herlofson, N. 1951 Arkiv Fysik, 3, 247.Google Scholar
O'Neil, T. 1965 Phys. Fluids, 8, 2255.CrossRefGoogle Scholar
Stenzel, R. L. & Gould, R. W. 1971 J. Appl. Phys. 42, 4225.CrossRefGoogle Scholar
Tataronis, J. A. & Crawford, F. W. 1970 J. Plasma Phys. 4, 231.CrossRefGoogle Scholar
Tonks, L. 1931 Phys. Rev. 37, 1458.CrossRefGoogle Scholar
Waletzko, J. A. & Bekefi, G. 1967 Rad. Sci. 2, 489.CrossRefGoogle Scholar