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Approximate theory of large-amplitude wave propagation

Published online by Cambridge University Press:  13 March 2009

H. Kim
H. Kim
Affiliation:
Institute for Plasma Research, Stanford University, Stanford, California 94305
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Extract

An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 17 , Issue 3 , June 1977 , pp. 519 - 535
Copyright
Copyright © Cambridge University Press 1977

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. (eds.) 1965 Handbook of Mathematical Functions, pp. 361, 363. Dover.Google Scholar
Al'tshul', L. M. & Karpman, V. I. 1966 Soviet Phys. JETP, 22, 361.Google Scholar
Armstrong, T. P. 1967 Phys. Fluids, 10, 1269.CrossRefGoogle Scholar
Bailey, V. L. & Denavit, J. 1970 Phys. Fluids, 13, 451.CrossRefGoogle Scholar
Benford, G. & Thomson, J. J. 1972. Phys. Fluids, 15, 1496.CrossRefGoogle Scholar
Bernstein, I. B., Greene, J. M. & Kruskal, M. D. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Bud'ko, N. I.Karpman, I. & Shklyar, D. R. 1972 Soviet Phys. JETP, 34, 778.Google Scholar
Canosa, J. M. 1975 IBM Palo Alto Scientific Ctr. Report No. G320–3343.Google Scholar
Canosa, J. M. & Gazdag, J. 1974 Phys. Fluids, 17, 2030.CrossRefGoogle Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic Press.Google Scholar
Dawson, J. M. & Shanny, R. 1968 Phys. Fluids, 11, 1506.CrossRefGoogle Scholar
Dewar, R. L. 1972 Phys. Fluids, 15, 1712.Google Scholar
Dupree, T. H. 1966 Phys. Fluids, 9, 1773.CrossRefGoogle Scholar
Franklin, R. N., Hamberger, S. M., Ikezi, H., Lampis, G. & Smith, G. J. 1972 b Phys. Rev. Lett. 28, 1114.CrossRefGoogle Scholar
Franklin, R. N., Hamberger, S. M. & Smith, G. J. 1972 a Phys. Rev. Lett. 29, 914.CrossRefGoogle Scholar
Frisch, U. 1968 Probabilistic Methods in Applied Mathematics, vol. I (ed. Bharucha-Reid, A. T.), p. 75. Academic.Google Scholar
Goldstein, H. 1950 Classical Mechanics. Addison-Wesley.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Tables of Integrals, Series and Products, pp. 400–402. Academic.Google Scholar
Imamura, T., Sugihara, R. & Taniuti, T. 1969 J. Phys. Soc. Japan, 27, 1623.CrossRefGoogle Scholar
Jahns, G. & Van Hoven, G. 1973 Phys. Rev. Lett. 31, 436.CrossRefGoogle Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Kubo, R. 1962 J. Phys. Soc. Japan, 17, 1100.CrossRefGoogle Scholar
Landau, L. 1946 J. Phys. (USSR), 10, 25.Google Scholar
Lee, A. & Pocobelli, G. 1972 Phys. Fluids, 11, 2351.CrossRefGoogle Scholar
Lee, A. & Pocobelli, G., 1973 Phys. Fluids, 16, 1964.CrossRefGoogle Scholar
Lee, A. & Schmidt, G. 1970 Phys. Fluids, 13, 2546.CrossRefGoogle Scholar
Louisell, W. H. 1964 Radiation and Noise in Quantum Electronics, p. 102. McGraw-Hill.Google Scholar
Malmberg, J. H. & Wharton, C. B. 1967 Phys. Rev. Lett. 19, 775.CrossRefGoogle Scholar
Manheimer, W. M. & Flynn, R. W. 1971 Phys. Fluids, 14, 2393.CrossRefGoogle Scholar
Matsuda, Y. & Crawford, F. W. 1975 Phys. Fluids, 18, 1336.CrossRefGoogle Scholar
Mazitov, R. K. 1965 J. Appl. Mech. Tech. Phys. 1, 22.Google Scholar
Misguich, J. H. & Balescu, R. 1975 J. Plasma Phys. 13, 385.CrossRefGoogle Scholar
Morales, G. J. & O'Neil, T. M. 1972 Phys. Rev. Lett. 28, 417.CrossRefGoogle Scholar
Nakamura, Y. & Ito, M. 1971 Phys. Rev. Lett. 26, 350.CrossRefGoogle Scholar
Oei, I. H. & Swanson, D. G. 1972 Phys. Fluids, 15, 2218.CrossRefGoogle Scholar
O'Neil, T. M. 1965 Phys. Fluids, 8, 2255.CrossRefGoogle Scholar
Orszag, S. A. & Kraichman, R. H. 1967 Phys. Fluids, 10, 1720.CrossRefGoogle Scholar
Rudakov, L. I. & Tsytovich, V. N. 1971 Plasma Phys. 13, 213.CrossRefGoogle Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin.Google Scholar
Sato, N., Ikezi, H., Takahashi, N. & Yamashita, Y. 1969 Phys. Rev. 183, 278.CrossRefGoogle Scholar
Sugihara, R. & Kamimura, T. 1972 J. Phys. Soc. Japan, 33, 206.CrossRefGoogle Scholar
Sugihara, R. & Yamanaka, K. 1975 Phys. Fluids, 18, 114.CrossRefGoogle Scholar
Taniuti, T. 1969 J. Phys. Soc. Japan, 27, 1634.CrossRefGoogle Scholar
Tsytovich, V. N. 1970 Nonlinear Effects in Plasmas. Plenum.CrossRefGoogle Scholar
Tsytovich, V. N. 1972 An Introduction to the Theory of Plasma Turbulence. Pergamon.Google Scholar
Tasi, S. 1974 J. Plasma Phys. 11, 213.Google Scholar
Vidmar, P. J., Malmberg, J. H. & Starke, T. P. 1975 Phys. Rev. Lett. 34, 646.CrossRefGoogle Scholar
Weinstock, J. 1969 Phys. Fluids, 12, 1045.CrossRefGoogle Scholar
Wharton, C. B., Malmberg, J. M. & O'Neil, T. M. 1968 Phys. Fluids, 11, 1761.CrossRefGoogle Scholar