Hostname: page-component-84b7d79bbc-g78kv Total loading time: 0 Render date: 2024-07-30T14:56:55.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation centres and mode coupling in non-uniform Vlasov plasma

Published online by Cambridge University Press:  13 March 2009

Shayne Johnston  and
Allan N. Kaufman
Shayne Johnston
Affiliation:
Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Allan N. Kaufman
Affiliation:
Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Get access Rights & Permissions [Opens in a new window]

Abstract

The general coupling coefficient for three electromagnetic linear modes of an inhomogeneous and relativistic plasma is derived from the oscillation-centre viewpoint. A concise and manifestly symmetric formula is obtained; it is cast in terms of Poisson brackets of the single-particle perturbation Hamiltonian and its convective time-integral along unperturbed orbits. The simplicity of the compact expression obtained is shown to lead to a new insight into the essence of three-wave coupling and of the Manley–Rowe relations governing such interactions. Thus, the interaction Hamiltonian of the three waves is identified as simply the trilinear contribution to the single-particle (new) Hamiltonian, summed over all non-resonant particles. The relation between this work and the Lie-transform approach to Hamiltonian perturbation theory is discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 22 , Issue 1 , August 1979 , pp. 105 - 119
Copyright
Copyright © Cambridge University Press 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Al'tshul', L. & Karpman, V. 1965 Soviet Phys. JETP, 20, 1043.Google Scholar
Arnol'd, V. I. 1963 Russian Math. Surveys, 18, 6.Google Scholar
Burshtein, E. & Solov'ev, L. 1962 Soviet Phys. Doklady, 6, 731.Google Scholar
Cary, J. R. & Kaufman, A. N. 1977 Phys. Rev. Lett. 39, 402.CrossRefGoogle Scholar
Deprit, A. 1969 Celestial Mech. 1, 12.Google Scholar
Dewar, R. L. 1973 Phys. Fluids, 16, 1102.Google Scholar
Dewar, R. L. 1976 J. Phys. A 9, 2043.Google Scholar
Drake, J. F., Kaw, P. K., Lee, Y. C., Schmidt, G., Liu, C. S. & Rosenbluth, M. N. 1974 Phys. Fluids, 17, 778.Google Scholar
Hori, G. 1966 Publ. Astron. Soc. Japan, 18, 287.Google Scholar
Johnston, S. & Kaufman, A. N. 1976 Bull. Am. Phys. Soc. 21, 1094.Google Scholar
Johnston, S. & Kaufman, A. N. 1977 Plasma Physics (ed. Wilhelmsson, H.), p. 159. Plenum.Google Scholar
Johnston, S. & Kaufman, A. N. 1978 Phys. Rev. Lett. 40, 1266.Google Scholar
Johnston, S., Kaufman, A. N. & Johnston, G. L. 1978 J. Plasma Phys. 20, 365.Google Scholar
Kaufman, A. N. 1971 Phys. Fluids, 14, 387.Google Scholar
Kaufman, A. N. 1972 Phys. Fluids, 15, 1063.CrossRefGoogle Scholar
Kaufman, A. N. 1978 Topics in Nonlinear Dynamics (ed. Jorna, S.). American Institute of Physics.Google Scholar
Laval, G. & Pellat, R. 1975 Plasma Physics (Les Houches) (ed. Dewitt, C. and Peyraud, J.), p. 261. Gordon and Breach.Google Scholar
Sturrock, P. A. 1960 Ann. Phys. (N.Y.) 9, 422.Google Scholar