Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T00:26:02.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Functional calculus in strong plasma turbulence

Published online by Cambridge University Press:  13 March 2009

Goodarz Ahmadi  and
Akira Hirose
Goodarz Ahmadi
Affiliation:
Department of Mechnical Engineering, Shiraz University, Shiraz, Iran
Akira Hirose
Affiliation:
Department of Physics, University of Saskatchewan, Saskatoon, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory of electrostatic plasma turbulence is considered. The basic equations for the dynamics of the hierarchy of the moment equations are derived and the difficulty of the closure problem for strong plasma turbulence is discussed. The characteristic functional in phase space is introduced and its relations to the correlation functions are described. The Hopf functional equation for dynamics of the characteristic functional is derived, and its equivalence to the hierarchy of the moment equations is established. Similar formulations were carried out in velocity-wave vector space. characteristic functional are considered and their relationships are studied. An approximate solution for Hopf's equation for the nearly normal turbulence is obtained which is shown to predict diffusion of the mean distribution function in velocity space.

Type
Research Article
Information
Journal of Plasma Physics , Volume 24 , Issue 3 , December 1980 , pp. 489 - 501
Copyright
Copyright © Cambridge University Press 1980

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

Ahmadi, G. 1975 Z. Naturforech. 30a, 1572.CrossRefGoogle Scholar
Cook, J. 1974 Plasma Physics (ed. Keen, B. E.), pp. 225–241. Institute of Physics, London.Google Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Dupree, T. H. 1966 Phys. Fluids, 9, 1773.CrossRefGoogle Scholar
Dupree, T. H. 1974 Phys. Fluids, 17, 100.CrossRefGoogle Scholar
Edwards, S. F. 1969 Nonlinear Effects in Plasma (ed. Kalman, G. & Feix, M.), pp. 57–85. Gordon and Breach.Google Scholar
Frisce, U. 1977 J. Physique Paris, 28, C3–225.Google Scholar
Hopf, E. 1952 J. Ratl. Mech. Anal. 1, 87.Google Scholar
Hopf, E. 1962 Hydrodynamic Instability (ed. Birkhoff, G., Bellman, R. and Lin, C. C.), p.157. American Mathematical Society.CrossRefGoogle Scholar
Hosakawa, I. & Yamamoto, K. 1970 Phys. Fluids, 13, 1683.CrossRefGoogle Scholar
Ichimaru, S. 1970 Phys. Fluids, 13, 1560.CrossRefGoogle Scholar
Ichimaru, S. 1973 Basic Principles of Plasma Physics. Benjamin.Google Scholar
Jones, F. C. & Birmingham, T. J. 1975 Plasma Phys. 17, 15.CrossRefGoogle Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Kapland, S. A. & Tsytovich, V. N. 1973 Plasma Astrophysics. Pergamon.Google Scholar
Misguich, J. H. & Balescu, R. 1978 J. Plasma Phys. 19, 147.CrossRefGoogle Scholar
Montgomery, D. C. 1971 Theory of the Unmagnetized Plasma. Gordon and Breach.Google Scholar
Orszag, S. A. & Kraichnan, R. H. 1967 Phys. Fluids, 10, 1720.CrossRefGoogle Scholar
Tsytovich, V. N. 1972 An Introduction to the Theory of Plasma Turbulence. Pergamon.Google Scholar
Vedenov, A. A. 1968 Theory of Turbulent Plasma. American Elsevier, New York.Google Scholar
Weinstock, J. 1969 Phys. Fluids, 12, 1045.Google Scholar