Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T15:33:36.372Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian approach to non-linear wave interactions in a warm plasma

Published online by Cambridge University Press:  13 March 2009

J. J. Galloway  and
H. Kim
J. J. Galloway
Affiliation:
Institute for Plasma Research, Stanford University
H. Kim
Affiliation:
Institute for Plasma Research, Stanford University
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.

Type
Articles
Information
Journal of Plasma Physics , Volume 6 , Issue 1 , August 1971 , pp. 53 - 72
Copyright
Copyright © Cambridge University Press 1971

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

Dougherty, J. P. 1970 J. Plasma Phys. 4, 761.Google Scholar
Dysthe, K. B. 1970 Int. J. Elect. 29, 401.CrossRefGoogle Scholar
Eckart, C. 1960 Phys. Fluids 3, 421.CrossRefGoogle Scholar
Galloway, J. J. 1970 Stanford University Institute for Plasma Research Rep. 362.Google Scholar
Galloway, J. J. & Crawford, F. W. 1970 Proc. 4th European Conf. on Controlled Fusion and Plasma Physics, Rome (CNEN), p. 161.Google Scholar
Goldstein, H. 1959 Classical Mechanics. Addison.Wesley.Google Scholar
Harker, K. J. & Crawford, F. W. 1969 J. Geophys. Res. 74, 5029.Google Scholar
Harker, E. G. 1969 Advances in Plasma Physics. New York: Interscience.Google Scholar
Katz, S. 1961 Phys. Fluids 4, 421.Google Scholar
Lamb, H. 1945 Hydrodynamics. New York: Dover.Google Scholar
Louisell, W. H. 1960 Coupled Mode and Parametric Electronics. New York: Wiley.Google Scholar
Low, F. E. 1958 Proc. Roy. Soc. A 248, 282.Google Scholar
Pennfield, P. 1960 Frequency-Power Formulas. New York: Wiley.Google Scholar
Sagdev, R. Z. & Galeev, A. A. 1969 Non-linear Plasma Theory. New York: Benjamin.Google Scholar
Sturrock, P. A. 1958 Ann. Phys. 4, 306.CrossRefGoogle Scholar
Sturrock, P. A. 1960 Ann. Phys. 9, 422.CrossRefGoogle Scholar
Sturrock, P. A. 1962 Plasma Hydromagnetics. Stanford University Press.Google Scholar
Suramlishvili, G. I. 1967 Soy. Phys. JETP 25, 165.Google Scholar
Suramlishvili, G. I. 1970 Soy. Phys. Tech. Phys. 14, 1334.Google Scholar
Tsytovich, V. N. 1970 Non-linear Effects in Plasma. New York: Plenum.Google Scholar
Vedenov, A. A. 1967 Reviews of Plasma Physics 3. New York: Consultants Bureau.Google Scholar
Vedenov, A. A. 1968 Theory of Turbulent Plasmas. New York: American Elsevier.Google Scholar