Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-26T20:19:53.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-linear constant-profile plane waves in a cold plasma under an applied magnetic field†

Published online by Cambridge University Press:  13 March 2009

Yves J. Alloucherie
Yves J. Alloucherie
Affiliation:
Theoretical Division, Goddard Space Flight Center, Greenbelt, Maryland and University of Maryland, College Park, Maryland
Get access Rights & Permissions [Opens in a new window]

Abstract

Periodic plane waves propagating in a homogeneous cold Vlasov plasma under the influence of an external magnetic field B0 have been studied in this paper. Non-linear coupled differential equations for the two transverse components of the local magnetic field have been obtained for any angle α between B0 and the wave vector. Starting from the previously obtained exact solution for α = 90° and the zeroth-order solution for α = 0, two perturbation methods are used to obtain first-order solutions for α = 0 and intermediate angles. A numerical example has been worked out in detail for a specific value of the field energy density; although it is not possible to match the two sets of results rigorously, they seem to converge smoothly to the same limit.

Type
Articles
Information
Journal of Plasma Physics , Volume 1 , Issue 1 , February 1967 , pp. 55 - 74
Copyright
Copyright © Cambridge University Press 1967

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

Bogoliubov, N. N. & Mitropolsky, Y. A. 1961 Asymptotic Methods in the Theory of Non-linear Oscillations. New York: Gordon and Breach Science Publishers.Google Scholar
Byrd, P. E. & Friedman, M. D. 1954 Handbook of Elliptic Integrals for Engineers and Physicists. Berlin: Springer Verlag.CrossRefGoogle Scholar
Davis, L., Lüst, R. & Schlüter, A. 1958 Z. Naturforsch. 13 a, 916.CrossRefGoogle Scholar
Ferraro, V. C. A. 1955 Proc. Roy. Soc. (London) A 233, 310.Google Scholar
Jahnke, E. & Emde, F. 1945 Tables of Functions with Formulae and Curves. Now York: Dover Publications.Google Scholar
Kellogg, P. J. 1964 Phys. Fluids, 7, 1555.CrossRefGoogle Scholar
Montgomery, D. C. 1959 Phys. Fluids, 2, 585.CrossRefGoogle Scholar
Montgomery, D. C. & Tidman, D. A. 1964 Plasma Kinetic Theory. New York: McGraw Hill.Google Scholar