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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
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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

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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