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Self-focusing of electormagnetic waves as a result of relativistic electron-mass variation

Published online by Cambridge University Press:  13 March 2009

Karl H. Spatschek
Karl H. Spatschek
Affiliation:
Fachbereich Physik, Universität Essen, D-4300 Essen, F. R. G.
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Abstract

Relativistic electron-mass variations due to the presence of intense electromagnetic radiation in the plasma cause a nonlinear refractive index. Using a variational principle the latter is obtained up to fourth order in the electric field amplitude and it is shown that nonlinear effects of the second order lead to self-focusing of a beam of radiation. By nonlinear optics considerations, the self- focusing length of an axially symmetric beam is obtained. Including higher- order dispersive effects it is shown that within the thin-beam approximation thecomplex electric field envelope obeys a cubic nonlinear Schrödinger equation with an attractive self-consistent potential. The cylindrically symmetric nonlinear Schrödinger equation predicts collapse of the radiation at the self-focusing distance. The nature of the self-focusing singularity is analysed and it is shown that higher-order nonlinearities saturate the amplitude. Then oscillations of beam radius along the axial direction occur.

Type
Research Article
Information
Journal of Plasma Physics , Volume 18 , Issue 2 , October 1977 , pp. 293 - 303
Copyright
Copyright © Cambridge University Press 1977

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