Journal of Chemical and Pharmaceutical Research (ISSN : 0975-7384)

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Original Articles: 2010 Vol: 2 Issue: 4

A Mathematical Modeling Self-Focusing Of Langmuir Waves in Relativistic Plasma


In this paper we study the self-focusing of a Langmuir wave with a Gaussian distribution of intensity along its wave front. The relativistic oscillation of the mass of the electrons in the field of Langmuir waves and also the relativistic electron ponderomotive force are shown to have a major effect on nonlinear dynamics of Langmuir waves. Both the relativistic oscillation of the mass and the electron ponderomotive force promote self-focusing of the Langmuir wave. The Landau damping of the Langmuir wave opposes the self-focusing effect. When damping is unimportant, the beam gets more and more focused as it advances. A paraxial ray theory of selffocusing, through relativistic nonlinearity, reveals that the self focusing length Rn ~a vth/ vosc where a is the radial width of the Langmuir wave and vth and vosc are the electron thermal and oscillatory velocities