Relativistic nonlinear effects in plasmas

Abstract

The purpose of this article is to present a review of the nonlinear effects associated with relativistic electron-mass variation and the ponderomotive force in unmagnetized as well as magnetized plasmas. Many high-frequency waves can become unstable with respect to the electron-mass modulation and the excitation of low-frequency density fluctuations. The nonlinear equations which govern the evolution of the modulationally unstable waves are derived. The phenomena of soliton formation, radiation collapse, and profile modification are investigated. Finite amplitude theories of the envelope solitons are reviewed. In a multidimensional situation, the electromagnetic waves can undergo self-focusing. The use of the variational methods allows one to calculate the nonlinear wavenumber and radius of the self-focused laser beams. Analytical solutions for the self-trapped radiation and the three-dimensional relativistic solitons are obtained. It is found that magnetized plasmas can support the propagation of new types of ultrarelativistic electromagnetic waves. The modulational instability of the latter is analyzed. Furthermore, it is shown that the relativistic ponderomotive force in a magnetized plasma can produce large amplitude field-aligned electrostatic potentials which can effectively accelerate particles to very high energies. Finally, we consider the nonlinear propagation of intense electromagnetic waves in electron-positron plasmas. Possible applications in inertial fusion, beat-wave particle accelerator, rf heating of magnetically confined plasmas, and pulsar radiation are pointed out.