Analysis and simulation of Raman backscatter in underdense plasmas*

A new formalism to describe the spatiotemporal evolution of relativistic Raman backscatter ~RBS! of ultrashort laser pulses in underdense plasma has been developed. This theory is based on an eikonal representation for the RBS field and averaging over the oscillation frequency. Equations are derived for the evolution of the RBS radiation field amplitude and phase and for particle motion in the ponderomotive potential of the pump and RBS fields. A technique similar to that used in Raman free electron lasers is used to include the plasma density oscillation and its electric field in the particle equations. The equations have been solved numerically in a code that provides an accurate description of the nonlinear electron motion on a short spatial scale of half the radiation wavelength, while at the same time evolving the laser field on a much coarser scale, characteristic of the growth rate of the instability. Two-dimensional nonlinear effects, such as the return current, are analytically estimated and phenomenologically incorporated in the numerical code. The results of recent ~RBS! experiments are compared with the analytical and numerical predictions of the theory. A statistical theory of the linear RBS instability growing from plasma noise is developed. It is found that in the nonlinear regime backscattered radiation, seeded by random density fluctuations in the plasma, breaks up into spikes, which exhibit superradiant behavior. These effects might explain the spikiness of the RBS spectra in the nonlinear regime. © 1997 American Institute of Physics. @S1070-664X~97!93005-6#