Scattering of relativistically intense laser pulses in cold underdense plasmas

Analytical theory is developed for plane linearly polarized relativistically intense electromagnetic waves propagating in cold underdense plasmas. Growth rates of the instability of these waves, both quasi-monochromatic and comprising a flux of photons with different frequencies, are calculated using a special numerical technique. For the relativistically high intensities both forward and backward Raman scattering by plasmons occurs and radiation harmonics are generated. The shape of the growth rate distribution at the center of each harmonics band is formed primarily by the fluid dynamics analog of the Compton effect and its edges are due to excitation of Langmuir noise.