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Backward Raman amplification of laser pulses in plasmas can produce nearlyrelativistic unfocused output intensities and multi-exawatt powers in compactdevices. The largest achievable intensity depends on which of major competitiveprocesses sets this limit. It is shown here that the relativistic electronnonlinearity can cause saturation of the leading amplified spike intensitybefore filamentation instabilities develop. A simple analytical model for thesaturation, which supports numerical simulations, is suggested. The upper limitfor the leading output spike unfocused intensity is calculated.

Saturation of the leading spike growth in backward Raman amplifiers