Saturation of the leading spike growth in backward Raman amplifiers

Backward Raman amplification of laser pulses in plasmas can produce nearly relativistic unfocused output intensities and multi-exawatt powers in compact devices. The largest achievable intensity depends on which of major competitive processes sets this limit. It is shown here that the relativistic electron nonlinearity can cause saturation of the leading amplified spike intensity before filamentation instabilities develop. A simple analytical model for the saturation, which supports numerical simulations, is suggested. The upper limit for the leading output spike unfocused intensity is calculated.