  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.
