Pulse evolution and plasma-wave phase velocity in channel-guided laser-plasma accelerators

The self-consistent laser evolution of an intense, short-pulse laser exciting a plasma wave and propagating in a preformed plasma channel is investigated, including the effects of pulse steepening and energy depletion. In the weakly relativistic laser intensity regime, analytical expressions for the laser energy depletion, pulse self-steepening rate, laser intensity centroid velocity, and phase velocity of the plasma wave are derived and validated numerically.