Driving laser pulse evolution in a hollow channel laser wakefield accelerator

An analytic and numerical study of the coupling between a high-intensity laser pulse and a plasma wake is presented, in the context of laser wakefield acceleration in a hollow channel. Laser wavelength reddening and pulse length shortening are qualitatively described using simple scaling laws. One-dimensional self-consistent equations are derived and numerically solved to provide a more detailed description of the laser pulse evolution for the case of propagation in a uniform plasma. These equations are extended to treat the case of laser pulse propagation in a hollow channel. The coupling between the plasma and the laser pulse is calculated using energy conservation. The model obtained provides a simple method for inferring the plasma wake characteristics from measurement of changes in phase and amplitude of the driving laser pulse.