Spatial Phase Reconstruction for Plasma Diagnostic by TW-class Laser in the Proton Driven Plasma Wakefield Acceleration Experiment, AWAKE, in CERN

The spatial phase of a TW-class laser was reconstructed for establishing the laser initial conditions for the ionization and propagation process in a ten meter Rubidium vapor source. The near field intensity and the intensity at the entrance of the vapor source were unitized to reconstruct the spatial phase by a modified Gerchberg-Saxton algorithm. The other two downstream intensity profiles were taken for examining the reconstructed phase by propagating the beam with the reconstructed phase for five and ten meters. A defined root mean squared error between the reconstructed intensity profile and the entrance intensity data has been demonstrated decreasing as the algorithm iterates. The agreement between the downstream data and the reconstructed profiles increases as the algorithm iterates as well.