Effect of pulse slippage on resonant second harmonic generation of a short pulse laser in a plasma

The process of second harmonic generation of an intense short pulse laser in a plasma is resonantly enhanced by the application of a magnetic wiggler. The wiggler of suitable wave number (k) over right arrow (0) provides necessary momentum to second harmonic photons to make harmonic generation a resonant process. The laser imparts an oscillatory velocity to electrons and exerts a longitudinal ponderomotive force on them at (2omega(1), 2 (k) over right arrow (1)), where omega(1) and (k) over right arrow (1) are the frequency and the wave number of the laser, respectively. As the electrons acquire oscillatory velocity at the second harmonic, the wiggler magnetic field beats with it to produce a transverse second harmonic current at (2omega(1), 2 (k) over right arrow (1) + (k) over right arrow (0)), driving the second harmonic electromagnetic radiation. However, the group velocity of the second harmonic wave is greater than that of the fundamental wave, hence, the generated pulse slips out of the main laser pulse and its amplitude saturates.