Dynamics of space-charge waves in the laser beat wave accelerator

The excitation of plasma waves by two laser beams, whose frequency difference is approximately the plasma frequency, is analyzed. Our nonlinear analysis is fully relativistic in the axial and transverse directions and includes mismatching of the laser beat frequency to the plasma frequency, time dependent laser amplitudes, and an applied transverse magnetic field (surfatron configuration). Our analytical results for the large amplitude plasma waves include an axial constant of motion, accelerating electric field, and its phase velocity. The analytical results in the weak laser power limit are in good agreement with numerical results obtained from the complete equations. The imposed transverse magnetic field is found to increase the effective plasma frequency, but has little effect on the plasma dynamics.