Evolution of the autoresonant plasma wave excitation in two-dimensional particle-in-cell simulations

The generation of an autoresonantly phase-locked high amplitude plasma waves to the chirped beat frequency of two driving lasers is studied in two dimensions using particle-in-cell simulations. The two-dimensional plasma and laser parameters correspond to those that optimized the plasma wave amplitude in one-dimensional simulations. Near the start of autoresonant locking, the two-dimensional simulations appear similar to one-dimensional particle-in-cell results [Luo et al., Phys. Rev. Res. 6, 013338 (2024)] with plasma wave amplitudes above the Rosenbluth-Liu limit. Later, just below wave-breaking, the two-dimensional simulation exhibits a Weibel-like instability and eventually laser beam filamentation. These limit the coherence of the plasma oscillation after the peak plasma wave field is obtained. In spite of the reduction of spatial coherence of the accelerating density structure, the acceleration of self-injected electrons in the case studied remains at $70\%$ to $80\%$ of that observed in one dimension. Other effects such as plasma wave bowing are discussed.