  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.
