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Experiments were performed on laser wakefield acceleration in the highly nonlinear regime. With laser powers P2. 5 GeV, in fields exceeding 500 GV m^-1, with more than 80 pC of charge at energies E>1 GeV. Three-dimensional particle-in-cell simulations show that using an oversized spot delays injection, avoiding beam loss as the wakefield undergoes length oscillation. This enables injected electrons to remain in the regions of highest accelerating fields and leads to a doubling of energy gain as compared to results from using half the focal length with the same laser.
Põder et al. (Fri,) studied this question.