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Cross-beam energy transfer between spatially smoothed laser beams

The crossing of two spatially smoothed laser beams amounts to the crossings of a large number of speckles. The energy transfer between two of these speckles is mediated by laser induced electron/ion density ripples that act as a Bragg grating. In a weakly Landau-damped plasma, this ion acoustic wave (IAW) may propagate from one crossing region to another, hence perturbing the local electron/ion grating [Oudin et al. Phys. Rev. Lett. 127, 265001 (2021)] even without phase shift between IAWs. In this paper, we investigate how the phase-shifted IAWs generated at the speckle scale interfere and affect the overall energy exchange. To this aim, we perform 2D particle-in-cell simulations with in-phase and out-of-phase Gaussian beams. In the latter situation, which better matches a smoothed laser beam, we find that the destructive interferences between the ion waves significantly reduce the energy exchange compared to the plane wave case. Additional 2D particle-in-cell simulations with random phase plate smoothed laser beams confirm the relevance of this effect in carbon plasma. A second effect is that cross-beam energy transfer (CBET) inhibition persists in strongly damped plasmas when the speckle radius is comparable with the IAW damping distance. There, the reduction in the IAW amplitude is attributed to the smallness of the speckle's envelop. These results are supported by a simple model that analytically estimates the CBET and clearly shows that neglecting the inhomogeneities in the laser intensity would usually lead to an overestimate of the energy exchange.