Scaling laws of laser ponderomotive electron acceleration for characterizing ultra-intense laser focal parameters

Electron scattering offers a promising approach for directly characterizing the focal parameters of ultrashort high-intensity laser pulses. Nevertheless, a robust quantitative correlation between the quality of the scattered electrons and the laser parameters has yet to be established. Here we study the scaling laws of electron scattering driven by a relativistic Gaussian laser both with ponderomotive theory and multiparametric test-particle simulations. It is shown that the electron exhibits three typical kinds of scattering trajectories under different ratios of cτ 0 /w 0 , each associated with a distinct scaling relation. The electron scattering angle θ c dependence on three laser parameters, i.e., peak amplitude a 0 , spot size w 0 , and pulse duration τ 0 , thus degenerates to a dependence on only two parameters, a 0 and cτ 0 /w 0 . These theoretic predictions are confirmed by the multiparametric test-particle simulations. Based on theoretically derived formulas combined with numerical fitting, a robust scaling relation of the electron scattering angle with respect to three critical laser focal parameters is obtained. This scaling relation is validated by comparing with previous experiment results and it is shown to be applicable over a wide range of laser parameters. This scaling relation can provide a sound theoretical basis for electron scattering to characterize laser focal parameters at full power.