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Spatial distributions of electrons ionized and scattered from ultra-lowpressure gases are proposed and experimentally demonstrated as a method todirectly measure the intensity of an ultra-high intensity laser pulse. Analyticmodels relating the peak scattered electron energy to the peak laser intensityare derived and compared to paraxial Runge-Kutta simulations highlighting twomodels suitable for describing electrons scattered from weakly paraxial beams($f_{\#}>5$) for intensities in the range of $10^{18}-10^{21}$Wcm$^{-2}$.Scattering energies are shown to be dependant on gas species emphasizing theneed for specific gases for given intensity ranges. Direct measurements of thelaser intensity at full power of two laser systems is demonstrated both showinga good agreement between indirect methods of intensity measurement and theproposed method. One experiment exhibited the role of spatial aberrations inthe scattered electron distribution motivating a qualitative study on theeffect. We propose the use of convolutional neural networks as a method forextracting quantitative information of the spatial structure of the laser atfull power. We believe the presented technique to be a powerful tool that canbe immediately implemented in many high-power laser facilities worldwide.

Towards direct spatial and intensity characterization of ultra-high intensity laser pulses using ponderomotive scattering of free electrons