Abstract
The measurement of peak laser intensities exceeding $10^{20} \text{W/cm$^2$}$ is in general a very challenging task. We suggest a simple method to accurately measure such high intensities up to about $10^{23} \text{W/cm$^2$}$, by colliding a beam of ultrarelativistic electrons with the laser pulse. The method exploits the high directionality of the radiation emitted by ultrarelativistic electrons via nonlinear Thomson scattering. Initial electron energies well within the reach of laser wake-field accelerators are required, allowing in principle for an all-optical setup. Accuracies of the order of 10% are theoretically envisaged.
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