Imaging electron angular distributions to assess a full-power petawatt-class laser focus

We present a novel technique to assess the focal volume of petawatt-class lasers at full power. Our approach exploits quantitative measurement of the angular distribution of electrons born in the focus via ionization of rarefied gas, which are accelerated forward and ejected ponderomotively by the field. We show that a bivariate ($\theta, \phi$) angular distribution, which was obtained with image plates, not only enables the peak intensity to be extracted, it also reflects nonideality of the focal-spot intensity distribution. In our prototype demonstration at intensities of a few $\times 10^{19}$ to a few $\times 10^{20}$ $\mathrm{W/cm^2}$, an f/10 optic produced a focal spot in the paraxial regime, allowing a plane-wave parameterization of the peak intensity ($\tan{\theta} \propto 1/a_0$) to be compared with our measurements; qualitative agreement was found. Furthermore, we show that scintillation detection of electrons is sensitive to real-time, shot-to-shot fluctuations, which means the technique would support single-shot measurement. Finally, we estimate that this approach should be usable with electrons up to intensities $\sim 10^{21}\ \mathrm{W/cm^2}$ before angular measurements start to be less effective. However, angular measurements will again be possible at $\sim 10^{24}\ \mathrm{W/cm^2}$ when protons become relativistic within a single cycle.