Fig. 1. Illustration of the experimental setup, showing the orientation of the laser–plasma interaction and the main diagnostics. The laser was focused, with an f/2.5 90° diamond-turned off-axis parabolic mirror (OAP), to a 1.6 μm radius focal spot containing a median of of pulse energy. The plane of the laser–plasma interaction was monitored by imaging self-emission at 800 nm at to the laser propagation axis.

Fig. 2. (a) Proton and (b) electron energy spectra from the rear side of the target during an automated target position scan () with a 12 μm Kapton tape and an on-target laser energy of mJ. (c) Average proton spectra (and standard deviation) for different positions as indicated in the legend. The proton spectra are recorded by the time-of-flight diamond detector. Each column of the waterfall plots is the average of the 10 shots from each burst. The scan comprises 31 bursts at different target positions spaced at 7.3 μm intervals along the laser propagation axis. Negative values of are when the target plane is closer to the incoming laser pulse and is the target at the best focus of the laser pulse. The magenta data points, connected with a guide line, indicate the burst-averaged 95th percentile energy as well as the standard deviation of this value across the burst.

Fig. 3. One-dimensional scans of (a) and (c) target z-position and (b) and (d) astigmatism for 12 μm thickness Kapton tape and a pre-plasma laser energy of mJ. The electron and proton flux are plotted in (a) and (b), and the specularly reflected fundamental and second harmonic laser signals are plotted in (c) and (d). All fluxes are normalized to their observed maxima over the 2D parameter scans. Two-dimensional scans of electron and proton flux are shown in (e) and (f), with the average detected electron energy and the maximum (95th percentile) proton energies shown in (g) and (h), respectively. The 2D scan is a result of 143 bursts of 15 shots and the datapoints are the mean of each individual burst.

Fig. 4. Laser pulse temporal profiles as measured by the on-shot SPIDER diagnostic for the results of the 1D scan (Figure 2), 2D scan (Figure 3) and optimization (Figure 5). The integrals of the signals are set by independent measurements of the on-target laser energy, which were mJ (1D scan), mJ (2D scan) and mJ (optimization). The corresponding measured FWHM pulse widths were fs, fs and fs.

Fig. 5. Optimization of the 95th percentile proton energy determined by the rear-surface time-of-flight diagnostic through the adjustment of the laser wavefront and position of target along the laser propagation direction (). The top panel shows the measured values of the proton energy (median and median absolute difference of each burst) as a function of the burst number (black points and error bars, respectively), together with the model predicted optimum after each burst (red line and shaded region) as well as the final optimal value from the model (blue horizontal line). The variation of each control parameter (given in micrometres) is shown in the lower plots (black points) along with the final optimized values (blue horizontal line), also as functions of the burst number. The best individual burst is indicated by the vertical magenta line in each plot and it can be seen that, for all parameters, the experimental parameters fall very close to the optimum value predicted by the model (e.g., they are close to the horizontal blue line). For this data series, each burst contained 20 shots, the target was 12 μm Kapton tape and the laser energy was mJ.

Fig. 6. Reconstructed laser intensity profiles at for (a) , (b) , (c) μm and (d) for the optimal pulse (burst 53) from the optimization shown in Figure 5. The peak intensity of each focus was 2.7 × 10¹⁹, 5.1 × 10¹⁹, 2.9 × 10¹⁹ and 3.2 × 10¹⁹ W cm⁻², respectively.