Fig. 3. Experimental target density scan showing maximum proton energies, emission distributions, and transmitted light fractions.

a Acquired data set of maximum proton energies $E_{\max }$ detected in laser propagation direction with respect to the shadow diameter d determined by optical probing for each shot. The blue dashed line indicates the trend of the average $E_{\max }$ as a guide for the eye. The orange circles highlight best performing shots within 4 μm bins of the shadow diameter. The labels (1)-(3) refer to the proton energy spectra in Fig. 2 (rows from top to bottom). b shows the ratio between $E_{\max }$ measured along 0^∘ with respect to the 45^∘ emission direction, increasing with growing pre-expansion of the target. c The laser light which is transmitted through the jet, captured by the ceramic screen and normalized to shots without a target increases with growing pre-expansion. Shadow diameter values ≥ 30 μm in a, c are set in brackets as they correspond to targets which are already transparent to the 515 nm probe beam light, and therefore only represent a lower limit.