Performance envelope of laser wakefield accelerators

Laser wakefield accelerator experiments have made enormous progress over the past $\sim 20$ years, but their promise to revolutionize high-energy particle sources is only beginning to be realized. To make the next step toward engineering LWFAs for different accelerator outcomes, we need more reliable and quantitative models to predict performance. Using the data from $>50$ published experiments, we estimate scalings and the performance envelope. We compare the observed scalings with several models in the literature. We find that the total beam energy (centroid energy times beam charge) scales almost linearly with laser energy, supporting the value of investment in progressively higher energy driver lasers. The dataset includes pulse durations from 8 to 160 fs, but only laser wavelengths of 800 nm and 1 \si{\micro\meter}, meaning we could not check proposed wavelength scalings for alternative laser technologies. As a benchmark next-generation case, the observed scalings suggest that achieving a 100-GeV LWFA stage will require a $\gtrsim 30$ PW laser operating at electron density $<10^{17}/$cm$^3$.