Attaining a strong-field QED signal at laser-electron colliders with optimized focusing

Colliding bunches of high-energy electrons with intense laser pulses provides a basis for studying strong-field QED processes enabled by high values of quantum non-linearity parameter $\chi$. Nevertheless, the signal deconvolution is intricate due to probabilistic nature of the processes and shot-to-shot variation of the impact parameter, which disfavors the use of tight focusing. We propose a concept for distinguishing the signal of high-$\chi$ emissions that enables the use of optimal focusing to attain the highest $\chi \approx 5.25 \left(\varepsilon / (\text{1 GeV})\right)\left(P/(\text{1 PW})\right)^{1/2}\left((\text{1 }\mu\text{m})/\lambda\right)$ for a given electron energy $\varepsilon$, laser power $P$ and wavelength $\lambda$. Reaching such $\chi$ with f/2 focusing requires more than 10 times higher power.