  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.
