Exploiting high-energy electron beams colliding into high-intensity laser pulses brings an opportunity to reach high values of the dimensionless rest-frame acceleration $\chi$ and thereby invoke processes described by strong-field quantum electrodynamics (SFQED). Measuring deviations from the results of Furry-picture perturbation theory in SFQED at high $\chi$ can be valuable for testing existing predictions, as well as for guiding further theoretical developments. Nevertheless, such experimental measurements are challenging due to the probabilistic nature of the interaction processes, dominating signals of low-$\chi$ interactions and limited capabilities to control and measure the alignment and synchronization in such collision experiments. Here we elaborate a methodology of using approximate Bayesian computations for drawing statistical inferences based on the results of many repeated experiments despite partially unknown collision parameters that vary between experiments. As a proof-of-principle, we consider the problem of inferring the effective mass change due to coupling with the strong-field environment.

The availability of ever stronger, laser-generated electromagnetic fields underpins continuing progress in the study and application of nonlinear phenomena in basic physical systems, ranging from molecules and atoms to relativistic plasmas and quantum electrodynamics. This raises the question: how far will we be able to go with future lasers? One exciting prospect is the attainment of field strengths approaching the Schwinger critical field ${E}_{\mathrm{cr}}$ in the laboratory frame, such that the field invariant ${E}^2-{c}^2{B}^2>{E}_{\mathrm{cr}}^2$ is reached. The feasibility of doing so has been questioned, on the basis that cascade generation of dense electron–positron plasma would inevitably lead to absorption or screening of the incident light. Here we discuss the potential for future lasers to overcome such obstacles, by combining the concept of multiple colliding laser pulses with that of frequency upshifting via a tailored laser–plasma interaction. This compresses the electromagnetic field energy into a region of nanometre size and attosecond duration, which increases the field magnitude at fixed power but also suppresses pair cascades. Our results indicate that laser facilities with peak power of tens of PW could be capable of reaching ${E}_{\mathrm{cr}}$. Such a scenario opens up prospects for the experimental investigation of phenomena previously considered to occur only in the most extreme environments in the universe.

Although, for current laser pulse energies, the weakly nonlinear regime of laser wakefield acceleration is known to be the optimal for reaching the highest possible electron energies, the capabilities of upcoming large laser systems will provide the possibility of running highly nonlinear regimes of laser pulse propagation in underdense or near-critical plasmas. Using an extended particle-in-cell (PIC) model that takes into account all the relevant physics, we show that such regimes can be implemented with external guiding for a relatively long distance of propagation and allow for the stable transformation of laser energy into other types of energy, including the kinetic energy of a large number of high energy electrons and their incoherent emission of photons. This is despite the fact that the high intensity of the laser pulse triggers a number of new mechanisms of energy depletion, which we investigate systematically.