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We present a Monte Carlo collisional scheme that models single Compton scattering between leptons and photons in particle-in-cell codes. The numerical implementation of Compton scattering can deal with macro-particles of different weights and conserves momentum and energy in each collision. Our scheme is validated through two benchmarks for which exact analytical solutions exist: the inverse Compton spectra produced by an electron scattering with an isotropic photon gas and the photon-electron gas equilibrium described by the Kompaneets equation. It opens new opportunities for numerical investigation of plasma phenomena where a significant population of high energy photons is present in the system.

We demonstrate the possibility of probing for the first time the fully nonperturbative regime of quantum electrodynamics. By using tightly compressed and focused electron beams in a 100 GeV-class particle collider, beamstrahlung radiation losses can be mitigated, allowing the particles to experience extreme electromagnetic fields. Three-dimensional particle-in-cell simulations confirm the viability of this approach. The experimental forefront envisaged has the potential to establish a novel research field and to stimulate the development of a new theoretical methodology for this yet unexplored regime of strong-field quantum electrodynamics., Comment: Main paper: 7 pages 4 figures, 1 table; Supplement : 9 pages including 3 figures 1 table

The collision of ultrashort high-density $e^-$ or $e^-$ and $e^+$ beams at 10s of GeV, to be available at the FACET II and in laser wakefield accelerator experiments, can produce highly collimated $\gamma$ rays (few GeVs) with peak brilliance of $10^{27}~\mathrm{ph/s~mm^2 mrad^2 0.1\% BW}$ and up to $10^5$ nonlinear Breit-Wheeler pairs. We provide analytical estimates of the photon source properties and of the yield of secondary pairs, finding excellent agreement with full-scale 3D self-consistent particle-in-cell simulations that include quantum electrodynamics effects. Our results show that beam-beam collisions can be exploited as secondary sources of $\gamma$ rays and provide an alternative to beam-laser setups to probe quantum electrodynamics effects at the Schwinger limit.