One of the most striking nonlinear quantum effect is the production of an electron-positron pair by an electric field in vacuum. The probability of this process was determined by Schwinger in 1951 and shows that the production of electron-positron pairs is exponentially small for electric fields small compared to the Schwinger field (which is the field necessary for an electron or positron to gain its rest mass energy in a Compton length). Unfortunately, despite the tremendous progress observed in the development of ultra-intense lasers in the last decades, the electric fields generated by current lasers are many orders weaker than the Schwinger field, so that many effects have exponentially small probabilities and are therefore unobservable. One can nevertheless observe certain nonlinear quantum effects in fields small compared to the Schwinger field by using ultra relativistic particles such that the field amplitude in the rest frame of the particles will be on the order of the Schwinger field. In this configuration, the stimulated pair production is a two-step process: nonlinear Compton scattering (emission of a hard photon) + Breit-Wheeler (decay of a hard photon into a pair).

We have included the two-step process in our massively parallel PIC code (using the OSIRIS 2.0 framework) via a Monte Carlo module, focusing on implementing in a self-consistent manner and multi-dimensions the interaction of the intense fields with the pair plasma dynamics. As an illustration we have investigated the pair cascades seeded by electrons in counter-propagating lasers pulses for ELI parameters.

The self-consistent modelling of these scenarios is challenging since some localized regions of ultra-intense field will produce a vast number of pairs that may cause memory overflow during the simulation. To overcome this issue, we have developed a merging algorithm that allows merging a large number of particles into fewer particles with higher particle weights while conserving local particle distributions. This algorithm is crucial to investigate the laser absorption in self-generated pair plasmas.

The movie shows the creation of a pair plasma in counter-propagating lasers pulses. The two lasers have each an intensity of 5 x 10²⁴ W/cm² and are initially focused on a thin target composed of cryogenic hydrogen. During the early interaction, the number of pairs increase exponentially until the plasma density reaches the critical density associated to the laser frequency. At this point the laser energy is severely depleted and absorbed to heat the plasma and to create a large number of photons. In this example, 50 % of the initial laser energy has been converted into pairs and photons.