Description
When a high-energy electron or positron interacts with a strong external field a part of its energy is converted into a photon through radiation reactions. Similarly, a high-energy photon interacting with the field can convert all its energy to an electron-positron pair. The combination of these two processes leads to a cascade of secondary particles (electrons, positrons, and photons that result from a series of electromagnetic interactions) also known as an Electromagnetics Shower (EMS).
With several petawatt laser facilities being functional worldwide and the long-standing objective to generate a plasma of electron-positron in the laboratory, EMS has become one of the most promising pathways to this goal [1]. Despite important progress in understanding the shower properties emerging from SF-QED interaction [2,3], no study provides an exact solution for the number of pairs, particle spectrum and electron-positron density generated during such interaction. Although advanced numerical tools to explore showers are readily available, a complete theory of QED showers in all regimes is yet to be found.
We introduce a generation-splitting method to investigate in depth its kinetic structure and time evolution [4]. Starting from the general kinetic equations, we derive explicit expressions for the shower multiplicity and particle spectra for short-time (before the incident particle has cooled down) and long-time (after the incident particle energy is exhausted) regimes.
We apply our approach to showers developing in the Coulomb field of neutral targets and strong external electromagnetic fields. We validate our analytical results through comparisons with numerical simulations using particle-in-cell codes, Geant 4, and an in-house Monte Carlo code. Our results are predictive for realistic future experiments: the collisions of electrons with a high-intensity laser and the collision of two electron beams [4]. Additionally, we consider the interaction of an electron beam with matter, to provide a simple criterion for pair plasma production as a function of the incident beam properties [5].
[1] G. Sarri et al., Nature Communications 10.1038/NCOMMS7747 (2015); C. D. Arrowsmith et al., Nature Communications 15, 10.1038/s41467-024-49346-2 (2024), H. Chen and F. Fiuza, Physics of Plasmas 30 , 020601 (2023).
[2] H. J. Bhabha and W. Heitler, Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences 159, 432 (1937); J. Carlson and J. Oppenheimer, Physical Review 51, 220 (1937); L. D. Landau and G. Rumer, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 166,213 (1938).
[3] T. Blackburn et al., Physical Review A 96, 022128 (2017); A. Mercuri-Baron et al., New Journal of Physics 23, 085006 (2021); M. Pouyez et al., Physical Review E 110, 065208 (2024)
[4] M. Pouyez et al., Physical Review Letters 134.13, 135001 (2025)
[5] M. Pouyez et al., arXiv:2505.18843 (2025)
