Towards Laboratory Electron-Positron Plasma via Electromagnetic Showers in Matter

The kinetic equations describing electromagnetic showers from high-energy electron beams interacting with targets are solved, building on the analytical framework developed in [Phys. Rev. Lett. 134, 135001 (2025)]. Two regimes are defined by the ratio of the target thickness L to the radiation length Lr , which depends on the electron energy and target composition. For thin targets (L < Lr ), we derive explicit expressions for the spectra of produced photons and pairs, as well as the number of pairs. For thick targets (L>Lr ), we obtain the total pair number and photon spectrum. Analytical results agree well with Geant4 simulations, which show that significant pair escape requires L<Lr . The divergence, density and characteristic dimensions of the escaping pair jets are obtained, and a criterion for pair plasma formation is derived. While current laser wakefield beams are not well adapted, multi-petawatt lasers may provide new electron or photon sources suitable for laboratory pair plasma production, opening new avenues for studying extreme plasma astrophysics in the laboratory.