Properties of Pair Plasmas Emerging from Electromagnetic Showers in Matter
Electromagnetic showers from high-energy electron beams interacting with a target are a promising path to creating pair plasmas in the laboratory. Here, we solve analytically the kinetic equations describing this process. Two regimes are defined by the ratio of the target thickness $L$ to the shower length $L_{\rm{sh}}$, which depends on the electron energy and target composition. For thin targets ($L < L_{\rm{sh}}$), we derive explicit expressions for the spectra of produced photons and pairs, as well as the number of pairs. For thick targets ($L > L_{\rm{sh}}$), we obtain the total pair number and photon spectrum. Analytical results agree well with Geant4 simulations, and it is found that significant pair escape requires $L < L_{\rm{sh}}$. The divergence, density and characteristic dimensions of the escaping pair jets are derived, and a criterion for pair plasma formation is obtained. 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.