Scaling laws for positron production in laser--electron-beam collisions

Showers of $\gamma$-rays and positrons are produced when a high-energy electron beam collides with a super-intense laser pulse. We present scaling laws for the electron beam energy loss, the $\gamma$-ray spectrum, and the positron yield and energy that are valid in the non-linear, radiation-reaction–dominated regime. As an application we demonstrate that by employing the collision of a $>$GeV electron beam with a laser pulse of intensity $>5\times {10}^{21}{\text{Wcm}}^{-2}$, today’s high-intensity laser facilities are capable of producing $O({10}^4)$ positrons per shot via light-by-light scattering.