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

Showers of γ rays and positrons are produced when a high-energy electron beam collides with a superintense laser pulse. We present scaling laws for the electron-beam energy loss, the γ-ray spectrum, and the positron yield and energy that are valid in the nonlinear, 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 >5×1021Wcm-2, today's high-intensity laser facilities are capable of producing O(104) positrons per shot via light-by-light scattering.