Signatures of quantum effects on radiation reaction in laser–electron-beam collisions

Two signatures of quantum effects on radiation reaction in the collision of a ${\sim}$ GeV electron beam with a high intensity ( ${>}3\times 10^{20}~\text{W}~\text{cm}^{-2}$ ) laser pulse have been considered. We show that the decrease in the average energy of the electron beam may be used to measure the Gaunt factor $g$ for synchrotron emission. We derive an equation for the evolution of the variance in the energy of the electron beam in the quantum regime, i.e. quantum efficiency parameter $\unicode[STIX]{x1D702}\not \ll 1$ . We show that the evolution of the variance may be used as a direct measure of the quantum stochasticity of the radiation reaction and determine the parameter regime where this is observable. For example, stochastic emission results in a 25 % increase in the standard deviation of the energy spectrum of a GeV electron beam, 1 fs after it collides with a laser pulse of intensity $10^{21}~\text{W}~\text{cm}^{-2}$ . This effect should therefore be measurable using current high-intensity laser systems.