Scaling laws for direct laser acceleration in a radiation-reaction dominated regime

We study electron acceleration within a sub-critical plasma channel irradiated by an ultra-intense laser pulse ($a_0>100$ or $I>10^{22}~\mathrm{W/cm^2}$). In this regime, radiation reaction significantly alters the electron dynamics. This has an effect not only on the maximum attainable electron energy but also on the phase-matching process between betatron motion and electron oscillations in the laser field. Our study encompasses analytical description, test-particle calculations and 2-dimensional particle-in-cell simulations. We show single-stage electron acceleration to multi-GeV energies within a 0.5 mm-long channel and provide guidelines how to obtain energies beyond 10 GeV using optimal initial configurations. We present the required conditions in a form of explicit analytical scaling laws that can be applied to plan the future electron acceleration experiments.