Overcoming the laser wakefield acceleration dephasing limit using multiple driver pulses

The electric field in laser-driven plasma wakefield acceleration is orders of magnitude higher than conventional radio-frequency cavities, but the energy gain is limited by dephasing between the ultra-relativistic electron bunch and the wakefield, which travels at the laser group velocity. We present a way to overcome this limit within a single plasma stage, by using a train of laser pulses in a modulated density profile. This creates a succession of acceleration sections, where the pulses' wakefields combine constructively, and non-resonant drift sections, where the wakefield disappears and the electrons rephase. In a two-dimensional particle-in-cell simulation, electrons were accelerated to over three times the energy obtained from a uniform plasma. Minimising laser depletion limits the scheme to sub-relativistic laser intensities.