Superluminal plasma wakefield acceleration

Laser wakefield acceleration (LWFA) experiments have demonstrated acceleration gradients of over 40 GV/m, almost three orders of magnitude above conventional radio-frequency accelerators. This tremendous acceleration cannot be maintained indefinitely, however, primarily due to dephasing~and depletion.~Recent advances in optics~have shown that reflective elements such as axi-parabolas [Smartsev et al, Optics Letters, 2019] can produce a line-focus. When used in~conjunction with an echelon, it becomes possible to tune the speed at which the laser peak intensity travels along this line-focus. As a result, this scheme can prevent dephasing by driving a wakefield at the vacuum speed of light [Palastro et al. PRL 2020]. Here, we perform particle-in-cell simulations with Osiris of superluminal plasma~waves excited by superluminal perturbations. By comparing to equivalent subluminal cases, we found that at superluminal speeds, plasma waves can~support arbitrarily high electric fields, free from the wave-breaking limits typical of subluminal plasma waves. We discuss the implications of these results~in the development of more compact and efficient LWFAs.