Proton Acceleration in a Laser-driven Relativistic Electron Vortex

We show that when a solid plasma foil with a density gradient in the front surface is irradiated by an intense laser pulse at a grazing angle ~ 10^o, a relativistic electron vortex is excited in the near-critical-density layer after the laser pulse depletion. Due to the asymmetry introduced by nonuniform background density, the vortex drifts at a constant velocity, typically 0.2 - 0.3 of the speed of the light. The strong magnetic fields inside the vortex lead to significant charge separation where the initially stationary protons can be captured and accelerated to twice of the drifting velocity (100-200 MeV). A representative case with laser intensity at 10²¹ W/cm² is discussed, in which a 140 MeV quasi-monoenergetic proton beam (energy spread ~10%) is obtained. We demonstrating the vortex velocity, and therefore the maximum proton acceleration energy, are determined by E x B drift of the laser-driven electrons in the self-generated fields. We derive an analytical model that can describe the main findings of the simulations.