  We show that when a solid plasma foil with a density gradient on the front
surface is irradiated by an intense laser pulse at a grazing angle, around 80
degrees, a relativistic electron vortex is excited in the near-critical-density
layer after the laser pulse depletion. The vortex structure and dynamics are
studied using particle-in-cell simulations. Due to the asymmetry introduced by
nonuniform background density, the vortex drifts at a constant velocity,
typically 0.2 to 0.3 times the speed of light. The strong magnetic field inside
the vortex leads to significant charge separation; in the corresponding
electric field initially stationary protons can be captured and accelerated to
twice the velocity of the vortex (100-200 MeV). A representative scenario -
with laser intensity of 10^21 W/cm^2 -is discussed: two dimensional simulations
suggest that a quasi-monoenergetic proton beam can be obtained with a mean
energy 140 MeV and an energy spread of about 10%. We derive an analytical
estimate for the vortex velocity in terms of laser and plasma parameters,
demonstrating that the maximum proton energy can be controlled by the incidence
angle of the laser and the plasma density gradient.
