Direct particle acceleration by two identical crossed radially polarized laser beams

Electrons and α particles injected midway between two ultrahigh intensity crossed laser beams of radial polarization are shown to be accelerated in vacuum to several gigaelectron volts and to have average energy gradients in excess of $150$ GeV/m. A unique model of the crossing beams is suggested, which maximizes the particle energy gain and minimizes the particle-beam diffraction.