A high intensity laser can accelerate electrons in a helium gas jet to hundreds of MeV in less than a mm. The acceleration takes place in a plasma wave set up in the wake of the laser pulse. In accelerators widely in use today, the limiting accelerating potential is determined by the threshold for electric breakdown in vacuum. Here, the plasma is already effectively at electric breakdown and accelerating fields several orders of magnitude (~4) larger are possible.
When a beam of light is focused in gas, the length of the focal spot is normally limited by diffraction. If the laser intensity is high enough, the gas will first be ionized forming a plasma. Electrons in the plasma will then oscillate in the laser electric field, approaching the speed of light for light intensities exceeding 1018 W/cm2. This leads to a relativistic mass increase of the electrons, and in turn a decrease of the refractive index of the plasma (through the plasma frequency). As the transverse profile of the laser intensity in the focal spot has a maximum in the centre, the refractive index will have a maximum here. The plasma medium will act as a positive lens induced by the laser itself as it travels through the gas.
Laser wake-field acceleration
The ponderomotive force expels electrons from the interior of the laser focus. A large electrostatic restorative force pulls the electrons back after the light pulse has passed. This sets up a plasma wave in the wake of the laser pulse. The wave travels with the group speed of light in the plasma. Electrons injected into the plasma wave at a speed close to that of the wave can surf along, gaining substatial energy before outrunning it.