Lasers generate the most extreme fields achievable in the laboratory on mesoscopic and macroscopic spatial scales (only highly ionised heavy ions have higher fields, but only over lengths of Angstroms). Ultra-intense lasers achieve fields of 1013V/m and greater, or in different units this fields are a 10 MV/µm or a 10GV/mm. Particle accelerators using radiofrequency waves typically accelerate particles to MeV to GeV over distances of many metres to kilometres – making the use of laser fields very attractive.
Electron accleration is most efficient if an accelerating field can co-move with electrons over large distances. This is achieved by driving a wake-wave (like the wave following a ship) using a powerful laser: The laser expels the electrons in its path (just like a ship pushes away the water) and the electrons feel a force that accelerates them. The figures show simulations oft the plasma wave without and with electron bunch being accelerated (the accelerating bunch ist the dot in V-shape).