Unlimited Electron Acceleration in Laser-Driven Plasma Waves

It is shown that the limitation to the energy gain of $2{\left(\frac{\omega }{{\omega }_p}\right)}^{2}m{c}^2$ of an electron in the laser-plasma beat-wave accelerator can be overcome by imposing a magnetic field of appropriate strength perpendicular to the plasma wave. This accelerates particles parallel to the phase fronts of the accelerating wave which keeps them in phase with it. Arbitrarily large energy is theoretically possible.