Relativistic Self-Focusing of Short-Pulse Radiation Beams in Plasmas

An envelope equation is derived which describes the radial evolution of a radiation beam propagating through a plasma. The radiation envelope equation contains a defocusing term due to diffraction spreading and a focusing term due to relativistic oscillations of the plasma electrons. The case of a constant density background plasma is analyzed in detail and an expression for a critical laser power is derived. For powers exceeding the critical power, the radiation envelope oscillates and does not diffract. Under certain conditions the radiation beam propagates through the plasma with a constant radius envelope.