Self-focusing of an optical beam in a plasma

Self-focusing of an intense optical beam in a plasma is studied, including the nonlinear effects of both the relativistic electron mass and the ponderomotive potential due to the electromagnetic wave. An exact steady-state asymptotic solution of beam propagation in a localized solitary waveform is obtained in slab geometry. Amplitude-width scaling relations are obtained, which imply that the width is limited to be less than the square root of three collisionless skin depths. In the weakly relativistic limit our solution reduces to the solution obtained by Schmidt and Horton [Comm. Plasma Phys. Controlled Fusion E 9, 85 (1985)]. Solutions where the beam profile is of oscillatory nature, which correspond to the presence of the steady-state solution of a multiple-beamlet profile, are also presented. Finally, the asymptotic nature of the solitary wave is tested using a recently developed numerical particle simulation code.