Relativistic focusing and ponderomotive channeling of intense laser beams

The ponderomotive force associated with an intense laser beam expels electr ons radially and can lead to cavitation in plasma. Relativistic effects as well as ponderomotive expulsion of electrons modify the refractive index. A n envelope equation for the laser spot size is derived, using the source-de pendent expansion method with Laguerre-Gaussian eigenfunctions, and reduced to quadrature. The envelope equation is valid for arbitrary laser intensit y within the long pulse, quasistatic approximation and neglects instabiliti es. Solutions of the envelope equation are discussed in terms of an effecti ve potential for the laser spot size. An analytical expression for the effe ctive potential is given. For laser powers exceeding the critical power for relativistic self-focusing the analysis indicates that a significant contr action of the spot size and a corresponding increase in intensity is possib le.