Relativistic filamentation of laser beams in plasma

We describe the results of a numerical code which models the relativistic selffocussing of high-intensity laser beams in plasmas by the nonlinear relativistic dependence of the optical constants on laser intensity. The plasma dynamics of 10¹³ W Nd glass lasers of 30 m initial beam diameter in nearly cut-off density plasmas is followed for a few picoseconds interaction time and 25 m depth into the plasma. Rapid relativistic selffocussing down to a beam diameter of one micron in a distance of the order of the original beam diameter is observed, as well as the production of GeV ions moving against the laser light.