Relativistic self-focusing leading to conditions for the fast ignitor

Based on relativistic self-focusing and results using the paraxial approximation. Relativistic self-focusing for the conditions of the fast ignitor are studied in comparison with the results gained from different numerical methods. Cases of different degrees of the paraxial approximation are evaluated. Introduction: There have been numerous discussions on the concept of the fast ignitor and the formation of a channel through the ablating plasma to the compressed core, where the ignition is to occur. Although we are unable to present all the relevant calculations needed here, we apply a Fourier transform and convolution method to solving the wave equation and getting gaussian solutions for the laser beam. These are then applied to the relativistic self-focusing of the laser beam in plasma to determine the self-focusing length of the beam at the laser-plasma interface.