Spatial evolution of a q-Gaussian laser beam in relativistic plasma

In a recent experimental study, the beam intensity profile of the Vulcan petawatt laser beam was measured; it was found that only 20% of the energy was contained within the full width at half maximum of 6.9 mu m and 50% within 16 mu m, suggesting a long-tailed non-Gaussian transverse beam profile. A q-Gaussian distribution function was suggested therein to reproduce this behavior. The spatial beam profile dynamics of a q-Gaussian laser beam propagating in relativistic plasma is investigated in this article. A non-paraxial theory is employed, taking into account nonlinearity via the relativistic decrease of the plasma frequency. We have studied analytically and numerically the dynamics of a relativistically guided beam and its dependence on the q-parameter. Numerical simulation results are shown to trace the dependence of the focusing length on the q-Gaussian profile.