Analytic theory of relativistic self-focusing for a Gaussian light beam entering a plasma: Renormalization-group...

Using the renormalization-group approach, we consider an analytic theory describing the formation of a self-focusing structure of a laser beam in a plasma with relativistic nonlinearity for a given radial intensity distribution at the entrance and derive approximate analytic solutions. We study three stationary self-focused waveguide propagation modes with respect to controlling laser-plasma parameters for a Gaussian radial intensity distribution at the plasma boundary. The proposed theory specifies the domains and their boundaries on the plane of the controlling parameters where (1) self-trapping, (2) self-focusing on the axis, and (3) tubular self-focusing solutions occur. We review the concept of the critical power and show that it must be correlated to the form of the entering light pulse and its value corresponding to the minimum power that admits self-channeling can be significantly lower than the widely used value 17(ω^{2}/ω_{pe}^{2}) GW.