Comparison of ponderomotive self-channeling and higher-order relativistic effects on intense laser beams propagating in plasma channels

Nonlinear focusing of an intense laser beam propagating in a plasma channel is studied by means of the variational method including the effects of relativistic self-focusing (RSF), ponderomotive self-channeling (PSC), and higher-order relativistic nonlinearity (HRN). The effect of HRN defocuses the beam and has the same order of magnitude in the spot size evolution equation as that of PSC. The beam focusing singularity for laser power exceeding the critical power for RSF is prevented in the presence of HRN. And expression for the matched power is calculated.