Relativistic and ponderomotive self-focusing at laser–plasma interaction

The nonlinear plasma dielectric function due to relativistic electron motion is derived. From this, one can obtain the nonlinear refractive index of the plasma and estimate the importance of relativistic self-focusing in comparison with ponderomotive non-relativistic self-focusing at very high laser intensities. When the laser intensity is very high, ponderomotive self-focusing will be dominant. However, at some point, when the oscillating velocity of the plasma electrons becomes very large, relativistic effects will also play a role in self-focusing.