Analytical Theory of Relativistic Self-Trapping of Laser Light in Plasmas and Conditions for Its Implementation

Based on a nonlinear Schrödinger equation with relativistic nonlinearity, we derive an analytical solution describing waveguide propagation of a laser beam in plasma—the relativistic self-trapping (RST) regime of laser light. The developed theory of relativistic self-trapping is applicable over the entire range of laser intensities, from the weakly relativistic regime through the relativistic domain and up to the ultrarelativistic limit. From a practical standpoint, this all-range theory yields an important result: a relatively simple and easily applicable quantitative formula that analytically defines the condition for the implementation of the RST regime. This condition is expressed as a relationship between the transverse size of the plasma channel, the plasma density, and the laser intensity.