Short-range laser beam self-focusing in a plasma due to relativistic effects on the refractive index

The existing theory of relativistic self-focusing is extended to electron densities n_e close to and above the cutoff density n_ec. It is shown that relativistic self-focusing is possible at densities n_e≤n_ec for laser intensities of the order of 10^-3 times the relativistic intensity of 3.66×10¹⁸ W/cm² for an Nd glass laser. Additionally, very-short-range self-focusing is predicted over distances of the order of the initial beam diameter. The lowest threshold intensity is calculated and its dependences on the plasma temperature and ionization number are found. The increase in the effective collision frequencies due to instabilities is evaluated.