Conditions for amplification of light in a plasma filament formed at the caustic of an axicon as a result of optical breakdown of a gas

An analysis is made of the conditions favoring formation of a long thin filament of a multiply charged plasma at the caustic of an axicon as a result of optical breakdown of a gas and the conditions for the amplification of light in such a filament. Estimates are obtained of the energy and duration of a heating laser pulse necessary for the ionization and heating of the plasma. The ranges of electron densities and temperatures in which the gain can exceed 1 cm^{– 1} are estimated for C VI and He II ions.