The light source contains a gas-filled chamber with a plasma sustained by a focused beam of a continuous wave laser. The means for plasma ignition is a solid-state laser system which generates two pulsed laser beams: in a free running mode and in a Q-switched mode. The solid-state laser system contains single active element and its optical cavity is equipped with a Q-switch overlapping only part of a cross section of the intracavity laser beam. One pulsed laser beam provides an optical breakdown after which another pulsed laser beam ignites the plasma, the volume and density of which are sufficient for stationary sustenance of the plasma by the focused beam of the continuous wave laser. EFFECT: simplification of the design of the light source, increase of its reliability and ease of use, creating on this basis of powerful electrode-free high-brightness broadband light sources with high spatial and energy stability.