A Nd-glass laser system is described which emits a 4 GW diffraction-limited laser pulse, at a radiance of 2×1017 W/cm2-sr. The device consists of a spatially mode-selected Q-switched oscillator, operating in the lowest-order HE11 transverse mode, followed by a series of amplifiers that are coupled with appropriate beam-expanding optics. A beam with a far-field pattern corresponding to Fraunhofer diffraction, is approached through use of the proper gain distribution in the first amplifier and a 50% over-expanded beam to allow uniform illumination of a physical aperture placed in front of the second amplifier. This system requires high optical-quality laser rods capable of transmitting a diffraction-limited beam. The induced optical distortions of the amplifiers during the pumping are minimized by appropriate Nd-doping concentration, surface treatment, flashtube arrangement, and filtering of the pump light, yielding uniformity of pumping over almost the full cross section. Some experimental results on long-path air breakdown, efficient second-harmonic generation, and durability of laser glasses are described. © 1969 The American Institute of Physics.