[en] A method of producing x-rays by directing radiant energy from a laser onto a target is described. Conversion efficiency of at least about 3 percent is obtained by providing the radiant energy in a low-power precursor pulse of approximately uniform effective intensity focused onto the surface of the target for about 1 to 30 nanoseconds so as to generate an expanding unconfined coronal plasma having less than normal solid density throughout and comprising a low-density (underdense) region wherein the plasma frequency is less than the laser radiation frequency and a higher-density (overdense) region wherein the plasma frequency is greater than the laser radiation frequency and, about 1 to 30 nanoseconds after the precursor pulse strikes the target, a higher-power main pulse focused onto the plasma for about 10^-3 to 30 nanoseconds and having such power density and total energy that the radiant energy is absorbed in the underdense region and conducted into the overdense region to heat it and thus to produce x-rays therefrom with the plasma remaining substantially below normal solid density and thus facilitating the substantial emission of x-rays in the form of spectral lines arising from nonequilibrium ionization states