A method and a system for generating intense, ultrashort pulses of XUV and soft X-ray radiation via high-order harmonic generation (HHG), the method comprising selecting a nonlinear solid target and a laser source; separating a beam from the laser source into a first laser beam and a second laser beam; focusing the first laser beam onto the nonlinear solid target, thereby generating a laser ablated plume; and compressing and frequency-doubling the second laser beam and directing a resulting second compressed and frequency-doubled laser beam to the laser ablated plume, thereby yielding high-order harmonic generation of radiation of photon energies in a range between 12 eV and 36 eV. A high-order harmonic source of radiation, comprising a nonlinear solid target; a laser source; a beam splitter separating a beam from the laser source into a first beam line and a second beam line; the first beam line comprising a first focusing unit directing a first, uncompressed, laser beam onto the nonlinear solid target, to generate a laser ablated plume; and the second beam line directing a second, compressed and frequency-doubled laser beam, to the laser ablated plume, yielding high-order harmonic generation of radiation of photon energies in a range between 12 eV and 36 eV.