Hard X-ray emission by clusters in an intense femtosecond laser field during collective recombination

We consider the new mechanism of X-ray generation by clusters under irradiation by femtosecond laser pulses, the so-called collective photorecombination. We develop the theory of the photo-recombination of electrons that pass from atomic clusters at the outer ionization to the ground level of a homogeneously charged cluster. Such a cluster is considered to be a quantum potential well. The dipole approximation is inapplicable for this process. We conclude that X-ray photons in collective photorecombination on a charged cluster as a whole have an energy that is much larger than that for photorecombination on separate atomic ions inside the cluster. For a typical cluster of 2.25 × 10⁶ electrons, with a radius R = 300 Å, and a number density of plasma electrons n _e = 2 × 10²² cm^?3, we find that at a 5% outer ionization of this cluster, the energy of hard X-ray photons is 7.2 keV.