A gain model for x-ray lasing at ∼2.8 A in an intense laser irradiated gas of xenon clusters

A variety of experiments have been carried out (Borisov et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 105602) in which a gas of xenon clusters containing between 5 and 20 atoms/cluster (Schroeder et al 2001 J. Phys. B: At. Mol. Opt. Phys. 34 297) was irradiated with a ∼230 fs pulse of 248 nm laser radiation focused to an intensity level of ∼1.6 x 1019 W cm-2. In these experiments, a channel was formed as the laser beam self-focused. Amplified x-ray emissions at ∼2.8 A were observed along the direction of the channel with measured gain coefficients of between 27 and 104 cm-1 being cited. In this paper, a xenon gain model is assembled, built from FAC generated data (Gu 2008 Can. J. Phys. 86 675), which allows gains comparable in magnitude to be calculated under a set of restrictive assumptions about the laser beam-cluster dynamics. The model includes a detailed description of the ionization and excitation dynamics of the Ni- and Co-like ionization stages into which a description of hole state generation in Co-like xenon is made through the photoionization (or collisional ionization) of 2s and 2p electrons. Our calculations show that, under specialized initial conditions and sufficiently high pumping rates, gains larger than 50 cm-1 are achievable in one of the seven radiative decays of the Co-like hole states. The calculated gains are sensitive to the ion density, the risetime of the photoionization rates and the early time heating rate of the cluster plasma.