X-ray amplification dynamics at ∼2.8 Å in intense laser irradiated xenon clusters: multiple hole dynamics

Abstract

In a series of experiments (Borisov et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 105602, and references 1 through 7 cited in this paper), the amplification of 2.71–2.88 Å x-rays was observed, gain coefficients between 27 and 104 cm−1 were measured, and a number of conjectures were made concerning the ionization stages that were involved in the x-ray amplification. It was conjectured, for example, that x-ray emissions from hole states in Cl-, K-, Ca-, and Ti-like xenon were being amplified. In this paper, our earlier xenon gain model (Petrova et al 2010 J. Phys. B: At. Mol. Opt. Phys. 43 025601) is extended to include single- and double-hole state production within the Fe-like ionization stage in addition to single-hole state production within the Co-like ionization stage in order to assess these conjectures. The gain model, based on flexible atomic code generated data (Gu 2008 Can. J. Phys. 86 675), includes Co-like and Fe-like hole-state generation in xenon through photoionization of 2s and 2p electrons. The hole-state dynamics is self-consistently coupled to an extensive collisional-radiative dynamics of the Ni-, Co-, and Fe-like ionization stages of xenon. In addition, the model includes tunnelling ionization rates that confirm the initial condition assumptions that were made in our earlier paper, and they are needed to support the interpretations of the measured broadband x-ray data. With the use of tunnelling ionization rates, we demonstrate how all of the N-shell, n = 4, electrons are striped from a xenon atom in less than a femtosecond at laser intensities larger than 1019 W cm−2. Our calculations also show that, under these initial conditions and with sufficiently high pumping rates (⩾1014 s−1), a range of gains larger than 50 cm−1 are achievable under select conditions from both Co- and Fe-like xenon single hole radiative decays, in conformity with experimental observations. However, the calculated gain coefficients are sensitive to the laser intensity, laser pulse risetime, the magnitude of the hole-state pumping rates, ion density, and electron and ion heating rates, and, in general, Co-like holes are found to have much higher gains than Fe-like hole states. These model calculations are also capable of producing gains from the double-hole states in Fe-like xenon, but they are much smaller than those generated in the Fe-like single-hole states in the cases included in this paper. Thus, our model calculations do not support the experimental data interpretation in which the measured gains were attributed to double holes in much higher ionization stages of xenon (Xe32+, Xe34+, Xe35+, and Xe37+). Our calculations suggest that these ionization stages can be reached either early in time at much higher laser intensities (in excess of 1.5 × 1020 W cm−2 for a 248 nm, ∼230 fs pulse) or later in time, and only because of tunnelling ionization. In this latter case, however, the measured gains cannot be achieved since cluster densities have fallen by several orders of magnitude from their initial values and ion population have been spread over a much wider range of states.