Non-equilibrium modeling of the Fe XVII 3C/3D ratio for an intense X-ray free electron laser

Abstract

We present a review of two methods used to model recent LCLS experimental results for the 3C/3D line intensity ratio of Fe XVII [1], the time-dependent collisional-radiative method and the density-matrix approach. These are described and applied to a two-level atomic system excited by an X-ray free electron laser. A range of pulse parameters is explored and the effects on the predicted Fe XVII 3C and 3D line intensity ratio are calculated. In order to investigate the behavior of the predicted line intensity ratio, a particular pair of A-values for the 3C and 3D transitions was chosen (2.22 × 10 13 s −1 and 6.02 × 10 12 s −1 for the 3C and 3D, respectively), but our conclusions are independent of the precise values. We also reaffirm the conclusions from Oreshkina et al. [2,3]: the non-linear effects in the density matrix are important and the reduction in the Fe XVII 3C/3D line intensity ratio is sensitive to the laser pulse parameters, namely pulse duration, pulse intensity, and laser bandwidth. It is also shown that for both models the lowering of the 3C/3D line intensity ratio below the expected time-independent oscillator strength ratio has a significant contribution due to the emission from the plasma after the laser pulse has left the plasma volume. Laser intensities above ∼ 1 × 10 12 W/cm 2 are required for a reduction in the 3C/3D line intensity ratio below the expected time independent oscillator strength ratio.

Change of the relative line strengths due to the resonance induced population transfer between Fe XVII and FeXVI ions

“…We can clearly see that with the pulse duration time less than 20 fs, or, substantially smaller than the lifetime of the Fe XVI C line, the contribution from the autoionization of the Fe XVI ion is small. For those XFEL parameters, the decrease of 3C/3D ratio should be attributed to the non-equilibrium effects discussed in refs 14,15 . By contrast, with the pulse durations longer than 90 fs (in consistent with the typical LCLS X-ray pulse parameters 11,16,17,33 ), the resonance induced population transfer effect contributes more than a half.…”

“…12 is unreliable due to a limited and unbalanced treatment of electron correlations 13 . Alternatively, it was proposed that other physical processes beyond those included in the atomic structure calculation of an isolated atomic system, such as the one due to the ultra-high intensities of XFEL with ultra-short pulse period, may be responsible for this discrepancy 10,14,15 . By scrutinizing the experimental conditions at the LCLS 5,11,16–18 , the intensities of the XFEL pulses are not sufficiently high to support this proposed interpretation 10,14,15 and it is not likely that the discrepancy between theory and experiment could be attributed to the high order nonlinear effect.…”

High Resolution Photoexcitation Measurements Exacerbate the Long-Standing Fe XVII Oscillator Strength Problem

“…In this Letter, we report on new measurements of resonantly excited Fe XVI and Fe XVII with a synchrotron source at tenfold improved spectral resolution and millionfold lower peak photon flux than in [25], suppressing nonlinear dynamical effects [32,34,38] and undesired ion population transfers [35]. We also carry out improved large-scale calculations using three different advanced approaches [39][40][41], all showing a five-sigma departure from our experimental results.…”

“…Open green diamonds: previous EBIT results [18,21,25]. Note that the spread seen in various astrophysical sources and in tokamak in part arises from insufficient removal of Fe XVI C line contamination of Fe XVII 3D line, at varying Fe XVI/Fe XVII abundance ratios [6,20]; nonlinear dynamical effects [32,34,38] (see main text) may have reduced the LCLS ratio [25].…”

“…Calculations using a density-matrix approach by Oreshkina et al [32,33], and the time-dependent collisional-radiative model of Loch et al [34], pointed to a possible nonlinear response of the excited upper state populations in [25], reducing the observed oscillator strength ratio [38], which would depend on photon pulse parameters, like intensity, duration, and spectral distribution. It has been estimated that peak intensities above 10 12 W=cm 2 would give rise to nonlinear effects [32,38]. Fluctuations of the self-amplified spontaneous emission process at LCLS can conceivably generate some pulses above that threshold.…”