# Non-Equilibrium Modeling of the Fe XVII 3C/3D ratio for an Intense X-ray Free Electron Laser

## TL;DR

This paper models the Fe XVII 3C/3D line ratio under intense X-ray laser excitation using two approaches, revealing the importance of non-linear effects and laser parameters on the ratio's behavior, with implications for interpreting experimental results.

## Contribution

It compares the time-dependent collisional-radiative and density-matrix methods for modeling Fe XVII line ratios, highlighting the impact of laser pulse parameters and non-linear effects.

## Key findings

- Non-linear effects significantly influence the line ratio.
- Laser pulse duration, intensity, and bandwidth affect the ratio.
- Post-pulse plasma emission contributes to the ratio reduction.

## 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 (Bernitt et al. 2012), 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 $\times$ 10$^{13}$ s$^{-1}$ and 6.02 $\times$ 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.(2014, 2015): 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 $\sim 1\times 10^{12}$ W/cm$^{2}$ are required for a reduction in the 3C/3D line intensity ratio below the expected time independent oscillator strength ratio.