Theoretical Tracking of Resonance-Enhanced Multiple Ionization Pathways in X-ray Free-Electron Laser Pulses

We present an extended Monte Carlo rate equation approach to examine the inner-shell ionization dynamics of atoms in an intense x-ray free-electron laser (XFEL) pulse. In addition to photoionization, Auger decay, and fluorescence processes, we include bound-to-bound transitions in the rate equation calculations. Using an efficient computational scheme, we account for “hidden resonances” unveiled during the course of an XFEL pulse. For Ar, the number of possible electron configurations is increased ten-billion-fold over that required under nonresonant conditions. We investigated the complex ionization dynamics of Ar atoms exposed to an 480-eV XFEL pulse, where production of ions above charge state $10+$ is not allowed via direct one-photon ionization. We found that resonance-enhanced x-ray multiple ionization pathways play a dominant role in producing these nominally inaccessible charge states. Our calculated results agree with the measured Ar ion yield and pulse-duration dependence. We also predict the surprising ion yields reported earlier for Kr and Xe. The Monte Carlo rate equation method enables theoretical exploration of the complex dynamics of resonant high-intensity x-ray processes.

Figure 1

(a) Experimental argon charge state distribution for 50-fs, 0.15 mJ pulses at 480-eV photon energy, resonant-excitation (RE) and No-RE theory. (b) Average number of absorbed photons, resonant excitation and Auger events predicted by the RE theory.

Figure 2

A Sankey diagram illustrating transition probabilities between the accessible ECs of an Ar atom exposed to an intense XFEL pulse at 480 eV. In this diagram, the vertical bars represent ECs, and the width of each green branch, going from left to right, indicates the the transition probability between two ECs. Some ECs are transients that do not survive (dark blue bars). The EC fractions that survive are colored red and are ground state ECs. The branches that are not green correspond to a prominent pathway to reach ${\mathrm{Ar}}^{11+}$ from neutral Ar. The branch color is explained in the legend. The inset gives the responsible ECs for this prominent path which accounts for $\sim 10\%$ of the ${\mathrm{Ar}}^{11+}$ yield. The charge state is shown in parentheses and lifetime to left of the arrow. Another prominent pathway to ${\mathrm{Ar}}^{11+}$ that involves multiple resonant excitation is shown by the three labeled ECs with a $2s$ hole.

Figure 3

Pulse-duration dependence of Ar ion production. (a) Experiment, abundance normalized to value for 30-fs pulse. (b) RE theory. The inset shows absolute yield of Ar ions calculated for different pulse durations.

Figure 4

Experimental (a) krypton and (b) xenon charge state distribution (bars) obtained at photon energies of 2.0 and 1.5 keV and comparison to RE and No-RE theory (lines with circles and dash lines) calculated with similar experimental pulse parameters [9, 10].