T. Q. Thelen, D. A. Rehn, C. J. Fontes, and C. E. Starrett∗Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, U.S.A.(Dated: March 29, 2024)In a dense plasma environment, the energy levels of an ion shift relative to the isolated ion values. This shift is reflected in the optical spectrum of the plasma and can be measured in, for example, emission experiments. In this work, we use a recently developed method of modeling electronic states in warm dense matter to predict these level energies. In this model, excited state energies are calculated directly by enforcing constrained one-electron occupation factors, thus allowing the calculation of specific transition and ionization energies. This model includes plasma effects selfconsistently, so the effect of continuum lowering is included in an ab-initio sense. We use the model to calculate the K-edge and K-alpha energies of solid density magnesium, aluminum, and silicon over a range of temperatures, finding close agreement with experimental results. We also calculate the ionization potential depression (IPD) to compare to widely used models, and investigate the effects of temperature on the lowering of the continuum.
In Fig. 5, we show K-edge results from our model for several temperatures. Importantly, the temperature of the plasma was not directly measured in the experiments . The predicted K-edge energies become sensitive to temperature at higher charge states. For all elements, the calculated K-edge values for lower charge states are very close to each other, despite being calculated over a large range of temperatures. However, at higher charge states, the calculated K-edge values vary more over the same range of temperatures. This is due to a larger fraction of ionized electrons that thermalize and, therefore, become more sensitive to temperature. Agreement between the model and the experiments is excellent, for all three materials. Even though temperature is not measured, the relative insensitivity of the K-edge values means that the experiment provides a useful constraint on the model.
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For comparison, Fig. 6 shows lineouts of the measured experimental emission for magnesium, showing our calculated K-edges over a range of temperatures for each charge state. For lower charge states, there exist very sharp edges in emission, indicating clear values for the K-edge locations. We see that as the charge state increases, the slope that indicates the edge gets shallower. This is clearly apparent at higher charge states, as we see that the edges for these higher charge states span a 4 Mg 5 5 6 6 6 1900 2 1350 40eV 20eV Exp. 1700 1600 1450 60eV 1300 2000 9 Si0.00.20.40.60.81.00.00.20.40.60.81.0 5 1750 1500 9 K-edge(eV) 1400 3 3 4 4 4 1650 7 1550 1950 8 8 8 80eV 1850 Al 9 7 7
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ChargeState 100eV FIG. 5. K-edges calculated with our model for temperatures of 20, 40, 60, 80, and 100 eV for solid density magnesium (top), aluminum (middle), and silicon (bottom), compared with experimental results (shaded) . Experimental K-edges for silicon were only reported up to charge state 7. much larger range of LCLS energies. The shallower slope of the K-edge reflects two things: first, for higher charge states, bound states relocalize due to the higher charge of the ion, leading to more states near the bound-free threshold; second, the Fermi edge becomes blurred due to the higher temperatures . This behavior makes it 1500 750eV 5 6 1800 2 2 2 2 20eV 3.0 1700 2.5 2.5 2.5 2.5 1600 60eV 90.00.20.40.60.81.00.00.20.40.60.81.0log10(Emission)(a.u.)LCLSenergy(eV) 3.0 250eV 3 3.0 3.5 3.5 3.5 3.5 7 500eV 1400 3 150eV 1300 3 3 4 4 40eV 8
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80eV 100eV 3 3.0 FIG. 6. Lineouts of experimental data taken at peak emitted photon energy for each charge state (labeled in the top left corners), compared with the K-edges calculated by our model at various temperatures (represented by colored vertical linessolid for falling within experimental range, dashed for falling outside), and the experimental edge (shaded region). The gaps in the lineout data are due to negative values of the emission. 5 2.0 1320 1280 3.5 1260 1340 1.5 1300 3.0 4.5 1515eVLCLS 1360 1350eVLCLS log10(Emission)(a.u.)
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