# Stark-Broadening of Ar K-Shell Lines: A Comparison between Molecular Dynamics Simulations and MERL Results

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## Abstract

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## 1. Introduction

## 2. Stark-Broadening Models

#### 2.1. Computer Simulation Models

#### 2.1.1. Independent-Particle Simulations

#### 2.1.2. Molecular Dynamics Simulations

#### 2.1.3. Numerical Solution of the Emitter Schrödinger Equation

#### 2.2. MERL Code

## 3. Results and Discussion

#### 3.1. Electron Broadening

#### 3.2. Complete Line Shapes

#### 3.3. Recombination Broadening

#### 3.4. Impact of Stark-Broadening Models on the Spectroscopic Diagnosis of OMEGA Implosions

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Electron-broadened line shapes for argon He${}_{\alpha}$, He${}_{\beta}$, and He${}_{\gamma}$ computed using the IPA simulation, MERL-PWF and MERL-CWF. Calculations were done for ${T}_{e}=1$ keV and two electron density values, ${N}_{e}=5\times {10}^{23}$ cm${}^{-3}$ and $3\times {10}^{24}$ cm${}^{-3}$. For the $H{e}_{\alpha}$, only the fine-structure resonance line, 1s2p ${}^{1}$P${}_{1}\to $1s${}^{2}$ ${}^{1}$S${}_{0}$, is shown. For He${}_{\beta}$ and He${}_{\gamma}$, the two fine-structure components, 1snp ${}^{1}$P${}_{1}\to $1s${}^{2}$ ${}^{1}$S${}_{0}$ and 1snp ${}^{3}$P${}_{1}\to $1s${}^{2}$ ${}^{1}$S${}_{0}$, lie within the displayed spectral range, but the high-energy component, 1snp ${}^{1}$P${}_{1}\to $1s${}^{2}$ ${}^{1}$S${}_{0}$, is by far the dominant one and ultimately determines the line shape.

**Figure 2.**Electron-broadening FWHM dependency on electron density for argon He${}_{\alpha}$, He${}_{\beta}$, He${}_{\gamma}$, Ly${}_{\alpha}$, Ly${}_{\beta}$, and Ly${}_{\gamma}$. Only FWHMs corresponding to the dominant fine-structure component of the lines are plotted—see the text for details. Results from IPA simulation, MERL-PWF and MERL-CWF are compared. For all cases, we set ${T}_{e}=1$ keV. For reference, dotted straight lines going over the IPA-simulation FWHM values for the lowest and highest density points have been added to point out the linear dependence on density—note the log-log scale. All models suggest a slightly weaker dependence, i.e., $FWHM\propto {N}_{e}^{a}$, with $a\approx 0.9$.

**Figure 3.**Procedure to extract the line-width from electron-broadened line shapes. The line shape is fitted using a linear combination of two-Lorentzians and from there line widths can be easily extracted. For illustration we show the case of Ly${}_{\beta}$ calculated using the IPA simulation at ${N}_{e}=2\times {10}^{23}$ cm${}^{-3}$ and ${T}_{e}=1$ keV.

**Figure 4.**Complete line shapes for argon Ly${}_{\alpha}$, Ly${}_{\beta}$, and Ly${}_{\gamma}$ computed using MERL-CWF, and IPA and MD simulations. Calculations are shown for ${T}_{e}=1$ keV and two electron density values, ${N}_{e}=2\times {10}^{23}$ cm${}^{-3}$ and ${10}^{24}$ cm${}^{-3}$.

**Figure 5.**Impact of recombination broadening on the line shapes. We show line shapes computed with the MD simulation including and removing the recombination broadening. For comparison, we also plot MERL-CWF results.

**Figure 6.**Spectroscopic fits of time-resolved Ar K-shell spectra recorded in an OMEGA implosion experiment using different line shape models. The analysis is based on a weighted least-squares-minimization procedure. In the figure, implosion time evolves from top to bottom and the corresponding values are indicated. The spherical D${}_{2}$-filled Ar-doped targets were driven by a 2.2-ns laser pulse shape with a total UV energy on target of ∼19 kJ.

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**MDPI and ACS Style**

Gigosos, M.A.; Mancini, R.C.; Martín-González, J.M.; Florido, R.
Stark-Broadening of Ar K-Shell Lines: A Comparison between Molecular Dynamics Simulations and MERL Results. *Atoms* **2021**, *9*, 9.
https://doi.org/10.3390/atoms9010009

**AMA Style**

Gigosos MA, Mancini RC, Martín-González JM, Florido R.
Stark-Broadening of Ar K-Shell Lines: A Comparison between Molecular Dynamics Simulations and MERL Results. *Atoms*. 2021; 9(1):9.
https://doi.org/10.3390/atoms9010009

**Chicago/Turabian Style**

Gigosos, Marco A., Roberto C. Mancini, Juan M. Martín-González, and Ricardo Florido.
2021. "Stark-Broadening of Ar K-Shell Lines: A Comparison between Molecular Dynamics Simulations and MERL Results" *Atoms* 9, no. 1: 9.
https://doi.org/10.3390/atoms9010009