Computer simulations of the Stark effect in the helium-beta complex of krypton in ICF conditions

TL;DR

This work develops and validates semiclassical computer simulations of Stark broadening for the krypton Kr He-$\beta$ line and its Li-like satellites under ICF-relevant conditions ($n_e$ up to $1\times10^{25}$ cm$^{-3}$, $T_e=3$ keV). By comparing three main codes—SIMULA, SIMULAm, and SimU (and variants SimU$_{SP}$ and DinMol)—across different levels of particle interaction, the study demonstrates qualitative agreement and highlights how emitter-perturber interactions and recombination broadening shape the spectra. It also analyzes interference terms in the electron-impact operator, finding negligible effects for $n=2$ satellites but significant impacts for $n=3$ satellites at higher densities, which helps reconcile discrepancies with prior results. Finally, a full spectrum for Kr in a 1:1 D/$^3$He mix is synthesized and contrasted with MERL predictions, showing the importance of ion dynamics in accurate spectral modeling and enabling improved spectroscopic diagnostics for ICF experiments.

Abstract

There is an ongoing interest in using spectroscopy in inertial confinement fusion (ICF) experiments, where dopants such as krypton can provide vital information about the temperature and density of the imploding plasma. While the most advanced tools for calculating Stark profiles are computer simulation models (CSMs), their application to complex lineshapes under the extreme conditions of ICF experiments is computationally challenging. In this manuscript, we present results of several CSM realizations applied to the Stark shape of the krypton He-beta line and its satellites at ICF-relevant conditions (ne = 1e24 to 1e25 cm-3, Te = 3keV). We demonstrate that codes with the same underlying physics but different numerical approaches yield identical results and analyze the differences in the line profile caused by various physical effects.

Figures (8)

• Figure 1: A comparison of Kr xxxv He-$\beta$ Stark line shapes, calculated for $n_e = \qty{1e24}{cm^{-3}}$ (a), 3e24cm^-3 (b), and 1e25cm^-3 (c), using different . $T = \qty{3}{keV}$ is assumed in all cases. The line shapes are area-normalized to unity.
• Figure 2: He-$\beta$ lineshape at $n_e=\qty{1e25}{cm^{-3}}$ and $T=\qty{3}{keV}$, comparing the results SIMULA (independent particles), SimU (interaction with the emitter), and DinMol (full molecular dynamics) with and without recombination effects. Effectively, this illustrates the differences in the lineshape resulting from varying levels of complexity in the simulation.
• Figure 3: Comparison of the obtained at the different density conditions by the presented here for the He-$\beta$ line. A solid-pink line indicating the typical $n_e^{2/3}$ scaling has been added to guide the eye. The plot axes are in logarithmic scale, so the $n_e^{2/3}$ scaling is a straight line.
• Figure 4: Same as \ref{['fig:He']}, but for $n=2$ (top) and $n=3$ (bottom) Li-like satellites. Figures \ref{['fig:HeBe2_1e24']} and \ref{['fig:HeBe3_1e24']} (left) correspond to $n_e=\qty{1e24}{cm^{-3}}$, \ref{['fig:HeBe2_3e24']} and \ref{['fig:HeBe3_3e24']} (center) to $n_e=\qty{3e24}{cm^{-3}}$, and \ref{['fig:HeBe2_1e25']} and \ref{['fig:HeBe3_1e25']} (right) to $n_e=\qty{1e25}{cm^{-3}}$. $T=\qty{3}{keV}$ is assumed in all cases.
• Figure 5: Comparison of the full spectrum of the Kr He-$\beta$ complex given in a previous study gallardo-diaz:2024a with our results. A $T=\qty{3}{keV}$, $n_e=\qty{1e24}{cm^{-3}}$ plasma with a trace minority of Kr in a 1:1 atomic mixture of D and $^3$He is assumed. The spectra are area-normalized.