The impact of plasma turbulence on atomic reaction rates in detached divertors

TL;DR

The paper evaluates how edge-SOL turbulence affects nonlinear atomic reaction rates in detached divertor conditions using full-$f$ GRILLIX simulations of ASDEX-Upgrade. Through a toy demonstration and realistic turbulence runs, it shows that fluctuation biases arise from nonlinear dependencies on $N$, $n_e$, and $T_e$, and that the detachment front hosts cold, dense fluctuations with negative $R_{n,T_e}$ that suppress ionization and enable recombination bursts. In the detached case, ionization and impurity radiation are reduced by about a factor of 2, while recombination increases by at least a factor of 4, leading to a net reduction of the plasma density source by at least 50% relative to mean-field estimates. The study also reveals that the sign of density–temperature correlations critically controls the bias (negative near the X-point vs positive at the outboard-midplane) and that decorrelated synthetic fluctuations can erase the bias while positively correlated fluctuations amplify it, underscoring the need to account for turbulence in atomic-rate modeling of detached divertor plasmas.

Abstract

Numerical modeling of the edge and scrape-off layer (SOL) must account for atomic processes such as hydrogenic ionization and recombination, charge-exchange, and line radiation. Their reaction rates depend non-linearly on density and temperature and are thus sensitive to turbulent fluctuations, whose inclusion/omission may significantly affect model outcomes. We quantify the impact of fluctuations by studying global turbulence simulations of the edge and SOL of ASDEX-Upgrade in both attached and detached conditions. While the effect of fluctuations is minimal for the attached state, pronounced discrepancies emerge in colder, detached conditions. When accounting for turbulent fluctuations, ionization and radiation rates at the detachment front are reduced by a factor of 2 when compared to mean-field calculations. The effect arises from fluctuations crossing below the ionization temperature threshold, facilitated by low mean temperature and increased fluctuation amplitudes at the detachment front. The rate reduction (rather than rate increase) is explained by the character of divertor fluctuations (negative density-temperature correlation, i.e. cold and dense blobs), notably distinct from characteristic fluctuations found at the outboard-midplane (positive correlation, i.e. hot and dense blobs). Furthermore, the cold and dense fluctuations enable efficient plasma recombination even at average temperatures above the recombination threshold. In detached conditions, the combined plasma particle source from ionization and recombination is therefore effectively reduced by at least 50% when compared to the standard mean-field source.

Figures (4)

• Figure 1: Histograms of normalized plasma density, electron temperature, and neutrals density values in the control volume $V_\mathrm{xpt}$ for the two simulation cases.
• Figure 2: Ionization source in the attached (top row) and detached (bottom row) simulations, averaged over time and toroidal angle. Left column: the rate is first computed from fluctuating input fields and then averaged. Middle column: the rate is computed on pre-averaged (smooth) fields. Right column: absolute difference between fluctuation-including and pre-averaged evaluations.
• Figure 3: Recombination sink (top row) and impurity radiation density (bottom row), both in the detached simulation, averaged over time and toroidal angle. Left column: the rate is first computed from fluctuating input fields and then averaged. Middle column: the rate is computed on pre-averaged (smooth) fields. Right column: absolute difference between fluctuation-including and pre-averaged evaluations.
• Figure 4: Contours of ionization source rate $S_\mathrm{iz}$ as a function of plasma density (x-axis) and electron temperature (y-axis), a constant neutrals density of $N = 10^{19}\,\mathrm{m^{-3}}$ is assumed. The blue and red point clouds represent 2D-histograms of $(n, T_\mathrm{e})$ samples from the attached and detached simulations, respectively. The left subplot indicates samples taken from the X-point control volume $V_\mathrm{xpt}$, the right subplot shows samples from the OMP control volume $V_\mathrm{omp}$.