Quantitative 3D non-linear simulations of shattered pellet injection in ASDEX Upgrade using JOREK

TL;DR

This study tackles the challenge of quantitatively modeling shattered pellet injection (SPI) disruptions in ITER-relevant conditions by performing 3D non-linear MHD simulations with the JOREK code for ASDEX Upgrade (AUG). A flux-limited parallel heat transport model is implemented by reducing the Spitzer–Härm parallel diffusivity to $0.1\cdot\chi_{\|,SH}$, which significantly improves agreement with experimental pre-TQ durations and radiation fractions. The authors re-evaluate neon content and fragment size under this baseline, finding a persistent two-stage cooling process and that neon fraction and fragment size modulate the timing and magnitude of energy loss and radiation, with larger fragments yielding slightly higher end-of-TQ assimilation. These results strengthen the predictive basis for SPI-driven disruption mitigation in ITER and outline avenues for further model enhancement, including a more realistic flux-limit model and the pellet rocket effect for small fragments.

Abstract

Shattered pellet injection (SPI) as primary mitigation method for major disruptions in ITER has a large parameter space available for optimization including the total amount of injected material, the size of the individual pellet fragments, the material composition, and the timing of multiple injections. This flexibility needs to be exploited to simultaneously minimize thermal heat loads, electromagnetic vessel forces, and formation of relativistic electrons and their impacts on plasma facing components. In this article, we apply 3D non-linear magnetohydrodynamic modelling to SPI experiments in the ASDEX Upgrade tokamak, going beyond our previous work [Tang et al Nucl. Fusion 65 116003 (2025)] by resolving some discrepancies between simulations and experiment and thus opening the path to quantitative model validation and experiment interpretation. The key element that enables the transition from merely qualitative comparisons to quantitatively reliable predictions of the thermal quench duration and the radiation fraction is the incorporation of a simplified treatment of parallel heat-flux limiting. The work increases the confidence of matching the key processes of disruption mitigation with this high fidelity modelling in view of predictive studies for ITER.

Figures (13)

• Figure 1: Speed and radius distributions of the fragments. The first row illustrates the distributions for the 53 fragment case (same as the LF_HV_Ne10 case in tang2025augspi), used to compare the effects of different $\chi_{\|}$ values and neon fractions. The second row illustrates the distribution of the 1105 fragment case, which has a similar speed distribution but different size distribution (both sampled based on Parks' fragmentation model parks) compared to the 53 fragment case, and is used to study the effect of different fragment size.
• Figure 2: Evolution of the thermal energy for the baseline simulation with $\chi_{\|,SH}$, the new case with reduced parallel thermal diffusivity $0.1\cdot\chi_{\|,SH}$, in comparison with the experiment discharge #40673. The thermal energy signal in experiment FPG_Wmhd is reconstructed through function parametrization Braams_1986_FPMcCarthy_1992_PhD. In this particular experimental discharge, the pellet speed is 221 m/s, the shatter angle is 25 degrees, and the neon fraction is 10%. The traces from the simulation are time-shifted so that the fragment arrival time coincides with that of the experiment, which is annotated by the purple dotted line.
• Figure 3: (a) Non-linear evolution of the MHD magnetic energy spectra for the cases with $\chi_{\|,SH}$ and $0.1\cdot\chi_{\|,SH}$. (b) Comparison of electron temperature $T_e$ and (c) Poincaré plot at the injection plane at simulation time 1.1 ms, corresponding to the time marked by the cyan dotted line in (a). In (c), red markers represent confined field lines, while blue markers indicate those lost to the boundary.
• Figure 4: Profiles of (a) electron pressure $p_e$, (b) electron temperature $T_e$ and (c) electron density $n_e$ at different simulation times. The dashed lines show the evolution for the case with $\chi_{\|,SH}$ and the solid lines display the case with $0.1\cdot\chi_{\|,SH}$.
• Figure 5: The perturbed electron pressure $\delta p_e=p_e-p_{e0}$ and non-axisymmetric part of stream function $u$ (electric potential) at simulation time 0.9 ms, for the case with $0.1\cdot\chi_{\|,SH}$ (left) and the case with $\chi_{\|,SH}$ (right).