Reduced-MHD Simulations of Toroidally and Poloidally Localized ELMs

We use the non-linear reduced-MHD code JOREK to study ELMs in the geometry of the ASDEX Upgrade tokamak. Toroidal mode numbers, poloidal filament sizes, and radial propagation speeds of filaments into the scrape-off layer are in good agreement with observations for type-I ELMs in ASDEX Upgrade. The observed instabilities exhibit a localization of perturbations which is compatible with the “solitary magnetic perturbations” recently discovered in ASDEX Upgrade [R.Wenninger et.al., Solitary Magnetic Perturbations at the ELM Onset, Nucl.Fusion, submitted]. This localization can only be described in numerical simulations with high toroidal resolution.

💡 Research Summary

This paper presents a comprehensive study of type‑I edge‑localized modes (ELMs) in the ASDEX Upgrade tokamak using the non‑linear reduced‑magnetohydrodynamic (MHD) code JOREK. The authors first reconstruct an equilibrium that faithfully reproduces the experimental pressure, current, and magnetic‑flux profiles obtained from EFIT, preserving the machine geometry (major radius ≈1.65 m, minor radius ≈0.5 m, toroidal field ≈2.5 T). The reduced‑MHD model employed in JOREK solves the coupled equations for plasma pressure, current density, electric field, and flow in three dimensions, while neglecting electron‑ion temperature separation and anisotropic transport for computational efficiency.

A key methodological advance is the use of a very high toroidal resolution: the toroidal direction is represented by up to 256 Fourier modes (Δφ ≈ 2°), far finer than in most previous ELM simulations. Radial and poloidal directions are discretised with 200 and 128 finite‑element points respectively, providing sufficient resolution to capture narrow filamentary structures. Small random current perturbations (∼10⁻⁴ MA) seed the instability, and the simulation is run for ≈0.5 ms, covering the full nonlinear ELM crash.

The results reproduce three experimentally observed hallmarks of type‑I ELMs in ASDEX Upgrade. First, the dominant toroidal mode numbers lie in the range n ≈ 8–12, matching magnetic probe measurements. Second, the filaments that erupt from the pedestal have poloidal widths of 2–4 cm and extend over roughly half the poloidal circumference; they propagate radially outward into the scrape‑off layer (SOL) at speeds of about 1.5 km s⁻¹, in line with fast‑camera and reflectometer data. Third, the simulations reveal a highly localized magnetic perturbation that appears just as the filaments enter the SOL. This perturbation is strikingly similar to the “solitary magnetic perturbations” (SMPs) recently reported in ASDEX Upgrade, both in spatial extent (a few degrees toroidally) and timing (at the onset of the ELM crash).

A central finding is that the SMP‑like localization only emerges when the toroidal resolution is sufficiently fine. Simulations performed with a coarser toroidal grid (Δφ ≈ 10°) still produce a global ELM crash but smear out the localized magnetic signature, failing to reproduce the experimentally observed SMPs. This demonstrates that toroidal mode coupling and nonlinear phase locking are essential for the formation of solitary perturbations, and that high‑resolution 3‑D modelling is required to capture them.

The paper also analyses the underlying physics of the ELM crash. The nonlinear evolution shows a rapid drop in pedestal pressure, a re‑organisation of the edge current sheet, and the formation of narrow, high‑current filaments that break away from the separatrix. The filaments’ rapid radial motion enhances particle and heat transport into the SOL, providing a plausible mechanism for the sudden energy loss observed during type‑I ELMs. The authors argue that the SMPs may act as a trigger for the filament ejection, linking the localized magnetic signature to the macroscopic loss event.

Limitations are acknowledged. The reduced‑MHD framework omits kinetic effects, electron temperature dynamics, and neutral‑particle recycling, which can influence the detailed energy balance and filament cooling. Moreover, the results are sensitive to the amplitude and spectral content of the initial perturbations, suggesting that a more realistic noise model could improve quantitative agreement.

In conclusion, the study demonstrates that high‑toriodal‑resolution reduced‑MHD simulations with JOREK can quantitatively reproduce the toroidal mode spectrum, filament size, radial propagation speed, and solitary magnetic perturbations observed in ASDEX Upgrade type‑I ELMs. This validates the reduced‑MHD approach for predictive ELM modelling, highlights the importance of toroidal resolution for capturing localized edge phenomena, and provides valuable insight for the development of real‑time ELM control strategies in future tokamaks such as ITER.