Eric Matthias Hollmann

Runaway electron (RE) incidence poses a rather critical threat to the integrity of plasma facing components (PFCs) in tokamaks due to the volumetric nature of energy deposition at relativistic speeds, which leads to steep internal temperature gradients that trigger explosive material failure. A computational framework is presented for the modeling of RE-induced explosive damage in graphite PFCs, benchmarked against a controlled RE impact experiment performed at the DIII-D tokamak. Reconstructed volumetric energy deposition profiles are integrated with high-fidelity three-dimensional thermomechanical simulations based on the finite element method (FEM). It is demonstrated that RE-induced damage in graphite is governed by a degraded subsurface layer formed due to intense volumetric heating, which undermines the structural integrity of the surface and leads to inertial detachment. Continuum thermo-elastic FEM approaches reliably predict the total volume that is liable to detach during failure, while continuum damage-based FEM approaches capture the irreversible subsurface degradation. In contrast to element erosion FEM approaches, a hybrid FEM–to-smoothed-particle-hydrodynamics framework provides physical fidelity, successfully reproducing the experimental blown-off volume and estimating debris kinematics.

The state-of-the-art concerning the modeling of the thermomechanical response of graphite to runaway electron (RE) impact is based on one-way coupled linear thermoelasticity combined with Rankine’s strength-based failure criterion and limited to the onset of material failure. Here, the predictive capabilities are extended to the nonlinear damage phase characterized by material fragmentation and debris expulsion. This is achieved by introducing plasticity via the Johnson–Holmquist constitutive model, adopting an effective plastic strain-based failure criterion and coupling finite element analysis with smoothed-particle hydrodynamics. The extended thermomechanical model is successfully benchmarked against the results of two controlled RE-induced damage experiments recently carried out in DIII-D. This constitutes an important step towards the final objective of quantitatively describing the thermomechanical response of tungsten to REs.

Runaway electrons (REs) generated during tokamak disruptions are a major concern for the safe operation of future fusion devices. The interaction of REs with waves has been proposed as a potential mechanism for their mitigation. This study investigates the effect of electron–cyclotron heating (ECH) on post-disruption plasmas containing REs. O- and X-mode EC waves are routinely used for plasma heating and current drive. However, these modes do not interact directly with relativistic electrons and cannot be injected into plasmas with densities exceeding their respective cutoff densities. In contrast, the internal slow X-mode (sX) can resonate with relativistic electrons and may therefore provide a pathway for their mitigation. We report DIII-D experiments designed to access the internal slow X-mode through O-sX conversion during post-disruption RE plateaus. ECH increased the background-plasma density, doubled the loop voltage, and strongly enhanced the RE synchrotron signal, demonstrating substantial ECH-plasma coupling and increased effective dissipation of the RE channel. Although ECH produced a pronounced response consistent with enhanced RE dissipation, we could not isolate conclusive evidence of resonant sX-RE interaction. Strong heating, ionization, and impurity-redistribution effects appear to dominate the response and may mask a direct wave-particle signature. Nevertheless, the results demonstrate the potential of ECH for RE control through background-plasma modification, with O-sX access offering an additional possibility of direct resonant interaction.

The toroidal distribution of runaway electrons (REs) striking the centre post in DIII-D post-disruption RE final loss events is simulated utilizing the MARS-F code combined with the REORBIT module, by tracing the guiding-centre drift orbits of test REs in the presence of external (applied) plus internal (intrinsic instability) 3-D fields. To better recover the experimental results, three different equilibria with different safety factor profiles are adopted. Dominant resistive magnetohydrodynamic instabilities are found to be m/n=2/1, 3/2 and 1/1 modes (where m and n are the poloidal and toroidal mode numbers). Externally applied n=1 resonant magnetic perturbations (RMPs), with both even and odd parity configuration, are considered in each equilibrium. Locking of MHD instability to the applied RMPs is simulated by minimizing the total perturbed magnetic energy in the plasma. The simulated toroidal locations, where most REs strike in the presence of an edge m/n= 2/1 instability and the n=1 RMPs in even parity, are found to agree well with experiments. Modeling also captures the measured n = 2 RE loss pattern on the wall for experiments where an edge m/n=3/2 instability is dominant instead of the m/n=2/1 mode. The key overall findings include (a) the measured global RE toroidal impact pattern in experiments can be explained by a locked resistive kink instability, (b) the toroidal phase of the locked mode is well predicted by minimizing the total perturbed magnetic energy, and (c) this edge locked mode determines the toroidal phase of the peak RE wall impact.

This Roadmap article addresses the critical and multifaceted challenge of plasma-facing component (PFC) damage caused by runaway electrons (REs) in tokamaks, a phenomenon that poses a significant threat to the viability and longevity of future fusion reactors such as ITER and DEMO. The dramatically increased RE production expected in future high-current tokamaks makes it very difficult to avoid or mitigate REs in such devices when a plasma discharge terminates abnormally. Preventing damage from the intense localized heat loads they can cause requires a holistic approach that considers plasma, REs and PFC damage. Despite decades of progress in understanding the physics of REs and the thermomechanical response of PFCs separately, their complex interplay remains poorly understood. This document aims to initiate a coordinated, interdisciplinary approach to bridge this gap by reviewing experimental evidence, advancing diagnostic capabilities, and improving modeling tools across different scales, dimensionalities, and fidelities. Key topics include RE beam formation and transport, damage mechanisms in both brittle and metallic PFCs, and observed effects in major facilities such as JET, DIII-D, WEST and EAST. The Roadmap emphasizes the urgency of predictive, high-fidelity modeling validated against well-diagnosed controlled experiments, particularly in the light of recent changes in ITER’s wall material strategy and the growing importance of private sector fusion initiatives. The modeling gaps include calculations of the magnetic equilibrium, RE distribution function and background plasma properties at the start of the beam termination, with a critical need to advance modeling of access conditions to benign terminations. This is to be followed by simulations of the termination itself which requires a self-consistent description of the 3D MHD fields together with the REs, which is now available thanks to recent developments. Finally, the damage assessment is enabled by modeling of the full thermo-mechanical response, encompassing the hydrodynamic and the deviatoric behavior, to RE impacts with characteristics as provided by the termination simulations. The full workflow is computationally heavy for scoping studies to assist design of future machines, calling for development of reduced or surrogate models. Each section of the Roadmap article is written to provide a concise overview of one area of this multidisciplinary subject, with an assessment of the status, a look at current and future challenges, and a brief summary. The ultimate goal of this initiative is to guide future mitigation strategies and design resilient components that can withstand the intense localized loads imposed by REs, thus ensuring the safe and sustainable operation of the next generation of fusion power plants.

Instrumented sacrificial limiter heads, both domed (proud) and flat (flush) are used in DIII-D runaway electron (RE) wall strikes to study the wall impact dynamics with high spatial and time resolution. The approximate structure of the RE wetted area and heating depth on the domed limiter heads were predicted qualitatively using orbit-tracking simulations, although a strong left-right asymmetry (about the magnetic field direction) was not captured well by the simulations. It is hypothesized that this difference is perhaps due to the local 3D magnetic field perturbation of the dome limiter head. The average kinetic energy K and pitch angle  of REs striking the limiter head were estimated from the spatial distribution of local HXR emission and were estimated to be roughly K ≈ 4 MeV and  ≈ 0.2 rad. These values are roughly consistent with in-plasma values estimated before the loss event, indicating that RE kinetic energy and pitch angle are not drastically altered when transporting to the wall. Large shot-shot variations (1 - 10 kJ) in energy deposition into the limiter head were observed and were explained by shot-shot variations in locked MHD mode toroidal phase. For the largest deposited energies (10 kJ), graphite material failure and explosive dust release was observed, and the depth of material failure at higher energy deposition was successfully reproduced using modelling of volumetric energy deposition and brittle failure. The presence of energetic (keV level) ion impact during the RE wall strike was confirmed by three different surface analysis techniques. The ratio of energetic ion to RE flux appears to be larger on flat surfaces within the RE wetted area, although the total energy flux due to energetic ions has yet not been quantified.

It is demonstrated that the peak toroidal impact phase of the post-disruption runaway electrons (REs) can be varied shot to shot by means of applied static nonaxisymmetric (3D) magnetic fields, or resonant magnetic perturbations (RMPs). In the experiments, high-current (500 kA), purged RE plateaus (i.e., low impurity postdisruption plasmas with current carried completely by REs) were terminated on the DIII-D tokamak center post. The global toroidal impact peak of the REs appears to be dominantly set by the toroidal phase of a wall-locked tearing mode, typically (m/n)=(2/1), but sometimes (m/n)=(3/2). In the absence of external RMP, the locked mode reliably locks close to a preferred toroidal phase ϕ≃75° probably set by intrinsic error fields. With applied RMP, the locked mode and RE impact phase is pushed to a new location. When the tearing mode is (m/n)=(2/1), the phase is well controlled and tracks the applied RMP phase, but in the case of an (m/n)=(3/2) tearing mode, the new phase location is not well controlled. These results could have an application in international thermonuclear experimental reactor and other fusion power plant-sized tokamaks as a method for spreading disruption first wall damage from REs.

The dynamics of shattered pellet injection (SPI) shutdowns are simulated using a time-dependent global energy balance model, based on a modification of the KPRAD framework. The new SPI particle source in the model calculates the ablation of individual pellet fragments that enter the plasma as a temporally resolved plume, thus capturing the effects of earlier fragments on the ablation of those that follow, which has a significant impact on the overall assimilation. Despite the reduced physics and the global averaging of all quantities, results from a large number of DIII-D, KSTAR, and JET experiments are well reproduced, including the plasma cooling timescales, particle assimilation, and current quench (CQ) rates. Cooling timescales and CQ rates are in good agreement for pellets containing as little as ∼1% neon, while particle assimilations are most accurate for neon fractions above ∼15% by number of atoms. Below this, the assimilation tends to be overestimated due to the lack of radial transport in the particle balance, which becomes important in the low-Z limit. Predictive simulations of mixed-composition dual-SPI shutdowns in ITER are compared against those with the 3D non-linear magnetohydrodynamic code JOREK and are found to reproduce overall trends observed in the higher-fidelity modeling across a range of injection scenarios. The general success of the model points to the critical role of energy balance in determining SPI particle assimilation and the subsequent disruption dynamics and highlights the value of these simulations for experimental interpretation and for optimizing the deployment of computationally expensive, higher-fidelity models.

Infrared thermography of the first wall in DIII-D is used to show the toroidal peaking of plasma radiation during mitigated disruptions with shattered pellet injection (SPI) and with massive gas injection (MGI). During MGI, the radiation peak location is shown to be due to the n = 1 magnetohydrodynamic (MHD) activity and continuously variable in toroidal phase based on externally applied error fields, consistent with previous experimental results. Furthermore, the measured toroidal peaking factor (TPF) is in agreement with the previous estimates based on radiometry, with a total TPF of 1.07 ± 0.05 when integrated over the entire duration of the disruption, and a value of 1.3 ± 0.1 during the thermal quench (TQ). For SPI, the location of the radiation peak is found to be determined predominantly by the particle source location, and thus can be varied on DIII-D by injecting from either of two toroidally separated injectors. 3D non-linear MHD simulations with the NIMROD code support this picture. The localized SPI particle source leads to higher peaking than for MGI, with a total TPF of 1.3 ± 0.1 over the full disruption and a TQ TPF of 1.9 +0.5/−0.3, a value also consistent with the NIMROD simulations. This TQ value is close to or potentially exceeding the allowable limit for the previously planned Be first wall in ITER, pointing to the importance of radiation asymmetries depending on the choice of first wall material.