Svetlana Ratynskaia

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.

The electron current density that escapes from multi-emissive magnetized sheaths constitutes a critical quantity in modern evaluations of ITER plasma-facing component (PFCs) deformation due to macroscopic melt motion. During ITER edge-localized modes, electrons can be emitted from the PFCs through field assisted thermionic emission, secondary electron emission (SEE) and electron backscattering (EBS). In the case of space-charge limited sheaths, an analytic semi-empirical expression is available for the total escaping current density. Here, an analytic empirical model is proposed for the unexplored case of classical monotonic sheaths comprising (i) an existing semi-empirical description of prompt re-deposition in the presence of surface electric fields based on particle orbit simulations; (ii) existing analytic expressions for the SEE and EBS currents as a function of the electron temperature; (iii) a new semi-empirical relation between the total electron emission yield and surface electric field; (iv) a novel correlation for the magnitude of the surface electric field in the absence of electron emission. The new predictive model is valid for arbitrary magnetic field inclination angles and is benchmarked against systematic particle-in-cell simulations.

The integrity of plasma-facing components (PFCs) in tokamaks is critically challenged by transient events such as runaway electron (RE) impacts. We report the first systematic analysis of the thermal damage to tungsten-based PFC tiles comprising the SPARC outboard off-midplane limiters that is induced by RE beams formed during vertical displacement events. Parametric scans in RE impacting characteristics as well as energy-pitch distribution functions from the Dream code are employed for calculations of the volumetric heat loads. A realistic panel design is adopted to enhance the fidelity of the thermal analysis. The PFC thermal responses are compared in terms of in-depth temperature profiles and damage characteristics, such as melt depth and vaporization losses.

Next step fusion devices will face unprecedented heat loads and particle fluence with thousands of hours of plasma exposure on plasma-facing components (PFC) cumulated over the entire lifetime of the device. These components must guarantee acceptable lifetime, reliable heat exhaust capabilities (10-15 MW/m2 power fluxes in steady state) and a high level of resilience after multiple thermal stresses generated by combined steady-state heat loads and transient events, such as ELMs or disruptions. An extensive tungsten (W) PFC testing work-program has been conducted in the WEST (Tungsten Environment in Steady State Tokamak) and ASDEX Upgrade (AUG) tokamaks, taking advantage of key capabilities and strengths of the two machines. WEST is a superconducting tokamak with long pulse duration capabilities currently equipped with an ITER-grade actively cooled divertor, including shaped monoblocks (MB) with the 0.5 mm height toroidal bevel as foreseen for ITER, while AUG allows the exposure of dedicated tile-sized samples (with different geometries, gap size, slopes and materials) in ELMy H-mode discharges using its divertor manipulator DIM-II system. The first part of the paper reports on the operation of the ITER-grade PFC in WEST since the commissioning of the divertor in 2022. The second part of the paper presents dedicated experiments performed in AUG and WEST in order to study W failure modes, W melting across toroidal gaps (during sustained or transient melting) and impact of the runaway electrons on W material. The results reported here provide new information on W material response (e.g. heating, cracking or melting) of direct relevance to ITER.

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.