Recent Publications

On the Shafranov shift in stellarators

Per Helander, Nikita Nikulsin

As first shown by Shafranov, toroidal plasmas in magnetohydrodynamic equilibrium tend to expand in major radius when the pressure is increased. Here, an average measure of the resulting Shafranov shift is introduced, and its properties are discussed for various classes of stellarator configurations. It is shown to be particularly small in quasihelical and quasi-isodynamic stellarators with a large number of field periods, which are thus relatively robust to variations in the plasma pressure.

Fusion digital twins from imperfect models

Ionuț-Gabriel Farcaș, Frank Jenko

Feedback control systems for plasma operation at Wendelstein 7-X

Thomas Wegner, Maciej Krychowiak, Laurent Krier

Real-time feedback control is essential for meeting the physics and operational demands of Wendelstein 7-X (W7-X), particularly the need to respond effectively to transient events, maintain stationary high-performance phases, and operate reliably across a wide range of magnetic configurations and plasma regimes. This work provides an overview of the feedback systems implemented and validated in recent campaigns, including the control of key plasma parameters such as density, radiation, and heating power under varying conditions. These systems rely on the W7-X segment control architecture and its millisecond-scale real-time network, which enable precise and deterministic coordination of sensors and actuators. Representative experiments highlight robust performance, including long stationary discharges and integrated multi-parameter control. Additional boundary conditions such as core electron temperature limits ensure protection against radiative collapse and other failure modes. Looking forward, planned developments include advanced actuators, neural-network-assisted control strategies, and long-term efforts toward full profile control of electron density and temperature. Overall, these developments establish real-time feedback control as an essential element of W7-X operation and a robust basis for advanced control concepts in future steady-state fusion devices.

A neural characteristic mapping method: Lagrangian PINNs based on flow maps for transport-dominated problems

Martin Campos Pinto, Victor Fournet, Emmanuel Franck, Philipp Krah, Victor Michel-Dansac

We propose a novel numerical method for transport-dominated problems using Physics-Informed Neural Networks (PINNs). In such problems, the solution can develop large gradients and fine structures over time. This is particularly challenging for classical PINNs, which represent the solution itself. In our approach, rather than the solution, we choose to approximate the flow map of the equation. The solution is then recovered by pulling back the exact initial condition, so that its fine structures are produced by the map rather than represented by the network. Our method is constructed by approximating the flow map of the equation with multiple PINNs, one per time subinterval, and composing them using the semigroup property of the flow, so that each network only has to represent a map close to the identity. To highlight the advantages of our method compared to classical PINNs or classical numerical schemes, we present numerical results on the linear advection equation, the incompressible Euler equation in vorticity formulation, the Vlasov-Poisson equation, and finally a drift-kinetic equation.

Stellarators Linking Axisymmetric Mirrors Part 1: Coil Design, MHD Equilibrium, and Physics Metrics

Rahul Gaur, Djin Patch, Robert Babin, Florian Hindenlang, Xu Chu, Tony Qian

We present a computational design study of a stellarator-mirror hybrid concept, Stellarators Linking Axisymmetric Mirrors (SLAMs), in which an optimized poloidally omnigenous (OP or QI) stellarator serves as the rotational-transform-generating element that links long, axisymmetric (circular cross-section) magnetic mirrors. Starting from an OP precursor configuration obtained from the DESC omnigenity database, we construct hybrid coil sets for field period nFP = 2 SLAMs by separating the OP modular coils along the device midplane and inserting axisymmetric planar mirror coils into the resulting gap. Field-line tracing shows that nested vacuum flux surfaces survive this extrusion across a range of mirror-section lengths, with the cross-section qualitatively preserved at the point where the mirror is inserted. We use the field-line tracing data to map the shape of a surface and use the GVEC fixed-boundary solver to calculate an ideal magnetohydrodynamic (MHD) equilibrium and evaluate physics metrics such as the neoclassical transport proxy (eps_eff), the vacuum magnetic well (W), and the gyrokinetic heat fluxes (Q), providing a first-principles analysis of such concepts using modern stellarator analysis tools.

Turbulent Origin of the Edge Radial Electric Field Asymmetry between Favourable and Unfavourable Drift Configurations

B. J. Frei, R. Bilato, W. Zholobenko, O. Grover, C. Angioni, M. Bergmann, P. Ulbl, F. Jenko, S. Rienäcker, L. Vermare, et al.

We study the influence of the ion magnetic-drift direction relative to the active X-point (favourable and unfavourable configurations) on edge turbulence, transport, and the radial electric field $E_r$ in ASDEX Upgrade and TCV. First-principles gyrokinetic simulations of the edge and scrape-off layer are performed in diverted X-point geometry using the spectral full-$f$ GENE-X code. Two matched pairs of L-mode discharges are simulated and validated against the available measurements in all four cases, showing good agreement, in particular for the $E_r$ profiles. A radial force-balance analysis shows that the deeper $E_r$ well in the favourable configuration is determined by the larger poloidal ion flow near the separatrix, which cannot be reproduced by neoclassical solvers and is identified in axisymmetric simulations as turbulence-driven. We then derive an exact evolution equation for the mean poloidal-flow acceleration from the full-$f$ gyrokinetic vorticity equation, which identifies the radial gradient of the total velocity stress as its nonlinear drive. The observed asymmetry is found to arise from stronger nonlinear energy transfer into the mean flow in the favourable configuration, associated with enhanced nonlinear $E\times B$ advection of vorticity near the separatrix and X-point. Flux-driven TCV simulations further show that the asymmetry persists at matched power more than six times the L-mode value. Assuming a critical $E_r$ at the L-H transition, this yields an estimated ratio of approximately 1.7 between the unfavourable and favourable L-H power thresholds, close to the experimental factor of two. Overall, the unfavourable configuration exhibits larger fluctuation amplitudes, a weaker $E_r$ well, stronger geodesic acoustic modes, and shorter energy confinement times for the same profiles, which may explain the observed difference in access to high-confinement regimes.

Validation of first-principles turbulence simulation in diverted negative triangularity plasmas on DIII-D

Philipp Ulbl, Alessandro Marinoni, Baptiste J. Frei, Filippo Scotti, Samuel D. Stewart, Gabriele Merlo, Frank Jenko, Kathreen E. Thome

We present a first-principles gyrokinetic simulation of the edge and scrape-off layer (SOL) region of negative triangularity (NT) plasmas in the DIII-D tokamak, achieving remarkable agreement with experimental data for density, ion temperature, and electron temperature profiles. Notably, our simulation validates edge and SOL ion temperature profiles in electrostatic turbulence dominated conditions for the first time. The NT edge region is found to be dominated by trapped electron modes, with a transition toward ion temperature gradient-like modes at the outer edge. The SOL heat fluxes on divertor targets exhibit an Eich profile shape, consistent with experimental observations, with a similar but slightly narrower width than measured experimentally. The simulation demonstrates the presence of geodesic acoustic modes, and our analysis reveals the characteristics of their interaction with turbulent fluctuations. This successful validation marks a significant step toward self-consistent predictions of turbulence, edge profiles, and heat exhaust in future fusion devices.

Numerical and diagnostic extensions to the gyrokinetic $δf$ code stella

Sven Stroteich, Georgia Acton, Michael Barnes, Pavlos Xanthopoulos, Ralf Schneider

Understanding turbulence in magnetised plasmas requires robust numerical tools capable of capturing complex free-energy transfer processes across scales. We demonstrate the utility of free energy as a diagnostic for both physical turbulence characteristics and numerical stability in gyrokinetic simulations with the stella code. Applied to the W7-X high-mirror configuration, free-energy diagnostics reveal characteristic power-law behaviour in the turbulent cascade, act as sensitive indicators of numerical instabilities undetected by conventional diagnostics, and expose localised structures in real space not apparent in the electrostatic potential alone. To support these analyses, we present a systematic comparison of explicit time-integration schemes, showing that the optimal choice depends critically on the regime: SSP22 achieves the lowest computational cost in linear ITG simulations, while SSP33 is most efficient in the nonlinear saturated state, with nonlinear simulations requiring two to three orders of magnitude more computational cost than linear cases. These results establish free-energy diagnostics as a valuable tool for interpreting plasma turbulence and provide practical guidance for scheme selection in stella simulations.

Increasing the Current Capacity of the Wendelstein 7-X In-Vessel Control Coils Power Supplies for Short Pulse Operation

Frank Füllenbach, Th. Rummel

Modeling first wall erosion and impurity migration: From fuel retention to W-core ingress

K. Schmid

Experimental analysis of Pt marker erosion in the outer divertor region of ASDEX Upgrade during L- and H-mode discharges

S. Saari, A. Hakola, J. Karhunen, K. Krieger, M. Rasinski, M. Balden, C. Baumann, I. Bogdanović Radović, S. Gouasmia, M. Mayer, et al.

The influence of ELM-like loading on tungsten under slow transient conditions in Magnum-PSI

T W Morgan, Martin Balden, Jos Scholte, Selanna Roccella, J H You

ITER is anticipated to operate with occasional slow transients, resulting in an increase in expected heat loads to the divertor from 10 to 20 MW m −2 and thus in the surface temperature increasing to > 2000 ◦C. At the same time mitigated ELMs may be expected to strike the surface. To investigate the consequences of this, two sets of experiments were carried out in Magnum-PSI, representing the first experiments to explore this regime. In the first set, seven ITER-like tungsten monoblocks were exposed to either hydrogen plasma, or impurity-seeded hydrogen plasma at a surface temperature of 2050 ◦C. Simultaneously five of the seven monoblocks were exposed to 10 5 ELM-like pulses using a 1 ms duration laser at an energy density of 0.1 − 0.19 MJ m −2 . Very strongly roughened and cracked laser exposed areas with localized melted regions were observed. These areas protruded several hundreds of micrometers above the original surface. In the second experiment, three tungsten plates, with either small, large or no castellations cut into the surface, were exposed to a hydrogen plasma at 2100 ◦C with a wider range of ELM-like pulse numbers (10 2 − 10 5 ) and energies (0.13 − 0.31 MJ m −2 ). The surface was found to evolve by roughening and pre-crack formation towards similar strongly protruding roughened structures as pulse number increased, while increasing the transient energy resulted in increasing the fraction of surface melting observed in the loaded region. Mass loss measurements of the plates indicated that erosion was significant, between 0.05-0.13 nm per pulse for the different plates. Extrapolating these results to ITER suggests that this mass loss rate would be relatively high and would constitute a significant tungsten source.

About the relevance of molecular processes in divertor plasmas: Which processes determine Tvib at Magnum-PSI?

R.C. Bergmayr, D. Wünderlich, K.J. Loring, K. Schutjes, J.W.M. Vernimmen, I.G.J. Classen, U. Fantz

Performance optimisation of tokamak operation in ASDEX Upgrade through novel feedback control capabilities

Wolfgang Treutterer, Marco Biasizzo, Pierre David, Emiliano Fable, Matthias Gehring, Louis Giannone, Igor Gomez Ortiz, Alexander Gräter, Johannes Illerhaus, Renat Kermenov, et al.

Optimising the performance of tokamak operation is not only a matter of tuning individual control loops, but needs a holistic approach with a focus on the effective interplay of all control system components. The ASDEX Upgrade Discharge Control System (DCS) has enabled outstanding results of physics effect studies and operation scenario development. This is facilitated by efficient and highly robust algorithms for measurements data processing and plasma state estimation, a versatile feedback control suite, a powerful actuator management approach that optimises the utilisation of the limited number of actuators, and pulse supervision control reacting to events and plasma state conditions to achieve a maximum exploitation of the pulse and protect device and investment. Moreover, Fenix, a fast “flight simulator” with a full model of the control system and a control-oriented plasma and plant model, assists in scenario design, validation and control method development, thus accelerating the turnaround time from the design of emerging capabilities to their exploitation in plasma pulses. Larger and more complex fusion devices such as ITER and DEMO in particular, will benefit from such a control structure and active contributions are being made to the architectural design of their control systems.

FIREWALL: A surrogate model for the rapid assessment of tokamak wall loading and melting by runaway electrons

Victor Johan Svensson, Tommaso Rizzi, Svetlana Ratynskaia, Hannes Bergström, Luca Venerando Greco, Matthias Hoelzl, Panagiotis Tolias

Runaway electron (RE) beams generated during tokamak disruptions can deposit highly localized heat loads on plasma-facing components, posing a serious risk of melting and damage. Monte Carlo particle transport simulations coupled with three-dimensional thermomechanical response modeling can quantify this damage but are too computationally demanding for device-scale assessments and extensive scenario scans. We present FIREWALL (Fast Integrated Runaway Electron WALL loads), a surrogate model that combines a database of \textsc{Geant4} volumetric energy-deposition profiles with a one-dimensional heat-diffusion solver for each wall element. FIREWALL retains the energy and incident angle distributions of impacting REs and predicts the spatiotemporal temperature evolution of detailed three-dimensional wall geometries up to the melting threshold. FIREWALL thus provides a fast physics-based framework for translating global RE simulations into global wall melting predictions, enabling large-scale screening of disruption scenarios while directing high-fidelity costly workflows to the limited wall regions where they are actually required.

High heat flux resilience of Low-pressure plasma sprayed tungsten coatings for fusion

Gunnar Schmidtmann, Johann Riesch, Andrey Litnovsky, Marcin Rasinski, Bernd Böswirth, Daniel Dickes, Jan Willem Coenen, Sebastijan Brezinsek, Robert Vaßen, Christian Linsmeier, et al.

Simplified conductance model for the subdivertor of Wendelstein 7-X based on high-fidelity simulations and comparisons with experimental data

V. Haak, L. Steiniger, C. Day, J. Igitkhanov, F. Litovoli, D. Naujoks, V. Perseo, G. Schlisio, H. Strobel, C. Tantos, et al.

Applications of Poincaré Boundary Condition for 3D Ideal MHD Equilibrium and Optimization

Yigit Gunsur Elmacioglu, Dario Panici, Rory Conlin, Daniel Dudt, Egemen Kolemen

Stellarator ideal magnetohydrodynamic (MHD) codes that assume nested flux surfaces such as \texttt{VMEC} and \texttt{DESC} solve the equilibrium problem by prescribing the total toroidal magnetic flux, plasma profiles and the last closed flux surface (LCFS), which analytically determines the unique field in vacuum, whereas at finite $β$ bifurcations and distinct equilibria sharing the same boundary have been reported in the literature. In this paper, we propose prescribing the Poincaré cross-section of the field at a single toroidal plane, and implement it in \texttt{DESC}, where the new condition enters only through the linear constraints and therefore costs no more than a fixed-LCFS solve. Fixing the geometry on one plane rather than on a full toroidal surface generally leaves more of the spectral coefficients free, and the ones it frees are those carrying the toroidal variation of the boundary flux surface, which a prescribed LCFS holds fixed at every toroidal angle; together these allow better-converged numerical solutions. We solve equilibria with the cross-section held fixed, starting either from the axisymmetric shape obtained by revolving that cross-section toroidally, or from an existing fixed-LCFS solution. In the latter case, the volume-averaged normalized force error falls by an order of magnitude while the configuration stays close to the original one, and re-solving the resulting boundary with the conventional fixed-LCFS solver recovers the same equilibrium. We further show that the Poincaré coefficients can be used directly as design variables by optimizing a quasi-helical configuration that maintains high-fidelity force balance throughout the process.

Estimating global energy fluxes during COMPASS disruptions via magnetic measurements

Nicola Isernia, Ondřej Ficker, Bojana Stefanoska, Daniil Kabirov, Victor Fernández-Pacheco Albandea, Gabriele Ferrari, Vadim Yanovskiy, Fabio Villone, Martin Imrisek, Petr Vondracek, et al.

During tokamak disruptions, a significant amount of poloidal magnetic energy is converted into other energy forms within the plasma, contributing to the thermal load on the first wall and the surrounding plasma facing components. The amount of magnetic energy converted to plasma thermal losses depends on the duration of the current quench as compared to the electromagnetic time of surrounding conductors. We implement a first-principle method to estimate plasma thermal losses during disruptions for the tokamak COMPASS. The method assumes the plasma evolves through MHD equilibrium states during the disruption, but it does not require any equilibrium reconstruction, elaborating exclusively raw magnetic measurements. The robustness of the method is validated against numerical simulations and different diagnostic measurements. An extensive analysis of energy fluxes during COMPASS disruptions is considered, showing how the poloidal magnetic energy influx contributes to losses and the role of halo currents in the task.

On the relationship between the H-mode separatrix density and engineering parameters across multiple tokamaks: physics-based models, regression, and extrapolations to next-step devices

Davide Silvagni, Ondřej Grover, Adriano Stagni, Jerry W Hughes, Marco Andrés Miller, Bartosz Lomanowski, L. Balbinot, Guido Ciraolo, Wouter Dekeyser, Michael G Dunne, et al.

The electron density at the separatrix (n e,sep ) plays a central role in balancing energy confinement, detachment achievement, and ELM suppression in tokamaks, thereby influencing core-edge integration. To study what determines this key parameter, a database of H-mode separatrix density measurements from the Alcator C-Mod, ASDEX Upgrade, and JET tokamaks has been assembled using a consistent analysis method across all devices. This dataset is used to assess the validity of a physics-based predictive model and to derive a regression scaling expression for n e,sep , both requiring only engineering parameters as input. The theory-based expression is obtained by coupling two-point model equations with simple geometrical relations, and successfully reproduces experimental measurements across all three devices, with the exception of a common multiplicative constant. The regression confirms similar parameter dependencies, revealing a positive dependence on divertor neutral pressure and the ratio of the power entering the scrape-off layer to the major radius, a negative dependence on the toroidal magnetic field and minor radius, and no significant dependence on the plasma current. Both the resulting scaling and theory-based expressions predict n e,sep within a factor of 1.5 across the three machines, and provide projections to next-step devices (ITER, SPARC, DTT, JT-60SA and COMPASS-U) that are in agreement with available SOLPS simulations.