Recent Publications

Non-diffusive pitch-angle scattering of runaway electrons in the presence of whistler waves

Yashika Ghai, D. Del-Castillo-Negrete, D. A. Spong, M. T. Beidler

Wave–particle interactions between high-energy electrons and whistler waves lead to pitch-angle scattering of electrons in space, astrophysical, and fusion plasmas. In this work, we present a first-principles-informed computational framework to study runaway electron (RE)–whistler interactions in realistic three-dimensional tokamak geometry, enabling investigation of RE pitch-angle transport beyond the assumptions of quasilinear theory. This framework is realized by coupling all-orders spectral algorithm, which solves the full-wave Maxwell–Vlasov system for whistler eigenmodes in a given tokamak equilibrium, with kinetic orbit runaway electrons code, a kinetic orbit code that follows full-orbit RE trajectories in prescribed wave fields. Statistical analysis of the pitch-angle distribution moments and displacement variance is used to characterize the RE transport behavior. We find that REs undergo significant pitch-angle scattering and exhibit energy-dependent, non-diffusive transport behavior. In particular, we observe transitions between diffusive, subdiffusive, and superdiffusive transport regimes depending on the initial RE kinetic energy, a behavior not captured within the standard quasilinear diffusion framework. These results provide new physical insights into RE transport driven by wave–particle interactions and are relevant to the development of wave-based control schemes for REs in fusion plasmas.

Bayesian Active Learning of Ion Loss-Cone Boundaries in Tokamaks

Omar E. Lopez, Minglei Yang, Mark Cianciosa, Gary M. Staebler

Loss-cone boundary determination in tokamaks is cast as an active learning problem in which a Bayesian logistic regression model with radial basis function features acts as the learner and the guiding-center orbit integrator acts as the labeling method. The approach is applied to an analytic tokamak equilibrium across a mesh of launch positions, producing a database of loss-probability models with approximate posterior uncertainty, each generated within a prescribed trajectory budget. Once generated, the database supports downstream applications, illustrated here with three examples. First, integrating the probability models against a Maxwellian distribution yields the lost-ion fraction and the energy and parallel momentum carried by lost ions, with posterior uncertainty propagated analytically to each integral. Second, a steady balance between the resulting orbit-loss torque and radial angular-momentum diffusion gives co-current edge rotation whose amplitude is set mainly by the prescribed momentum diffusivity and loss-region renewal rate. Third, a neural network surrogate trained on the database learns the in-domain mapping from launch position to loss-probability image, and transport integrals computed from its predictions closely reproduce the Bayesian reference values on held-out samples from the same mesh.

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.

Singularities of the cold plasma theory: Modeling challenges for ICRF operation in low-density edge plasma

Wouter Tierens, Chris Klepper, Raymond Diab, Guillaume Urbanczyk

Sustained ICRF operation in a fusion power plant may require low edge densities to mitigate plasma-wall interactions, a regime which was recently achieved in WEST with very little impurity sputtering. Cold plasma theory, however, predicts singular radiofrequency electric fields in this regime, both at the lower hybrid resonance and along the resonance cones, raising the question of whether standard collisional cold plasma models suffice to describe low-density edge ICRF at all. Collisions in principle remove these singularities, replacing them with finite but sharply peaked fields. We derive these peak length scales analytically and confirm them with a 2D finite-element simulation using exponential mesh refinement, achieving micrometer resolution where needed. We conclude that edge collisions in cold plasma do not remove the need to resolve length scales ordinarily associated with hot-plasma and Bernstein-wave physics.

AI-Accelerated Gyrokinetic Predictions of Turbulent Transport for Stellarator Design Optimization and Experimental Planning

R. Michael Churchill, Matt Landreman, Jong Youl Choi, Byoungchan Jang, Rory Conlin, Noah Mandell, Anima Anandkumar, Valentin Duruisseaux, Jeffrey Larson, Dario Panici, et al.

Previous work built AI-based surrogates for a nonlinear gyrokinetic simulation code with the goal of using them for fast, direct calculations of turbulent ion heat flux in stellarator design optimizations and scenario planning for experiments. These AI surrogates were trained on data from >200k nonlinear, adiabatic electron gyrokinetic simulations with the gyrokinetic flux-tube code GX, using a wide range of stellarator magnetic configurations ($\sim$23k), positions in the plasma, and gradient scale lengths. In this paper, we demonstrate the use of the AI-based turbulence surrogate in the optimization of stellarator magnetic equilibrium and to speed up stellarator transport solvers. Due to its speed ($\sim$ms), the AI-based surrogate enables previously unattainable optimization objectives, such as full radial profiles of ion turbulent heat flux, or directly optimizing to maximize the turbulent critical gradient at multiple locations across the plasma. These direct calculations provide a potentially more accurate optimization target and reduce reliance on ad-hoc heuristics that may not accurately capture the variation of turbulent transport with magnetic configuration. By including the AI-based surrogate for turbulent heat flux in a transport solver, we can quickly postprocess and confirm the improved ion temperature resulting from the optimized equilibrium. Finally, we demonstrate the use of AI agents with strong reasoning AI models to automate the outer loop, exploring many objective and hyperparameter configurations with this AI-based turbulence surrogate to discover improved turbulence optimized magnetic equilibria.

Numerical Analysis Supporting the Operation of an Open-Surface Fast-Flow Liquid Lithium Experiment for Divertor Cooling in Fusion Reactors

Daniel Suarez, Sergey Smolentsev, Anatoliy Vorobev

Development and preliminary validation of a Nek5000-based magnetohydrodynamics solver for fusion blanket relevant liquid metal and molten salt flows

Filipe L. Brandao, Arpan Sircar, Marco Delchini, Vittorio Badalassi

The poloidal fuelling location and its effect on the pedestal and H-mode plasma performance in MAST Upgrade

Steven Thomas, Jerry W Hughes, Alex Tookey, Bartosz Lomanowski, Davis Easley, Jack Lovell, Christopher Beckley, James R Harrison, Edward DeWit, Saskia Mordijck, et al.

This paper presents the first results exploiting the high-speed video (HSV) diagnostic on MAST Upgrade to infer neutral deuterium quantities from D α emission. We detail the process for absolute calibration of HSV which now produces 2D line-of-sight-integrated brightness (ph sr -1 m -2 s -1 ) of D α emission in the MAST-U main chamber, showing excellent quantitative agreement with other D α and neutral diagnostics. A typical workflow to combine HSV data with a collisional-radiative model, and electron density, n e , and temperature, T e , measurements to produce 1D radial profiles of neutral density, n 0 , and cold deuterium ionisation source rate, S 0 , is documented. The analysis is applied to a series of double null, neutral beam heated H-mode discharges in MAST-U changing the poloidal fuelling location. It is shown how the low-field side (LFS) pedestal electron density is resilient to, and remains largely unaffected by, the choice of poloidal fuelling location, as does n 0,sep despite differences in neutral pressure measured at the wall. LFS fuelling is seen to increase S 0 , reducing the pedestal electron temperature which decreases edge collisionality, ν*, and allows for core n e to be increased. S 0 is used to constrain inferences of deuterium ion flux, Γ, in a 1D radial transport model. When fuelling from the LFS, Γ becomes increasingly negative at the pedestal top, indicating an inward flux of particles, and is used with the diffusive-convective ansatz showing a negative convective transport coefficient, v, implying an inward particle pinch.

Comparison of the pressure drop and flow characteristics between two designs of a liquid metal blanket supply system

Yuchen Jiang, Yuqiao (Joy) Fan, Sergey Smolentsev

Experimental investigation of ICRF antenna operation and plasma-wall interaction in the regime of propagating slow waves in front of the antenna

Raymond Diab, Laurent Colas, Seung Gyou Baek, Nicolas Fedorczak, Benoit Guillermin, James Paul Gunn, Julien Hillairet, Curtis A Johnson, Ernesto A Lerche, Guillaume Urbanczyk

Ion cyclotron range of frequencies (ICRF) antenna operation and plasma-wall interaction were investigated on the WEST tokamak in the regime where the density at the antenna limiters was sufficiently low for the slow wave (SW) to propagate in front of the antenna. Using a reciprocating emissive probe magnetically connected to the antenna, we measured for the first time the DC plasma potential, VDC, during a radial scan of the LH resonance layer across the antenna limiter. VDC peaks when the density at the antenna limiter edge approaches the LH resonance density, but never exceeds typical values of a few hundred volts. From the plasma-wall interaction standpoint, this regime is highly favorable: because particle fluxes are reduced while sheath potentials remain comparable to standard operating conditions at the same antenna voltage, local tungsten sources at the ICRF antenna and other outer-wall components become nearly undetectable. In general, tungsten sputtering from active WEST ICRF antennas is dominated by the particle flux rather than the sputtering yield; that is, it follows variations in the local density rather than the plasma potential. By contrast, sputtering in the divertor is primarily governed by the sputtering yield. Core impurity contamination is likewise significantly reduced when the antennas are positioned far from the separatrix, both with and without ICRF power, and the radiated power fraction decreases accordingly. Despite the modest coupled powers obtained at large antenna-plasma clearance, satisfactory ICRF heating is maintained as the density at the antenna limiter edge falls below the LH resonance, and no deleterious effects are observed in any key core plasma metrics when operating the antenna from this low-density region. Overall, the experimental results point toward minimal coupling to the SW by the fast wave antenna despite it being located in a region where the SW can propagate.

Experimental observation of non-resonant divertor resiliency in the Compact Toroidal Hybrid experiment

N.R. Allen, D.A. Maurer, D.A. Ennis, K.A. Garcia, D.M. Kriete, O. Schmitz, A. Bader, J.C. Schmitt, M. Cianciosa

The first experimental measurements of a novel non-resonant divertor (NRD) magnetic topology, to exhaust particles and heat in stellarator plasmas, yields an order of magnitude improvement in strike line resiliency when compared to an island divertor. The NRD concept leverages resilient invariant manifolds near sharp flux surface boundaries in an otherwise chaotic magnetic field to decouple the exhaust channels within the plasma boundary from the three-dimensional equilibrium properties of the confined plasma. Ion flux profiles are measured during two different vacuum magnetic configurations within the Compact Toroidal Hybrid experiment, allowing for investigations of the strike line response to the evolution of the ohmically driven plasma current. During the NRD portion of the discharge, the majority of the strike line locations are observed to shift poloidally by ⩽ 80 mm/ Δ − ι when varying the edge rotational transform, − ι , by ⩽ 0.24. These observations are in agreement with diffusive field line modeling of the NRD magnetic topology and promote further investigation of this concept as a possible divertor solution for an optimized stellarator fusion power plant.

Pellet-Size Scaling of Quasi-Steady-State Plasma Performance in Wendelstein 7-X

Keisuke Fujii, Edgardo Villalobos Granados, Maryam Huck, Jürgen Baldzuhn, Naoki Tamura, Steven Meitner, Larry Baylor, Golo Fuchert, Kai Jakob Brunner, Jens Knauer, et al.

A continuous cryogenic-pellet injector has been used to realize long-pulse high-performance plasmas in Wendelstein 7-X (W7-X). A hydrogen ice pellet deposits particles directly in the confined region. If the particles are deposited sufficiently far inside the plasma, they produce a density gradient that suppresses ion-temperature-gradient turbulence and improves plasma confinement. However, after multiple pellets have been injected and the plasma density and temperature have increased, the plasma performance begins to saturate. In this work, we analyze multiple pellet-injection experiments conducted in 2024 and 2025, during which the injected pellet sizes varied unintentionally. This analysis reveals a positive correlation between pellet size and the quasi-steady-state stored energy of W7-X plasmas. Although this pellet-size dependence can be understood qualitatively from pellet-ablation physics, the measured deposition position differs quantitatively from the neutral-gas-shielding (NGS) model prediction. This discrepancy suggests significant inward transport of the pellet cloud. The trend identified here suggests that injection of even larger pellets could further improve plasma performance.

Electromagnetic gyrokinetic analysis in Tokamak Energy’s pre-concept design of the ST-E1 fusion power plant

Alexandra V Dudkovskaia, Jeff Candy, Emily A Belli, Michail Savvas Anastopoulos Tzanis, Steven A.M. McNamara, Andrew Oakleigh Nelson, Yang Ren, Timothy Stoltzfus-Dueck, Carl Friedrich Benedikt Zimmermann

ST-E1 is Tokamak Energy's fusion power plant concept. A series of reference flat-top plasma operating points were developed in [S McNamara et al. Nucl. Fusion 66 (2026) 086008]. The present work focuses on the low-density baseline conceptual power plant (BCP) operating point of [S McNamara et al. Nucl. Fusion 66 (2026) 086008], selected as representative of ST-E1, and investigates its micro-stability, turbulent transport and transport-informed optimisation using first-principles spectral flux-tube electromagnetic gyrokinetic simulations. Linear gyrokinetic calculations, involving electrons, thermal ions, impurities, and thermal and fast helium ions, complemented by dynamic mode decomposition to identify subdominant and stable drift-wave eigenmodes, reveal two principal long-wavelength electromagnetic instability branches: hybrid h-ITG modes driven by thermal gradients and FI-KBMs, i.e., kinetic-ballooning-like modes strongly influenced by plasma beta and fast-ion population. At shorter wavelengths, electron-temperature-gradient modes become unstable towards plasma edge while remaining stable in the core. A comprehensive sensitivity analysis identifies principal equilibrium parameters governing these instabilities. Building on these linear predictions, nonlinear electromagnetic gyrokinetic simulations quantify turbulent transport of thermal plasma and fast helium ions. The reference operating point is found to exhibit saturated, rather than runaway, electromagnetic turbulence, establishing it as a physically meaningful baseline for further optimisation. Turbulent transport is governed primarily by combined effects of plasma beta, safety factor and fast-ion fraction, with intrinsic-rotation-driven ExB shear providing complementary suppression. Although fast ions provide free energy driving FI-KBM branch, increasing fast-ion fraction is found to reduce saturated turbulent transport across all species through nonlinear self-organisation. To explore the resulting multidimensional parameter space, a physics-informed interpolation framework constrained and validated by nonlinear gyrokinetic simulations is developed to enable identification of transport-favourable operating points without exhaustive nonlinear parameter scans. This framework yields a family of transport-favourable operating points for ST-E1 low-density BCP equilibrium and provides quantitative targets for future self-consistent equilibrium optimisation.

RF-Specific Tungsten Erosion and Global Transport in ITER under Neon Seeding

Atul Kumar, Dhyanjyoti Nath, Wouter Tierens, Jeremy D. Lore, Andrei Pshenov, Tom Wauters, Andrea Galvan, Davide Curreli, Syun'ichi Shiraiwa, Nicola Bertelli, et al.

Ion cyclotron radio-frequency heating (ICRH) is a key auxiliary heating system in ITER, but high-power RF operation can enhance plasma-material interactions through rectified RF sheath potentials on antenna structures and nearby plasma-facing components. We present the first predictive application of the STRIPE (Simulated Transport of RF Impurity Production and Emission) framework to assess RF sheath-driven tungsten (W) erosion and global impurity transport from the ITER ICRH antenna under ITER-relevant neon-seeded conditions. STRIPE couples SOLPS-ITER plasma backgrounds, full-wave RF sheath calculations, geometry-specific ion energy-angle distributions, sputtering physics, and three-dimensional impurity transport. Simulations predict RF sheath potentials of 1 to 3 kV on antenna limiter sidewalls, increasing gross W erosion by about a factor of 64 relative to thermal sheath conditions and producing a gross source of 3.34e18 W atoms per second. Erosion is governed by RF-modified ion energy-angle distributions together with local plasma flux rather than sheath voltage alone. About 10 percent of sputtered W is locally redeposited, giving a net source of 3.01e18 W atoms per second. The RF-induced antenna source remains about three orders of magnitude smaller than the thermal divertor source and more than two orders of magnitude smaller than the integrated thermal main-chamber source. After 100 ms, about 22 percent of the mobile W inventory resides within the SOLPS-covered confined-plasma region, corresponding to an annular W concentration of 1.70e-6. These results indicate that the ITER ICRH antenna is unlikely to dominate the total W source budget under the conditions considered and demonstrate the need for coupled modeling of RF waves, sheaths, sputtering, redeposition, and global impurity transport.

Special Issue Featuring Papers from the Innovation Network for Fusion Energy (INFUSE)

Arnold Lumsdaine, Ales Necas

Lithium droplet transport in tokamak edge plasmas

A. Diaw, J. D. Lore, S. Smolentsev

A lithium droplet transport and evaporation model has been developed within the direct simulation Monte Carlo code OpenEdge. This model integrates gravity, collisional ion drag, orbital-motion-limited charging, energy-balance evaporation, and an anisotropic rocket recoil force using a Strang-split integrator. Validation against analytical drag-gravity solutions and independent RK45 evaporation integration demonstrates relative errors below 10−5 for droplet radii of 1.5, 2.5, and 3.5 mm. Simulations of ensembles containing 105 droplets, launched from inner and outer divertor surfaces in SOLPS-ITER plasma background for the CAT tokamak reactor concept, indicate that transport outcomes are determined by initial size, velocity, and launch location. Outer-divertor droplets predominantly redeposit locally, whereas inner-divertor droplets reach the low-field-sidewall. Smaller droplets lose most of their mass to evaporation before reaching the core, while larger droplets retain their mass and redeposit on nearby tiles. Both one-way and iterative two-way coupling frameworks map the evaporated lithium onto the SOLPS-ITER mesh as volumetric sources, facilitating self-consistent evaluation of lithium droplet impacts on edge-plasma performance.

Observation of significant non-collisional ion heating in helical plasmas with dominant electron heating by neutral beam injection on LHD

Kazuo Toi, Shigeru Morita, K Tanaka, Akihiro Shimizu, Masaki Nishiura, Kunihiro Ogawa, Novimir Antoniuk Pablant, Donald A. Spong, Tokihiko Tokuzawa, Ichihiro Yamada, et al.

In LHD, transient but significant increases in the central ion temperature T_io are observed in low density plasmas having a non-monotonic rotational transform profile produced by high energy neutral beam injection (NBI). The T_io-increase realizes T_io ~ T_eo (central electron temperature) on strong electron heating condition. The increase gradually decreases as the line-average electron density increases, and disappears once it exceeds 1×10¹⁹ m⁻³. During the T_io-increase phases, turbulent density fluctuations in the core plasma region are not suppressed but are enhanced slightly. The ion temperature increases are attributed to an addition of non-collisional ion heating, but not confinement improvement due to suppression of turbulent transport. The ion heating power density estimated from the time evolution of T_io is much higher than that of collisional ion heating by NBI. The estimated maximum power density averaged over the plasma volume becomes transiently comparable to or even higher than the volume-averaged total NBI heating power density. The observed amplitude of energetic ion driven geodesic acoustic modes (EGAMs) with a significant value 〖eϕ〗_EGo⁄T_io ~ 1 (ϕ_EGo: peak value of the EGAM amplitude at the plasma centre) decreases clearly during the initial T_io-increase phase but is maintained at a finite level, with some modulation, until the end of the NBI pulse. The EGAM damping rate expected from the observed ion heating power density is much higher than the linear Landau damping rate estimated from the GAM dispersion relation of a helical plasma. Nonlinear ion Landau damping in high-amplitude EGAM is thought to be one of the leading mechanisms for qualitatively explaining the observed significant ion heating. The significant T_io-increases always induced in the upward-sweeping phase of n=1 reversed shear Alfvén eigenmode (RSAE) frequency are suddenly suppressed, when nonlinear wave-wave coupling of EGAM with n=1 RSAEs and n=0 global Alfvén eigenmodes (GAEs) is activated noticeably (n: toroidal mode number) in the latter phase of the upward sweeping and the downward sweeping of the RSAE frequency. This observation shows a potentiality of a new energy channeling scenario based on EGAM in a future fusion plasma.

Impact of nitrogen injection on L-H transitions in JET with Be/W wall

Costanza F Maggi, Clarisse Bourdelle, Ephrem Delabie, Mathias Brix, Pedro Carvalho, Francis J Casson, Alex V Chankin, Nicholas Hawkes, Evie Litherland-Smith, Sheena Menmuir, et al.

L-H transition experiments in JET with Be/W wall (JET-ILW), with N2 injection into the divertor region, have revealed that the H-mode power threshold, PL-H, increases with nitrogen injection rate in the high-density branch and modifies the density at which the power threshold is minimum, ne,min. PL-H values approaching those obtained in JET with C wall are achieved for a sizeable increase in nitrogen concentration. At a given density in the high density branch of PL-H, both the total loss power (Ploss) as well as the power crossing the separatrix (Psep) at the L-H transition increase by a factor ~ 1.5 at high N2 levels. At a given line averaged density, while the edge density is similar in plasmas with and without N2 injection, the edge temperature at the L-H transition is higher in pulses with high nitrogen seeding levels and a larger shear of the edge radial electric field Er is measured. At low N concentrations, little change in PL-H is observed. Qualitative agreement is reported with Zeff impact on L-mode edge turbulence drive [1]. The enhanced L-mode edge turbulence drive with N2 seeding at higher Zeff implies that a higher PL-H is expected as, indeed, measured in experiment. It is assumed that the mean equilibrium Er×B shear is a key player for reduction of L-mode edge turbulence, leading to the L-H transition. In this framework, the L-H transition observations in JET-Be/W + N2 are interpreted by an increase in L-mode edge plasma turbulence with increased N concentration and the need for a larger stabilizing ErxB shear, thus higher Psep, to trigger the L-H transition. For future fusion reactors with scenarios with extrinsic low-Z impurity seeding for divertor heat load mitigation, our results suggest the need to predict Psep for H-mode access taking into account not only the high radiation fractions from the bulk plasma, but also the impact of low Z impurity concentration on Ploss and Psep at the L-H transition.

Tritium Management in an All-Carbon First Wall Tokamak Reactor

James Davis, Sellathurai Suppiah, Ezekial Unterberg, Donald Ryland, Peter Stangeby

Machine-agnostic Gaussian process-based surrogate model for electron cyclotron heating and current drive

Andrew M. Irvin, Livia Casali, Sebastian De Pascuale, Ehab Hassan