Recent Publications

Investigation of magnetic field ripple effects on charged particles transport in scrape-off layer of Heliotron J

Furui Cai, Shinichiro Kado, Gakushi Kawamura, Yuhe Feng, Ryota Matoike, Shinsuke Ohshima, Shigeru Inagaki, Fumiyoshi Kin, S Kobayashi, Shinichiro Inagaki, et al.

The impact of helical magnetic ripples on the transport of plasma and carbon impurities in the scrape-off layer (SOL) of a Heliotron J device was investigated using the EMC3-EIRENE code. Comparisons with a simplified one-dimensional fluid model revealed that the transport behavior varied with the Knudsen number (K), defined as the ratio of the ion-ion collisional mean-free path to the ripple scale length. In the weakly collisional regime (K≫1), the qualitative trends suggested by the fluid model indicate that the magnetic mirror effects become dominant, the conductive heat flux governs the heat transport, and the impurity density follows a Boltzmann distribution. Conversely, in the collisional regime (K≪1), the transport exhibits nozzle-like fluid behavior, convective heat flux governs heat transport, and impurities couple to the bulk plasma. These characteristics underscore the importance of charged-particle transport along magnetic field lines in the SOL of fusion devices, where magnetic ripples fluctuate significantly with changes in the magnetic field configuration.

Characterizing flux-surface shapes in tokamaks and quasi-symmetric stellarators

M. J. Gerard, M. J. Pueschel, S. D. Stewart, H. O. M. Hillebrecht, B. Geiger

Modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through flux-surface shaping. Here, we examine different methods for characterizing stellarator flux-surface shapes in a manner analogous to flux-surface shaping in tokamaks. The methods considered use a Fourier analysis to define the shaping modes (e.g., elongation, triangularity, squareness, etc.) of equilibrium cross sections. Relative to an axisymmetric equilibrium, the additional degree of freedom in a non-axisymmetric equilibrium manifests as a rotation of each shaping mode about the magnetic axis. This analysis is performed on non-axisymmetric configurations with a high degree of quasi-symmetry and equilibria with varying quasi-symmetry quality from the quasi-symmetric Stellarator Repository database. One method in particular is shown to reduce shape complexity in quasi-symmetric equilibria by defining a set of cross sections that efficiently fill out an equilibrium volume. This is accomplished by defining a cross section as the set of points that occupy the shortest distance between the magnetic axis and an equilibrium flux surface across all quasi-symmetry contours. Using this method, we find empirically that an equilibrium geometry can be described with significantly fewer non-negligible shaping modes relative to other shape characterization methods. Moreover, the method reveals that quasi-symmetry quality is strongly correlated with equilibrium shapes that exhibit a highly constrained linear distribution of shaping modes, where an increase in shape complexity is proportional to an increase in shape rotation about the magnetic axis. It is therefore argued that this method provides a way to efficiently characterize the shape of quasi-symmetric equilibria in a manner analogous to how equilibrium shapes are described in tokamaks.

Determining neutral fueling response to RMPs in MAST using a multi-reservoir particle balance model and EMC3‑EIRENE

K Flesch, James R Harrison, Andrew Kirk, Ian Waters, Heinke Frerichs, Oliver Schmitz, Livia Casali

The application of certain configurations of resonant magnetic perturbations (RMPs) has been shown to cause a plasma pump-out in both L- and H-mode discharges at MAST. In this paper we discuss the impact of neutral fueling on this density reduction. The neutral fueling and average particle confinement time $\tau_p$ of the main ion species were calculated using a 0-D particle balance analysis. When the RMPs were applied, it was found that there was an increase in ionizations and a 15$\%$ reduction in $\tau_p$ for L-mode discharges and a similar result for inter-ELM (edge localized modes) periods of H-mode discharges. A time-dependent global multi-reservoir particle balance (MRPB) was developed, which included atomic and molecular reservoirs, to further investigate the role neutrals had on the density change. We discuss how this model was able to accurately reproduce the experimentally measured density reduction and ionization increase due to either a reduction in $\tau_p$ or a reduction in particle fueling efficiency. Results from EMC3-EIRENE modeling indicate this change could be attributed to neutral particle fueling occurring in locations with now-opened fieldlines due to the chaotic edge-region from RMP applications.

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.

Adaptation of Nuclear Fission Cost Estimation Tools for Fusion Energy Systems

Matthew J. Nyberg, Virginia Lilly, Jia Zhou, Nicolas Stauff, Craig M. Jacobson, Ben A. Lindley

Exploration of an intrinsic low-collisionality, high performance, grassy ELM regime in the DIII-D tokamak

Zeyu Li, H Q Wang, Xi Chen, Xueqiao Xu, Rongjie Hong, Filipp Khabanov, V. S. Chan, Patrick H Diamond, Brian S Victor, Nami Li, et al.

Recent DIII-D tokamak experiments have demonstrated the integration of intrinsic low-collisionality grassy edge-localized mode (ELM) regime with high-performance hybrid core scenario, possibly offering a core-edge compatible solution for ITER and future fusion reactors. This regime features grassy ELMs (with ELM energy loss over pedestal stored energy <2%) at ITER-relevant pedestal top collisionality (ν_e^*~0.1), ITER similar shape, while maintaining high core confinement (H_98y2~1.5) in non-inductive hybrid scenarios. A small ELM-focused database is constructed to investigate the parametric dependence of the small/grassy ELM regimes. Access and sustainment of this regime appear to be favored by high poloidal beta (β_p>1.5), higher ratio of separatrix-to-pedestal density (n_(e,sep)⁄n_(e,ped) >0.4) and low pedestal top collisionality (υ_(e,ped)^*=0.1-0.4). In this scenario, the pedestal width exceeds the prediction from EPED–KBM scaling, consistent with the expectation of a turbulence-limited pedestal. Linear modeling using ELITE indicates that this grassy ELM regime is along the peeling boundary. Relative to a large-ELM phase, the grassy-ELM phase exhibits a broader inner-target heat-flux width and a substantially reduced ELM-induced transient heat-flux increment. These results motivate further evaluation of low-collisionality grassy ELMs as a potentially reactor-relevant operating regime, while full-duration sustainment and compatibility with divertor detachment remain unresolved.

An Investigation of Surrogate-Assisted, Gradient-Based Methods for Stellarator Breeder Geometry Optimization

Connor A. Moreno, Paul P. H. Wilson

Assessment of divertor structures arising from invariant features in Hamiltonian system for three-dimensional magnetic field in Heliotron J

Furui Cai, Shinichiro Kado, Gakushi Kawamura, Yuhe Feng, Fumiyoshi Kin, Ryota Matoike, Shinsuke Ohshima, Shigeru Inagaki, S Kobayashi, Shinichiro Inagaki, et al.

The divertor structures of Heliotron J were investigated by analyzing the three-dimensional magnetic field and plasma transport simulations. The magnetic field of Heliotron J typically exhibits a characteristic resonant structure, where the stable and unstable manifolds emanating from specific X-points determine the divertor legs and the boundary of a confined core region. Regions zoned according to the divertor helical period provide information about the plasma; the boundary of the shadowed region determines the plasma-occupied volume, and the first multi-fold layer determines the fluid acceleration in an island-like configuration. The divertor legs guide the transport of charged particles outside the core. Density accumulates, and the fluid velocity decreases at the intersection points of the legs. The particle and heat depositions on the target plate can be inferred from the lobe structures and their relative toroidal locations on the divertor legs. We found that a chaotic divertor structure can potentially reduce the peak particle and flux densities by creating multiple strike lines, which is preferred for the design of future devices.

FED Thea energy special edition editorial

B. Geiger, S. Henneberg

MHD simulation study on impurity assimilation efficiency and disruption dynamics during shattered pellet injection

Jinqiang Mao, Ping Zhu, Shiyong Zeng

Shattered pellet injection (SPI) has become a critical technique for mitigating plasma disruptions in fusion devices, yet optimizing its efficiency demands a proper understanding of the interaction between impurity dynamics and MHD response. We perform 3D nonlinear MHD simulations of SPI-induced disruption in a J-TEXT-like tokamak using the NIMROD code, systematically examining key parameters: fragment velocity and size, injection quantity, impurity composition, injection location and multiple injectors, resistivity, and parallel thermal conductivity. We find that slower fragment velocity enhances impurity assimilation and amplifies MHD activity. Smaller fragments significantly increase impurity ablation and cooling efficiency. Mixed deuterium-neon pellets effectively elevate electron density without compromising radiative cooling efficiency. Plasma poloidal rotation affects ablation and cooling efficiency, whereas toroidally uniform multi-pellet injection enhances impurity ablation by nearly a factor equal to the number of pellets and lowers radiation asymmetry. Higher plasma parallel thermal conductivity results in higher radiation cooling efficiency in parallel directions, enhances impurity transport, and reduces the toroidal peaking factor of radiation. Variations in resistivity significantly influence Ohmic heating, impurity deposition and current dynamics after thermal quench, with higher resistivity leading to stronger magnetic perturbations and more pronounced current spikes. These findings provide physical bases for optimizing SPI schemes in future tokamak devices.

First Observation of Currents Induced by Alfvén Eigenmodes in a Magnetic Confinement Device

W. W. Heidbrink, X. D. Du, M. E. Austin, K. J. Callahan, C. T. Holcomb, J. B. Lestz, L. Liu, G. R. McKee, L. Schmitz, M. A. Van Zeeland, et al.

Comparing HSX Reflectometer Measurements with a Full-Wave Synthetic Diagnostic

Henrique Oliveira Miller Hillebrecht, Michael Gerard, Michael Richardson, Gavin W Held, Gavin McCabe Weir, Benjamin J Faber, M J Pueschel, Xiang Han, Benedikt Geiger

A synthetic reflectometer diagnostic has been developed to model the reflectometer used at the Helically Symmetric Experiment (HSX) stellarator. The main purpose of the HSX reflectometer is to measure density fluctuations in order to study turbulence and coherent modes in HSX. A full-wave 2-D synthetic diagnostic modeling the HSX reflectometer has been used to investigate its radial localization, characterize its sensitivities, and relate gyrokinetic simulations to physical measurements. The synthetic diagnostic results show that signal localization peaks slightly outboard of the cutoff surface, with the main localization lobe spanning between 15% and 30% of the minor radius. The poloidal and radial wavenumber sensitivities are k θ < 1.7 cm -1 and k r < 6 cm -1 , respectively, with minimal variation in k r sensitivity across probing regions and density profiles. Conversely, k θ sensitivity increases to > 2 cm -1 in the core of the device, in accordance with an increase in local flux-surface curvature. Synthetic reflectometer signals scale linearly with density fluctuation amplitude over a large range of fluctuation levels. Multiple density fluctuation level estimators are tested to identify the optimal choice for use in HSX, with an equation from G.D. Conway Plasma Phys. Control. Fusion 1999 consistently performing best overall. Synthetic measurements of rescaled density fluctuations from a gyrokinetic simulation are then compared against experimental measurements, with coherent mode activity at 13 -15 kHz and 22 kHz observed in both experimental and synthetic frequency spectra. Synthetic spectra overestimated experimental spectra at low frequencies and underestimated at high frequency.

Determining neutral fueling response to RMPs in MAST using a multi-reservoir particle balance model and EMC3 EIRENE

Kurt Flesch, James Harrison, Andrew Kirk, Ian Waters, Heinke Frerichs, Oliver Schmitz, Livia Casali

The application of certain configurations of resonant magnetic perturbations (RMPs) has been shown to cause a plasma pump-out in both L- and H-mode discharges at MAST. In this paper we discuss the impact of neutral fueling on this density reduction. The neutral fueling and average particle confinement time $τ_p$ of the main ion species were calculated using a 0-D particle balance analysis. When the RMPs were applied, it was found that there was an increase in ionizations and a 15$\%$ reduction in $τ_p$ for L-mode discharges and a similar result for inter-ELM (edge localized modes) periods of H-mode discharges. A time-dependent global multi-reservoir particle balance (MRPB) was developed, which included atomic and molecular reservoirs, to further investigate the role neutrals had on the density change. We discuss how this model was able to accurately reproduce the experimentally measured density reduction and ionization increase due to either a reduction in $τ_p$ or a reduction in particle fueling efficiency. Results from EMC3-EIRENE modeling indicate this change could be attributed to neutral particle fueling occurring in locations with now-opened field lines due to the chaotic edge-region from RMP applications.

FIREFLY: heat load and particle exhaust approximations for rapid evaluation of divertor designs

Heinke Frerichs, Dieter Boeyaert, Yuhe Feng, Detlev Reiter

The divertor in a magnetic confinement fusion reactor is an essential component for power dissipation and particle removal. This article introduces the FIREFLY package for rapid evaluation of divertor designs based on an extension of the FLARE code for field line reconstruction from an unstructured flux tube mesh. First, divertor heat loads are approximated with a simplified heat transport model. Neutralized particles are then sampled from the resulting distribution, and the EIRENE code is used to track molecules and atoms in a plasma background while accounting for dissociation, charge exchange and ionization. Particles are removed on pumping surfaces in order to estimate the exhaust efficiency for a given divertor geometry. Optimization of the divertor geometry for more efficient particle exhaust is explored by using W7-X as an example, and the sensitivity to model parameters for the plasma background in the proxy calculations is evaluated.

Understanding carbon sourcing and transport originating from the helicon antenna surfaces during high-power helicon discharge in DIII-D Tokamak

Atul Kumar, Dhyanjyoti Nath, Wouter Tierens, Jeremy D Lore, R S Wilcox, Gilson Ronchi, Morgan W Shafer, Aditya Y Joshi, Onkar Sahni, Mark Shephard, et al.

The high-power helicon wave system in the DIII-D tokamak could potentially introduce new plasma--material interaction (PMI) challenges owing to rectified RF sheath potentials that develop near the antenna and surrounding plasma-facing components. We present the first application of the STRIPE (Simulated Transport of RF Impurity Production and Emission) framework to helicon-induced PMIs, extending previous STRIPE studies of ICRH antennas by incorporating net erosion, local re-deposition, and three-dimensional global impurity transport. The integrated workflow couples SOLPS, COMSOL, RustBCA, GITR, and GITRm to simulate carbon erosion, re-deposition, and impurity transport for two experimentally constrained DIII-D H-mode helicon operating scenarios with different antenna--plasma gaps, coupled RF powers, and edge plasma conditions. COMSOL predicts rectified RF sheath potentials of 1--5~kV localized near the lower portion of the antenna, where the magnetic field intersects the surface at grazing incidence. Carbon self-sputtering dominates the erosion source, whereas RF-accelerated D$^+$ ions contribute approximately 1\% of the total gross erosion. The smaller-gap operating scenario exhibits substantially stronger gross erosion, enhanced local re-deposition ($\sim$12\%), and a larger confined carbon inventory owing to increased plasma accessibility and broader RF sheath coverage. Comparison with available DIII-D measurements shows no distinct change in the global carbon signal that correlates with the helicon RF pulse, consistent with the simulations indicating that the helicon-generated carbon source remains small compared with the existing background carbon inventory under the present graphite-wall operating conditions. These results demonstrate the capability of STRIPE to integrate RF sheath modeling, plasma transport, surface interaction physics, and three-dimensional impurity transport for the interpretation of helicon-induced PMIs. The study further identifies the principal sources of modeling uncertainty, including grazing-angle RF sheath physics, slow-wave resolution, plasma-background extrapolation, and trace-impurity transport assumptions, providing a framework for future validation and model development.

Suppression of ion temperature gradient modes by Alfvén activity above a drive threshold in DIII-D

X. D. Du, W. W. Heidbrink, Z. Yan, P. H. Diamond, G. R. McKee, L. Schmitz, R. Hong, M. A. Van Zeeland, K. J. Callahan, H. Q. Wang, et al.

A recent study demonstrates that the suppression of ion temperature gradient (ITG) modes can occur during the nonlinear evolution of toroidicity-induced Alfvén eigenmodes (TAEs) in the DIII-D tokamak [Du et al., Phys. Rev. Lett. 135, 265101 (2025)]. In that work, ITG was suppressed by the formation of a narrow, TAE-induced shear flow layer, whose shearing rate exceeded the ITG decorrelation rate. The shear flow arises from an imbalance between Reynolds and Maxwell stress forces, as the TAE departs from the conventional shear Alfvén wave polarization. This follow-up paper systematically identifies the plasma conditions required for robust ITG suppression through a series of comparative experiments. The results show that TAEs routinely suppress ITG turbulence in plasmas with higher local safety factor (q), elevated fast-ion beta, and larger populations of fast ions on passing orbits, i.e., conditions consistent with the substantial TAE drive. Database analysis further reveals the existence of a threshold in TAE drive for ITG suppression. That is, once the drive exceeds a critical value within a favorable q window, the system undergoes the nonlinear bifurcation process, characterized by a sharp increase in TAE saturated amplitudes at a nearly fixed fast ion drive, suppression of ITG turbulence, and the formation of an internal thermal transport barrier at the localized radii.

Boundary turbulence simulations of the optimized HSX stellarator and comparison with experiments

Z. Tecchiolli, L. Da Silva, J. Loizu, D. Boeyaert, A. Wolfmeister, W. Guttenfelder, P. Ricci, N. Nikulsin, B. De Lucca, D. Mancini

We present the first-ever full- f , three-dimensional, two-fluid simulation of plasma turbulence based on the drift-reduced Braginskii equations in the optimized Helically Symmetric eXperiment (HSX) stellarator in its quasi-helical configuration. The simulation is carried out by using the GBS code, adapted to simulate 3D magnetic fields with large torsion and ellipticity. The simulation results are compared with edge measurements performed by Guttenfelder et al (2009 Phys. Plasmas 16 082508) using Langmuir probes and Thomson scattering. The comparison shows good agreement in time-averaged density, electron temperature, and electrostatic potential profiles. A good match is also observed in turbulent properties, namely in the frequency spectra of fluctuations and in spatial correlation measurements. Field-aligned turbulence is found to be curvature driven and developing at finite k ∥ , as proposed in a quasi-linear theory by Rafiq et al (2010 Phys. Plasmas 17 022502). Frequency spectra of E × B turbulent transport is consistent with experimental results. Fluctuations levels are underestimated by the simulation. For the first time in stellarator edge turbulent modeling, the effective transport coefficients in the HSX edge are provided.

A distributed computation library for common modeling tasks in magnetic confinement fusion

A. Knieps, D. Böckenhoff, D. Boeyaert, S. Bozhenkov, M. Endler, Y. Feng, Y. Gao, J. Geiger, Y. Liang, L. Liao, et al.

Real-time plasma monitoring framework for advanced plasma control and ML-research in DIII-D

SangKyeun Kim, Keith Erickson, Azarakhsh Jalalvand, Ramon Reed, Ricardo Shousha, Andy Rothstein, Jalal Butt, Filippo Scotti, Steve Allen, Semin Joung, et al.