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DOE OSTI2024

Nonlinear modeling of ELM mitigation with RMP on HL-2A

Abstract Nonlinear modeling of mitigation of the edge localized mode (ELM) with resonant magnetic perturbation (RMP) is performed for the HL-2A tokamak, utilizing the three-dimensional (3D) magnetohydrodynamic code JOREK. Based on the 3D equilibrium established after application of the n = 1 ( n is the toroidal mode number) RMP at 4.9 kAt coil current with odd parity, ELM mitigation is successfully simulated consistent with the experimental result. Nonlinear simulations show strong mode coupling among toroidal Fourier harmonics, allowing redistribution of the magnetic energy such that the most unstable toroidal mode saturates at a lower level. This magnetic energy cascade offers an explanation of the RMP-induced ELM mitigation achieved in HL-2A. Detailed examination of the simulation results shows persistent resonant field screening even during the ELM mitigation phase. Finite plasma resistivity however does enable partial penetration of the resonant field thus modifying the edge magnetic topology and characteristics of the edge transport. Plasma radial profiles undergo pronounced changes around the pedestal region, when the magnetic energy of the most unstable toroidal mode reaches the maximum value. Systematic scans of the applied RMP coil current with the JOREK simulations find a threshold value of around 4.5 kAt required for achieving the ELM mitigation on HL-2A.

Physics↗

DOE OSTI2024

Validation study of RWM stability in DIII-D high- β N plasmas

The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high-β N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

FLARE: field line analysis and reconstruction for 3D boundary plasma modeling

The FLARE code is a magnetic mesh generator that is integrated within a suite of tools for the analysis of the magnetic geometry in toroidal fusion devices. A magnetic mesh is constructed from field line segments and permits fast reconstruction of field lines in 3D boundary plasma codes such as EMC3-EIRENE. Both intrinsically non-axisymmetric configurations (stellarators) and those with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks) are supported. The code itself is written in Modern Fortran with MPI support for parallel computing, and it incorporates object-oriented programming for the definition of the magnetic field and the material surface geometry. Extended derived types for a number of different magnetohydrodynamic equilibrium and plasma response models are implemented. The core element of FLARE is a field line tracer with adaptive step-size control, and this is integrated into tools for the construction of Poincaré maps and invariant manifolds of X-points. A collection of high-level procedures that generate output files for visualization is build on top of that. The analysis modules are build with Python frontends that facilitate customization of tasks and/or scripting of parameter scans.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Ma, Yiming↗

DOE OSTI2024

MHD stability analysis against pressure and current-driven modes in the SMall Aspect Ratio Tokamak

Linear magnetohydrodynamic (MHD) simulations for the SMall Aspect Ratio Tokamak (SMART) have been carried out for the first time, for both positive (PT) and negative triangularity (NT) shaped plasmas using the MARS-F code. The MHD stability of projected SMART plasmas against internal kinks, infernal modes and edge peeling-ballooning modes have been analyzed for a wide range of realistic equilibria. A stabilization of internal kinks and infernal modes is observed when increasing the safety factor profile and reducing plasma beta. PT shaped plasmas are more stable against both internal kinks and infernal modes than their counterpart NT shaped plasmas. Toroidal flows have little impact on the MHD stability of the internal kinks, but they have a strong stabilizing effect on infernal modes, which can be further mitigated in NT shaped plasmas. The MHD stability of peeling-ballooning modes is reduced in NT shaped plasmas, as observed in conventional tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Performance prediction applying different reduced turbulence models to the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with β N ≈ 3.8.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Infernal instabilities in negative-triangularity plasmas with negative central shear

Abstract A systematic numerical investigation is carried out to understand magnetohydrodynamic stability of the ideal infernal-kink instability in tokamak plasmas with both negative triangularity (neg-D) shaping and negative central shear for the equilibrium safety factor profile. The latter is motivated by the desire to form the internal transport barrier in the neg-D configuration, which is known to have difficulty in forming the edge transport barrier. The infernal-kink mode is generally found to be more unstable in neg-D plasmas as compared to their positive D-shaped (pos-D) counterpart. This is mainly due to less favorable (or even unfavorable) average magnetic curvature near the radial location of the minimum safety factor ( q min ) as compared to the pos-D configuration. The larger Shafranov shift associated with the neg-D shape helps the mode stabilization but is not sufficient to overcome the destabilizing effect due to bad curvature. Strong poloidal mode coupling due to plasma shaping (toroidicity, elongation, triangularity, etc.) helps explain the slight shift with respect to that predicted by the analytic theory of the peak location of the computed mode growth versus q min .

Zhang, X. M.↗

DOE OSTI2025

Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfvén turbulence

The separatrix operational space (SepOS) model (Eich and Manz 2021 Nucl. Fusion 61 086017) is shown to predict the L–H transition, the L-mode density limit, and the ideal magnetohydrodynamic ballooning limit in terms of separatrix parameters for a wide range of Alcator C-Mod plasmas. The model is tested using Thomson scattering measurements across a wide range of operating conditions on C-Mod, spanning $\overline{n}_{\mathrm{e}}$ = 0.3–5.5 $\times 10^{20}\,$m −3 , $B_{\mathrm{t}} = 2.5$–8.0 T, and $B_{\mathrm{p}}$= 0.1–1.2 T. An empirical regression for the electron pressure gradient scale length, $\lambda_{{p}_{\mathrm{e}}}$, against a turbulence control parameter, $\alpha_{\mathrm{t}}$, and the poloidal fluid gyroradius, $\rho_{\mathrm{s,p}}$, is constructed for H-modes and found to require positive exponents for both regression parameters, indicating turbulence widening of near-scrape-off layer widths at high $\alpha_{\mathrm{t}}$ and an inverse scaling with $B_{\mathrm{p}}$, consistent with results on ASDEX Upgrade. The SepOS model is also tested in the unfavorable drift direction and found to apply well to all three boundaries, including the L–H transition as long as a correction to the Reynolds energy transfer term, $\alpha_\mathrm{RS} \lt 1$ is applied. I-modes typically exist in the unfavorable drift direction for values of $\alpha_{\mathrm{t}} \lesssim 0.3$. Finally, an experiment studying the transition between the Type-I ELMy and EDA H-mode is analyzed using the same framework. It is found that a recently identified boundary $\alpha_{\mathrm{t}} = 0.55$ at excludes most EDA H-modes but that the balance of wavenumbers responsible for the L-mode density limit, namely $k_\mathrm{EM} = k_\mathrm{RBM}$, may better describe the transition on C-Mod. The ensemble of boundaries validated and explored is then applied to project regime access and limit avoidance for the SPARC primary reference discharge parameters.

ELM suppression↗

DOE OSTI2025

Identification of a window for quiescent H-mode operation in MHD stability diagram of DIII-D plasmas

A window for quiescent H-mode (QH-mode) operation in DIII-D plasmas in the diagram of pedestal magnetohydrodynamic (MHD) stability was identified through linear MHD stability analysis, accounting for the effects of plasma rotation and ion diamagnetic drift. The operation window lies between the stability boundaries of the kink/peeling mode (K/PM) identified with and without the inclusion of plasma rotation effects. In this region, the mode remains unstable unless rotation effects are considered alongside the ion diamagnetic drift, which is consistently included in the analysis. The stabilization of the MHD mode, facilitated by the coupled effects of plasma rotation and ion diamagnetic drift, plays a crucial role in widening the window, enabling the attainment of the QH-mode state. Furthermore, the suppression of edge localized modes (ELM) can be achieved by controlling the pedestal structure to ensure the plasma state remains within the operation window. The location of the operation window in the stability diagram depends on the K/PM stability properties. Therefore, optimizing conditions for QH-mode requires adjustments based on changes in stability characteristics. A pressure pedestal and its associated bootstrap current density near the last closed flux surface are advantageous for situating the plasma state within the window. However, excessive current density can trigger ELMs. This trend was confirmed through comparisons of MHD stability diagrams between QH-mode and ELMy H-mode plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Operational space for lower hybrid heating scenarios in the full tungsten environment of WEST

In tungsten—W—Environment in Steady-state Tokamak (WEST), the lower hybrid current drive (LHCD) system is key for achieving long pulse operation by providing most of the non-inductive plasma current, as well as a crucial source of electron heating. Therefore, determining the operational space for its application is fundamental. In the present study, the LHCD operational space is deeply analyzed for 0.5 MA pulses. This space is bounded by three limits: (i) the ratio of the LHCD power over density must be above a threshold to compensate tungsten radiation with enough core heating, (ii) the line-averaged density must be high enough to allow good coupling of the hybrid wave with the plasma, and (iii) fast electron ripple losses must be below a limit to avoid reaching a thermal threshold on plasma-facing components. If the tungsten radiation peak or burn-through phase is not safely overcome, a maximum electron temperature of 1.5 keV is obtained, confinement is degraded, and magnetohydrodynamic activity is frequently triggered, potentially causing a disruption. From experimental measurements and interpretative simulations, we highlight the main mechanisms that prevent the plasma from heating up during LHCD power ramp-up. Three parameters play a major role: plasma density, tungsten concentration and LHCD power deposition. A strategy to overcome this limitation is found: a precise density ramp-up performed simultaneously with the increase in LHCD power. Additionally, we show that boronization greatly facilitates the burn-through of tungsten by lowering its content during the heating phase. Finally, taking into account the three constraints given above, the LHCD operational space is determined at power ramp-up and during constant heating phases.

lower hybrid heating and current drive↗

DOE OSTI2025

A code-to-code benchmark for magneto-convection in a horizontal duct

Liquid metals and magnetic fields are used in many technical applications such as metallurgy, crystal growth and nuclear fusion reactors. When an electrically conducting fluid moves in a magnetic environment, electric currents and electromagnetic forces are generated that affect velocity and pressure losses in the flow. These magnetohydrodynamic (MHD) interactions have to be investigated to optimize the engineering processes. The characteristics of MHD flows depend on the geometrical configuration, the strength of the applied magnetic field, the electrical properties of fluid and structural materials and the thermal conditions. In the so-called blankets for fusion reactors, where liquid metals are used to breed the plasma fuel component tritium and to extract the generated heat, magneto-convective flows play a crucial role in determining heat and mass transfer. Therefore, the availability of numerical codes to simulate this type of flow is mandatory and their validation is a necessary step to guarantee the reliability of the results. For that reason, a benchmark problem has been defined to simulate liquid metal flows in a horizontal rectangular duct heated from below and exposed to a non-uniform magnetic field. Results obtained by five research groups using different codes are compared.

benchmark↗

DOE OSTI2025

Validation of 3D MHD simulations of Ne/D 2 mixed shattered pellet injection in JET

Nonlinear 3D magnetohydrodynamic (MHD) modeling of shattered pellet injection (SPI) in JET tokamak plasmas is performed with the JOREK code. The study focuses on the validation of simulation result with respect to experimental observations, addressing in particular figures of merit for the efficiency of the SPI, as a technique to mitigate thermal loads by injecting radiative impurities like neon during the thermal quench (TQ) phase of disruptions. A set of JET pulses with neon/deuterium atomic mixture ratio in the shattered pellet varying from 10% to 100% provides the experimental data to be compared with. Simulations using different models for the ablation of solid fragments and the radiation of neon impurities are considered. Synthetic diagnostics are employed for a direct quantitative comparison with key JET diagnostic systems providing in particular radiation, electron temperature and density, and magnetic measurements. 3D radiation structures from MHD simulations are analyzed to estimate the toroidal asymmetry of radiation, which is difficult to measure in JET due to the presence of only two toroidally displaced multi-channel bolometry systems. JOREK simulations show that, before the TQ, the bulk of the radiation is concentrated in a toroidal region enclosing the radiating fragments that is missed by both multi-channel bolometers, suggesting a possible underestimation of the total radiation by such diagnostic systems in the pre-TQ phase. On the other hand, JOREK predicts that during the TQ the radiation becomes more toroidally symmetric, with positive implications for the heat load to plasma facing components.

JOREK↗

DOE OSTI2026

Spherical tokamak physics research in preparation for the operation of NSTX-U

The National Spherical Torus Experiment Upgrade (NSTX-U) is preparing to resume operation, representing a crucial step toward realizing compact, cost-effective fusion pilot plants. In advance of this, extensive modeling and data analysis have been conducted to advance the physics basis for low-aspect-ratio, high-performance plasma regimes, focusing on three core objectives: confinement and stability, power and particle handling, and steady-state operation. Significant progress has been made in understanding the electron temperature flattening in high-β plasmas, which is shown to be driven by a complex interplay of magnetohydrodynamic instabilities (e.g. non-resonant infernal modes), fast-ion-driven Alfvén eigenmodes, and electron and ion-scale micro-instabilities, particularly Kinetic Ballooning Modes (KBMs), whose destabilization is strongly dependent on parallel magnetic field fluctuations (δB ∥ ). Furthermore, a new gyrokinetic critical pedestal model was developed, accurately predicting pedestal structure by identifying KBMs as the primary stability limit, offering a critical constraint for future high-confinement scenarios. To address the challenge of high heat flux, novel liquid lithium plasma-facing components were modeled. The analysis confirmed that lithium vapor shielding is a self-regulating mechanism for heat mitigation, while also emphasizing that strong main ion parallel flow is essential to minimize core lithium contamination. Finally, progress toward steady-state operation was anchored by developing the required physics basis and control tools. This includes predictive modeling for reversed magnetic shear sustainment, demonstrating that magnetic island-induced bootstrap current reduction is negligible in STs, and advancing real-time control and disruption avoidance capabilities. The development of high-speed surrogate models (e.g. MMMNet) provides computationally efficient tools vital for non-inductive scenario optimization and integrated, low-disruptivity operations planned for NSTX-U.

NSTX-U↗

DOE OSTI2026

Instantaneous difference frequency locking observed during toroidicity-induced Alfvén eigenmode coupling in the DIII-D tokamak

In magnetic confinement fusion, toroidicity-induced Alfvén eigenmodes (TAEs) are well-studied, weakly stable solutions of the linearized ideal magnetohydrodynamic equations. Driven unstable by suprathermal populations of energetic particles, TAE pose a key vulnerability to the confinement of high-energy alpha particles generated by fusion reactions. Hence, it is paramount to understand TAE dynamics if a working reactor is to be realized. In this work, we detect and characterize signatures of nonstationary nonlinear coupling between TAE using a novel, time-resolved bispectral analysis; results are supported by analytic signal of band-passed data. Crucially, a stationary phase relationship between two TAE and a nascent low frequency fluctuation is observed precisely when the triple product of magnetic fluctuation amplitudes is enhanced. Local mode number and frequency spectrum, gleaned from beam-emission spectroscopy, corroborates simultaneous satisfaction of nonlinear matching conditions, and provides a tool to identify theorized pathways of energy transfer, e.g. TAE parametric instability.

bispectral analysis↗

DOE OSTI2026

MARS-Q modeling of low- n resistive kink-peeling modes and edge harmonic oscillations in DIII-D

Linear and quasilinear magnetohydrodynamic (MHD) modeling is carried out for two DIII-D discharges that both featured a transition from quiescent H-mode (QH) to wide-pedestal QH (WPQH). The MHD perturbations, associated with the edge harmonic oscillations (EHOs) observed during the QH-phase in both discharges, are identified as low-n (n is the toroidal mode number) resistive kink-peeling instabilities, with the ideal MHD counterpart remaining stable. The quasilinear model successfully simulates EHO-like perturbations during the QH phase in both discharges, confirming the experimental observations. A less intuitive finding is the EHO-like behavior involving the n = 2 perturbation, simulated for one of the discharges during the WPQH-phase. This result, while consistent with experimental observations, is obtained despite the fact that the initial perturbation is linearly stable. The eventual growth of the perturbation is solely due to nonlinear interaction between the MHD perturbation and the plasma toroidal flow. The occurrence of the EHO-like perturbation during the WPQH-phase is found to be sensitive to the initial profile of the plasma edge rotation. For DIII-D plasmas considered, the neoclassical toroidal viscosity, generated by three-dimensional low-n perturbations, is found to play a dominant role in modifying the edge flow during EHOs.

EHO↗

DOE OSTI2026

Verification of global gyrokinetic simulation of low frequency mode excited by thermal plasma in spherical tokamak

A low frequency Alfven eigenmode in the ST40 spherical tokamak (ST) is found to be resonantly excited by thermal ions from global gyrokinetic GTC simulations. The analyses of phase-space resonances and wave-particle energy exchanges show that the Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is primarily driven unstable by thermal ions, but is stabilized by energetic particles (EPs). When all kinetic effects are artificially suppressed, GTC simulations in the ideal magnetohydrodynamic (MHD) limit confirm the existence of the MHD eigenmode with a frequency in the BAAEs gap, as previously found by the ideal MHD code NOVA. The kinetic effects of thermal ions induce a frequency downshift compared to the stable BAAE in the MHD simulations. These results support the verification for global gyrokinetic simulations of the BAAE in the ST. However, the simulations do not explain the experimental observations of the BAAE in the ST40, possibly owing to the limitation of the collisionless gyrokinetic Monte Carlo model for the EPs.

Alfvén eigenmode↗

DOE OSTI2026

Modeling the effect of MHD activity on runaway electron generation during SPARC disruptions

Magnetohydrodynamic (MHD) instabilities and runaway electrons (REs) interact in several ways, making it important to self-consistently model these interactions for accurate predictions of RE generation and the design of mitigation strategies, such as massive gas injection (MGI). Using M3D-C1 – an extended MHD code with a RE fluid model – we investigate the effects of 3-D nonlinear MHD activity, material injection, and 2-D axisymmetric vertical displacement events (VDEs) on RE evolution during disruptions on SPARC – a high-field, high-current tokamak designed to achieve a fusion gain Q > 1. Several cases, comprising different combinations of neon (Ne) and deuterium (D 2 ) injection, are considered. Here, our results demonstrate key effects that arise from the self-consistent RE + MHD coupling, such as an initial increase in RE generation due to MHD instability growth, decreased saturation energies of the m/n = 1/1 mode driving sawteeth-like activity, RE losses in stochastic magnetic fields, and subsequent RE confinement and plateau formation due to re-healing of flux surfaces. Large RE plateaus (>5 MA) are obtained with Ne-only injection (2-5 × 10 21 atoms), while combined D 2 + Ne injection (2 × 10 21 Ne atoms; 1.8 × 10 22 D 2 molecules) produces a lower RE current (<2 MA). With D 2 + Ne injection, a post thermal quench "cold" VDE terminates the RE beam, preventing a steady plateau. These simulations couple REs, 3-D MHD instabilities, MGI, and axisymmetric VDEs for the first time in SPARC disruption simulations and represent a crucial step in understanding RE generation and mitigation in high-current devices like SPARC.

Datta, Rishabh [Massachusetts Inst. of Technology ↗

DOE OSTI2026

Numerical assessment of the impact of the guiding-centre approximation on fast ion simulations in NSTX

Guiding-centre (GC) and full-orbit (FO) simulations of the beam-injected fast ion distribution and the corresponding neutron emissivity have been carried out for magnetohydrodynamics-quiescent National Spherical Torus eXperiment (NSTX) plasmas, using a combination of ASCOT5 and DRESS, to assess the suitability of the GC approximation for fast ions in NSTX. It was found that GC and FO simulations predicted substantially different steady-state distributions in both position and velocity space and different neutron emissivity profiles, leading to a 15% reduction in the predicted global neutron rate for FO relative to GC. These changes accompany a higher magnetic moment in FO, and correspond to a change in particle orbits from co-passing to trapped and stagnation orbits. ASCOT5 was also benchmarked against TRANSP/NUBEAM with input loaded entirely from TRANSP/NUBEAM output files, with agreement found between the GC simulations when finite Larmor radius (FLR) corrections were omitted. ASCOT5 FO and TRANSP/NUBEAM with FLR produced fast ion distributions which differed in localised regions, but predicted global neutron rates which agree within 3%.

ASCOT↗