Resonant magnetic perturbations (RMPs) alter magnetic field topology via island formation and can modify core transport in toroidal fusion devices. Using the global gyrokinetic particle-in-cell code XGC-S, originally developed for stellarator geometries, we quantify how island topology affects neoclassical heat transport in a circular tokamak with RMP-induced islands. Electron radial heat diffusivity exhibits a two-peak structure with a dominant enhancement near the O/X-point region and a secondary peak at the outer island boundary, whereas ion transport remains close to the neoclassical prediction. The observed electron diffusivity is strongly enhanced over the neoclassical baseline but remains well below the Rechester-Rosenbluth estimate, consistent with the non-ergodic character of the island topology. The density dependence of diffusivity is weaker inside the islands than outside, indicating the presence of topology-driven transport channels that do not depend strongly on collisionality. Two-dimensional heat flux maps reveal an up-down antisymmetric structure at the island separatrices consistent with magnetic gradient and curvature drift effects, in contrast to the symmetric temperature flattening inside the islands. These results identify topology-dependent avenues for electron heat transport in RMP-perturbed cores and suggest regimes in which island geometry, rather than collisions alone, governs radial transport.

A new field solver has been implemented in the global electromagnetic total-f gyrokinetic particle-in-cell code XGC to extend the code's capability to large-scale reduced MHD-type instabilities in tokamak plasma. While XGC's regular field solver is accurate at typical microturbulence scales of the order of the ion Larmor radius in tokamaks with arbitrary aspect ratio, a more accurate field solver is required for large-scale (i.e., low toroidal mode number) MHD-type modes such as internal kink, tearing and peeling modes. The higher accuracy of the new field solver is achieved by dropping the (large aspect ratio) assumption that the poloidal magnetic field is much smaller than the toroidal magnetic field, while its numerical complexity is controlled by using a spectral discretization in the toroidal direction. To cover the entire spectrum from large-scale MHD-type modes to small-scale microturbulence, the regular and the new field solver can be run alongside each other. This work details the derivation of the new field solver, analyzes the differences between the XGC's regular and new field solvers, and verifies the new field solver against analytic predictions and the gyrokinetic code ORB5 and the MHD code NIMROD.

We review global gyrokinetic simulation studies on plasma transport in the Large Helical Device using XGC-S. XGC-S is an extended version of X-point Gyrokinetic Code for stellarators and has been progressively verified throughout the code development process. Verification tests of neoclassical transport successfully demonstrate the generation of an ambipolar electric field due to ripple-trapped particles. We perform quasi-linear analyses of the ion temperature gradient mode under the influence of the ambipolar electric field. The results reveal that the ambipolar electric field and the heavy hydrogen component in mixed isotope plasmas can lead to the favorable isotope effect observed in recent deuterium experiments. We also present recent efforts in code development toward whole-volume simulations, including the helical divertor region. A mesh generation scheme based on field-line tracing and the construction of curved surfaces perpendicular to the magnetic field would be promising for global field calculations in the whole-volume simulations.

Tungsten peaking is predicted in the core of a WEST plasma with total-f gyrokinetic simulations, including both collisional and turbulent transport. This prediction is validated with a synthetic diagnostic of the bolometry. Although nitrogen impurities are shown to reduce the neoclassical peaking of tungsten on-axis, the overall tungsten peaking increases when nitrogen impurities are present, as they reduce the turbulence screening off-axis. This finding is important for the plasma current ramp-up phase of ITER, where light impurities seeding will be desirable to achieve low temperatures at the plasma-facing components and reduce tungsten sputtering. It provides further argument for applying early ECRH heating to maintain margins on the core power balance. The neoclassical peaking factor is cross-verified between XGC and FACIT. The heat flux at separatrix and the heat load width are modeled by XGC and compared to WEST data.

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic‐field‐line‐following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root‐finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field‐line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X‐Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7‐X (W7‐X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet .

The magnetic separatrix surface is designed to provide the final and critical confinement to the hot stationary-operation core plasma in modern tokamak reactors in the absence of an external magnetic perturbation (MP) or transient magneto-hydrodynamic perturbation, while diverting the exhaust heat to divertor plates. All the stationary operational boundary plasma studies and reactor designs have been performed under this assumption. However, there has been a long-standing suspicion that a stationary-operation tokamak plasma even without external MPs or edge localized modes (ELMs) activities may not have a stable closed separatrix surface, especially near the magnetic X-point. Here, the first gyrokinetic numerical observation is reported that the divertor separatrix surface, due to homoclinic tangles caused by intrinsic electromagnetic turbulence, is not a stable closed surface in a stationary operation phase even without MPs or ELMs. Unlike the MP- or ELM-driven homoclinic tangles that could cause deleterious effects to core confinement or divertor plates, it is found that the micro-turbulence driven homoclinic tangles could connect the divertor plasma to the pedestal plasma in a constructive way by broadening the divertor heat-exhaust footprint and weakening the pedestal slope to the ELM-safe direction. Micro-turbulent homoclinic tangles can open a new research direction in understanding and controlling these two most troublesome and non-locally connected edge-plasma issues in a tokamak fusion reactor.

The DIII-D tokamak has elucidated crucial physics and developed projectable solutions for ITER and fusion power plants in the key areas of core performance, boundary heat and particle transport, and integrated scenario operation, with closing the core-edge integration knowledge gap being the overarching mission. New experimental validation of high-fidelity, multi-channel, non-linear gyrokinetic turbulent transport models for ITER provides strong confidence it will achieve Q 10 operation. Experiments identify options for easing H-mode access in hydrogen, and give new insight into the isotopic dependence of transport and confinement. Analysis of 2,1 islands in unoptimized low-torque IBS demonstration discharges suggests their onset time occurs randomly in the constant beta phase, most often triggered by non-linear 3-wave coupling, thus identifying an NTM seeding mechanism to avoid. Pure deuterium SPI for disruption mitigation is shown to provide favorable slow cooling, but poor core assimilation, suggesting paths for improved SPI on ITER. At the boundary, measured neutral density and ionization source fluxes are strongly poloidally asymmetric, implying a 2D treatment is needed to model pedestal fuelling. Detailed measurements of pedestal and SOL quantities and impurity charge state radiation in detached divertors has validated edge fluid modelling and new self-consistent 'pedestal-to-divertor' integrated modeling that can be used to optimize reactors. New feedback adaptive ELM control minimizes confinement reduction, and RMP ELM suppression with sustained high core performance was obtained for the first time with the outer strike point in a W-coated, compact and unpumped small-angle slot divertor. Advances have been made in integrated operational scenarios for ITER and power plants. Wide pedestal intrinsically ELM-free QH-modes are produced with more reactor-relevant conditions, Low torque IBS with W-equivalent radiators can exhibit predator-prey oscillations in T-e and radiation which need control. High-beta(P) scenarios with q(min) > 2, q(95)-7.9, beta(N) > 4, beta(T)-3.3% and H-98y2 > 1.5 are sustained with high density ((n) over bar = 7E19 m(-3), f(G)-1) for 6 tau(E), improving confidence in steady-state tokamak reactors. Diverted NT plasmas achieve high core performance with a non-ELMing edge, offering a possible highly attractive core-edge integration solution for reactors.

The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low- A , high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.

The accurate representation of a problem domain in terms of a geometric model and its effective discretization into a mesh plays an important role in achieving higher-quality simulation results and better computational efficiency. In this work, recent developments to extend an automated tokamak modeling and meshing infrastructure to better support the near flux field following meshing requirements of the XGC Gyro-kinetic Code are presented. The first extension is a procedure to effectively represent a general set of O-point and X-points configurations. The second extension is a procedure to decompose the geometric model that includes the tokamak wall, selected flux curves and the separatrix curves in a manner such that an appropriate set of mesh generation procedures can be applied to each subregion. The third extension is the application of appropriate mesh generation procedures in each subregion to create the desired final mesh.

The application of a bundling technique to model the diverse charge states of tungsten impurity species in total-f gyrokinetic simulations is demonstrated. The gyrokinetic bundling method strategically groups tungsten ions of similar charge, optimizing computational efficiency. The initial radial configuration of these bundles and their respective charges are derived from a coronal approximation and the quasi-neutrality of the plasma. A low-density JET H-mode like plasma is simulated using the neoclassical version of XGC across the entire plasma volume, spanning from the magnetic axis to the divertor. An accumulation of tungsten is observed at the pedestal top, as a result of low-Z tungsten ions moving inward from the scrape-off-layer into the core region and high-Z tungsten ions moving outward from the core into the pedestal. This organization of the fluxes cannot be captured by a single tungsten-ion simulation. Large up-down poloidal asymmetries of tungsten form in the pedestal and strongly influence the direction of neoclassical fluxes. The temperature screening effect and its correlation with asymmetries are analyzed.

Strong poloidal refueling asymmetry in the DIII-D tokamak is inferred from line radiation measurements. Synthetic diagnostics in neutral transport modeling coupled to gyrokinetic simulations illuminate implications for the plasma flow profile in the scrape-off layer of single-null beam-driven discharges. Recycling occurs primarily either on the inner or outer divertor legs, depending on the toroidal magnetic field direction. By reversing the toroidal magnetic field, the observed line radiation asymmetry is nearly eliminated or reversed. It is determined that, while relatively simple physics can describe the observed ionization asymmetry, predicting the overall brightness of the hydrogenic Lyman- α signal requires detailed simulation of the plasma and resulting turbulence. To this end, kinetic plasma simulations fully coupled to comprehensive neutral transport calculations—a novel capability—provide first-principles reproduction of Lyman- α observations on DIII-D.

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large rho(i)/a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite rho(i) effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new "effective trapping fraction" concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

Gyrokinetic tokamak plasmas can exhibit intrinsic toroidal rotation driven by the residual stress. While most studies have attributed the residual stress to the parallel-momentum flux from the turbulent E×B motion, the parallel-momentum flux from the drift-orbit motion (denoted Π_{∥}^{D}) and the E×B-momentum flux from the E×B motion (denoted Π_{E×B}) are often neglected. Here, we use the global total-f gyrokinetic code XGC to study the residual stress in the core and the edge of a DIII-D H-mode plasma. Numerical results show that both Π_{∥}^{D} and Π_{E×B} make up a significant portion of the residual stress. In particular, Π_{∥}^{D} in the core is higher than the collisional neoclassical level in the presence of turbulence, while in the edge it represents an outflux of countercurrent momentum even without turbulence. Using a recently developed "orbit-flux" formulation, we show that the higher-than-neoclassical-level Π_{∥}^{D} in the core is driven by turbulence, while the outflux of countercurrent momentum from the edge is mainly due to collisional ion orbit loss. These results suggest that Π_{∥}^{D} and Π_{E×B} can be important for the study of intrinsic toroidal rotation.

In this work, we investigate the dynamics of plasma blobs in the edge of magnetic confinement devices using a full-f gyrokinetic particle-in-cell code with X-point geometry. In simulations, the evolution of a seeded blob is followed as it approaches a naturally-forming zonal shear layer near the separatrix, where the blob is stabilized by a large spin induced by the self-consistent adiabatic electron response, and blob bifurcation and trapping are observed during the cross-field propagation of blobs. A new theoretical explanation in both the zonal free and zonal shear layer is constructed, where the dominant E x B spin motion is included. A theoretical condition for a transport barrier induced by the interaction between spinning blobs and the zonal shear layer is obtained, and its scaling is verified with simulations. The new theoretical framework, especially the transport barrier, is applicable to explain and predict various experimental phenomena. In particular, the transport barrier condition calculated with experimental parameters demonstrates that the blob radial transport for H mode is smaller than L mode in experiments.

Ion orbit loss has been used to model the formation of a strong negative radial electric field E ( r ) in the tokamak edge, as well as edge momentum transport and toroidal rotation. To quantitatively measure ion orbit loss, an orbit-flux formulation has been developed and numerically applied to the gyrokinetic particle-in-cell code XGC. We study collisional ion orbit loss in an axisymmetric DIII-D L-mode plasma using gyrokinetic ions and drift-kinetic electrons. Numerical simulations, where the plasma density and temperature profiles are maintained through neutral ionization and heating, show the formation of a quasisteady negative E ( r ) in the edge. We have measured a radially outgoing ion gyrocenter flux due to collisional scattering of ions into the loss orbits, which is balanced by the radially incoming ion gyrocenter flux from confined orbits on the collisional time scale. This suggests that collisional ion orbit loss can shift E ( r ) in the negative direction compared to that in plasmas without orbit loss. It is also found that collisional ion orbit loss can contribute to a radially outgoing (counter-current) toroidal-angular-momentum flux, which is not balanced by the toroidal-angular-momentum flux carried by ions on the confined orbits. Therefore, the edge toroidal rotation shifts in the co-current direction on the collisional time scale.

Isotope effects under the influence of a radial electric field are examined in a helical magnetic field configuration. We perform global gyrokinetic simulations with additional poloidal rotations to estimate quasi-linear heat flux due to ion temperature gradient mode under the mixing length model. In single-ion-species plasmas, the mass number dependency of heat flux agrees with gyro-Bohm scaling in the absence of a radial electric field. Favorable mass number dependencies violating gyro-Bohm scaling are observed in the presence of a global radial electric field or a heavy hydrogen component in multi-ion-species plasmas. The radial electric field and the heavy hydrogen component affect the heat flux through an increase of wavelength as well as mode stabilization. Poloidal Mach number characterizes the transition from unfavorable to favorable mass number dependency under radial electric fields. While the heat flux is independent of mass number for a given poloidal Mach number, the heat flux decreases for higher mass numbers in a given radial electric field. The heat flux is also independent of average mass number in multi-ion-species plasmas because the heavy hydrogen component effectively enhances the light hydrogen heat flux. The present results are potentially relevant to the violation of gyro-Bohm scaling observed in the recent deuterium experiments in the Large Helical Device.

Ion orbit loss is considered important for generating the radially inward electric field E r in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code XGC. As the first application of this diagnostic, a neoclassical DIII-D H-mode plasma is studied using gyrokinetic ions and adiabatic electrons. The validity of the diagnostic is demonstrated by studying the collisional relaxation of E r in the core. After this demonstration, the loss-orbit current is numerically measured in the edge pedestal in quasisteady state. In this plasma, it is found that the radial electric force on ions from E r approximately balances the ion radial pressure gradient in the edge pedestal, with the radial force from the plasma flow term being a minor component. The effect of orbit loss on E r is found to be only mild.