Since the publication of the review Progress in the ITER Physics Basis (PIPB) in 2007, significant progress has been made in understanding the processes at the plasma-material interface. This review, part of the ITPA Nuclear Fusion Special Issue On the Path to Burning Plasma Operation, presents these developments, focusing on key areas such as the physics of plasma exhaust, plasma-material interactions, and the properties of plasma-facing materials and their evolution under plasma exposure. The coordinated efforts of the ITPA Topical Group on Scrape-Off Layer and Divertor Physics (DivSOL) have been instrumental in identifying and addressing critical research and development issues in numerous collaborative experimental and modelling projects.

We review the physics of energetic particles (EPs) in magnetically confined burning fusion plasmas with focus on advances since the last update of the ITER Physics Basis (Fasoli et al 2007 Nucl. Fusion 47 S264). Topics include basic EP physics, EP generation, diagnostics of EPs and instabilities, the interaction of EPs and thermal plasma instabilities, EP-driven instabilities, energetic particle modes (EPMs), and turbulence, linear and nonlinear stability and simulation of EP-driven instabilities and EPMs, 3D effects, scenario optimization strategies based on EP phase-space control, EPs in reduced field scenarios in ITER before DT, and the physics of runaway electrons. We describe the simulation and modeling of EPs in fusion plasmas, including instability drive and damping as well as EP transport, with a range of approaches from first-principles to reduced models, including gyrokinetic simulations, kinetic-MHD models, gyrofluid models, reduced models, and semi-analytical approaches.

Progress in physics understanding and theoretical model development of plasma transport and confinement (TC) in the ITPA TC Topical Group since the publication of the ITER Physics Basis (IPB) document (Doyle et al 2007 Nucl. Fusion 47 S18) was summarized focusing on the contributions to ITER and burning plasma prediction and control. This paper provides a general and streamlined overview on the advances that were mainly led by the ITPA TC joint experiments and joint activities for the last 15 years (see JEX/JA table in appendix). This paper starts with the scientific strategy and scope of the ITPA TC Topical group and overall picture of the major progress, followed by the progress of each research field: particle transport, impurity transport, ion and electron thermal turbulent transport, momentum transport, impact of 3D magnetic fields on transport, confinement mode transitions, global confinement, and reduced transport modeling. Cross references with other Topical Groups are given in order to highlight overlapped topics, such as the 3D effect on the plasma transport in the edge and L-H transition physics. The increasing overlap between the topical groups is a reflection of the progress on integrating the known physics into comprehensive models that are better and better able to reproduce the plasma transport. In recent years, such integration has become increasingly prevalent when considering transport from the SOL, through the edge pedestal, and into the plasma core. In the near future, increased collaboration also with the magneto-hydrodynamic and energetic particles community will be important as we approach burning plasma conditions in next-step fusion devices. A summary of remaining challenges and next steps for each research field is given in the Summary section.

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10^2\times$ faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL's effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

Extrapolating the observed behavior of helium exhaust in current tokamaks towards future reactors requires the understanding of the underlying physical mechanisms determining helium transport, recycling and pumping. Helium compression is the main physics-based figure of merit characterizing how efficiently helium is transported towards the divertor and recycled at the target plates. Moreover, helium gas transport in the subdivertor region towards the pumps is strongly influenced by vessel geometry and installed pumps. The SOLPS-ITER code package is used to model H-mode He-seeded deuterium plasmas at the ASDEX Upgrade tokamak, and compared to recent experiments. The simulations generally indicate a poor recycling of helium in the divertor, compared to that of deuterium, in qualitative agreement with the experiment. This is mainly determined by a deeper edge transport barrier and a weaker parallel SOL transport of He ions, with respect to D ions, and by the higher first ionization energy of He atoms, which results in a deeper penetration of recycled atoms into the plasma. The simulated He compression is, however, much smaller than the experimentally measured one, despite the introduction of additional, non-default physics components into the code. Helium gas transport in the subdivertor region towards the pumps is conductance-limited, but moderately enhanced by the entrainment of He atoms into the stronger, viscous deuterium gas flow via friction. The observed poor helium recycling poses challenges in view of the requirements of helium exhaust in future reactors. Our results emphasize the need to investigate further strategies to optimize helium pumping, to guarantee an efficient removal of helium ash in future burning plasmas. Additionally, the observed difficulty of SOLPS-ITER in reproducing the experimental observations suggests a careful evaluation of the currently available extrapolations of impurity transport towards future devices obtained via edge transport modelling.

The Plasma Injector 3 (PI3) experiment at general fusion has been constructed to demonstrate the ability to form plasma targets suitable for compression in a Magnetized Target Fusion machine. To achieve compressive heating to fusion conditions, the target plasmas should have an energy confinement time sufficiently in excess of the compression time. In this work we present a methodology for calculating this timescale and present results for a large set of discharges. Characterization of the plasma current profiles reveals trends and groupings determined by machine settings. The largest energy confinement times have been obtained for discharges with a broad plasma current profile, fresh lithium coating on the device walls, and a near constant toroidal field. We find that PI3 plasmas at $5\,\mathrm{ms}$ into the discharge can have thermal confinement times in excess of $10\,\mathrm{ms}$. These meter-scale plasma can thus achieve significant heating if compressed on a timescale of milliseconds.

Deuterium (D) and beryllium (Be) fluxes are obtained in JET Low-confinement mode (L-mode) plasmas at the outer limiters of the first wall using calibrated visible cameras. They are inferred from the measured radiances using the spectroscopic S/XB method. From the fluxes, the effective gross erosion yield Y^eff of the limiter surface is estimated. After discussing the uncertainties in the proposed methodology, we show the dependence of the deduced particle fluxes and Y^eff of recent JET L-mode plasmas on: separatrix–limiter clearance, magnetic field and plasma current, neutral beam injection and ion cyclotron resonance heating power, average plasma density and majority ion mass, hydrogen (H), deuterium (D) and tritium (T). The results are in general accord with prior edge plasma L-mode understanding. Finally, the obtained Y^eff yields are discussed in view of updated SDTrim surface–particle interaction code calculations. The possible contribution of parasitic light due to reflections from the divertor is examined.

Sustainment of Q ∼ 10 operation with a fusion power of ∼500 MW for several hundred seconds is a key mission goal of the ITER Project. Past calculations and simulations predict that these conditions can be produced in high-confinement mode operation (H-mode) at 15 MA relying on only inductive current drive. Earlier development of 15 MA baseline inductive plasma scenarios provided a focal point for the ITER Design Review conducted in 2007–2008. In the intervening period, detailed predictive simulations, supported by experimental demonstrations in existing tokamaks, allow us to assemble an end-to-end specification of this scenario consistent with the final design of the ITER device. Simulations have encompassed plasma initiation, current ramp-up, plasma burn and current ramp-down, and have included density profiles and thermal transport models producing temperature profiles consistent with edge pedestal conditions present in current fusion experiments. These quasi-stationary conditions are maintained due to the presence of edge-localized modes that limit the edge pressure. High temperatures and densities in the pedestal region produce significant edge bootstrap current that must be considered in modelling of feedback control of shape and vertical stability. In this paper we present new results of transport simulations fully consistent with the final ITER design that remain within allowed limits for the coil system and power supplies. These self-consistent simulations increase our confidence in meeting the challenges of the ITER program.

Recrystallization, a critical issue that weakens the strength and thermal shock resistance of tungsten-based plasma-facing material in fusion devices, is effectively retarded by helium. In this study, the retarding effect of helium on recrystallization was studied using tungsten samples implanted by high-dose helium ions with doses ranging from 5 × 10²¹m⁻² to 1 × 10²³ m⁻² at two temperatures (room temperature and 673 K), and followed by annealing temperatures ranging from 1573 K to 2073 K. The results show that helium in all six samples exhibits retarding effect, with recrystallization beginning until 1773 K. Notably, the sample implanted at 673 K with a dose of 5 × 10²¹ m⁻² demonstrates the lowest recrystallization fraction of 13% at the annealing temperature of 1873 K, suggesting that the retarding effect weakens once the helium ion concentration exceeds a certain threshold. The hardness of high-dose helium ion-implanted tungsten samples exhibits distinct temperature-dependent patterns, different from the monotonic decline typically observed in previous helium-implanted tungsten samples. Additionally, the recovery of pinholes, created by the rupture of helium bubble, on {100} planes was observed to be the slowest, explained through molecular dynamics simulations. This work offers valuable insights into maintaining the retarding effect on recrystallization by tuning helium concentration in tungsten.

Laminar magnetohydrodynamics film flows in an open channel of arbitrary electrical conductivity under the influence of a transverse magnetic field are investigated. The effects of the magnetic field, channel conductivity, and channel width on current and velocity distributions are discussed. The present research establishes quantitative scaling law for the magnetic field's impact on the film thickness, utilizing Fourier eigenfunction series and comprehensive physical modeling. The scaling law is validated through direct numerical simulation results and experimental data, which accounts for factors that influence the film thickness, including the Reynolds number (volume flow rate), channel inclined angle, and magnetic field strength. Additionally, the physical mechanism governing the three-dimensional evolution of magnetohydrodynamics films is explored, which finds that a strong magnetic field introduces a Lorentz separation eddy and destabilizes the initially stable, flat film. The present investigations will contribute to the design of flowing liquid metal plasma facing components in tokamak fusion reactors.

In the control of large superconducting tokamaks, particularly for devices like DEMO reactors, where no stabilizing plates or in-vessel coils can be mounted due to the existence of tritium breeding blankets, position, shape, and current of plasmas must be controlled solely with superconducting coils, for which we developed novel control schemes (Inoue et al 2021 Nucl. Fusion61 096009); an adaptive voltage allocation (AVA) scheme automatically allocates power supply voltages for plasma current and position/shape control, and a last closed flux surface reconstruction scheme can robustly reconstruct the plasma shape in the presence of large eddy currents. This paper reports the first experimental demonstration of these schemes on JT-60SA, which is the world's largest tokamak and has DEMO-relevant device conditions, such as no stabilization plates and in-vessel coils. During the first operational phase at JT-60SA, interference in control of shape, position, and current of plasmas was successfully resolved by the AVA scheme, achieving several milestones such as an elongation of 1.7 (with a vertical instability growth rate of around 90 s⁻¹), and the world's largest plasma current of 1.2 MA as a superconducting tokamak.

The self-consistent nonlinear interaction of drift waves (DWs) and zonal flow (ZF) is investigated using nonlinear gyrokinetic theory, with both spontaneous excitation and beat-driving of ZF by DWs treated on the same footing. DW solitons are formed in nonlinear DW–ZF interactions and are confined between radially spaced micro-barriers induced by spontaneously excited ZF (SZF). The resulting radial structures in nonlinear DW–ZF interactions exhibit a similar pattern to the $\mathbf{E} \times \mathbf{B}$ 'staircase' observed in numerical simulations. These micro-barriers are generated by the repulsive response due to SZF, which, as a general property demonstrated in this work, also generates an attractive nonlinear potential in the DW equation. Meanwhile, the nonlinear potential due to beat-driven ZF is always attractive and, as such, always serves as a potential well to contribute to soliton formation. For SZF from initial noise, the simultaneous excitation of solitons and micro-barriers is found to be universal due to the zero-frequency nature of ZF and the spatial structure of the Reynolds stress. The present analysis thus provides a potential first-principles-based interpretation of the $\mathbf{E} \times \mathbf{B}$ staircase observed in simulations, which may contribute to the formation of micro transport barriers and enhance plasma confinement.

Pedestal turbulence spreading into a crape-off layer (SOL) can be used to explain the experimentally observed strong pedestal-SOL coupling and is expected to be important for the broadening of divertor deposition profiles in future devices (Xu et al 2019 Nucl. Fusion59 126039). In the EAST tokamak, it is found that an electromagnetic (EM) mode in the pedestal region can spread into the SOL and broaden the divertor particle flux width. Multi-channel fluctuation reflectometry is used to measure the density fluctuations at the plasma edge. The EM mode rotates in the electron diamagnetic drift direction in the lab frame with a frequency range of [40–90] kHz, toroidal mode number n= 12–13 and poloidal wavenumber k_θ = 0.41 cm⁻¹. The mode amplitude peaks around the maximum of the pedestal density gradient. As the mode amplitude increases, the reflectometry channel in the SOL can clearly capture the mode. This result suggests that the EM mode is excited in the pedestal gradient region and spreads into the SOL. It is further found that the particle flux deposition profile in the divertor is broadened as the EM mode appears.

A new record was set on the WEST Tokamak, designed to operate long duration plasmas in a tungsten (W) environment, with an injected energy of $1.15\,\mathrm{GJ}$ and a plasma duration $364\,\mathrm{s}$. Scenario development was supported by integrated modeling using the High Fidelity Plasma Simulator (HFPS), the European IMAS-coupled version of JETTO/JINTRAC, which integrates physics-driven modules into a unified framework. In particular, a reduced model for Lower-Hybrid heating and Current-Drive (LHCD) and the quasi-linear turbulent transport model TGLF are crucial for long pulses predictions up to the Last Closed Flux Surface (LCFS). Using this workflow, a 100 s reference discharge was modeled and plasma kinetic profiles and loop voltage were quantitatively well matched. In preparation for the recent long duration experiments, non-inductive current-drive actuators $(I_\mathrm P, n_\mathrm e, P_\mathrm {LHCD})$ were varied to determine the operational domain going towards fully non-inductive discharges. In particular, decreasing the plasma current is shown to ease the access to such conditions, with a careful monitoring of $(n_\mathrm e, P_\mathrm {LHCD})$ to avoid machine limitations. In addition, post-prediction experiments conducted within the investigated parameter range validated the predicted dependencies and were shown to be in quantitative agreement. Exploratory work on the use of ECCD for MHD stability purpose is also introduced.

We present simultaneous profiles of the poloidal distribution of electron temperature and density (T_e, n_e), the poloidal emissivity distributions of a range of spectral lines together with the corresponding ion temperatures, T_i, in the TCV divertor plasma. These measurements were performed over divertor plasma conditions evolving from strongly attached towards a detached regime. The poloidal n_e and T_e distributions were measured by Divertor Thomson Scattering (DTS) diagnostic and by exploiting TCV's flexibility to align divertor magnetic configurations to the DTS diagnostic laser path. T_i are inferred from Doppler broadening of C II, C III, and He II ions transitions measured by the high-resolution Divertor Spectroscopy System (DSS). The measured T_i represents an emissivity-weighted ion temperature along the DSS lines of sight. To study the electron/ion thermalisation, we compare T_i of each ion with a corresponding emission-weighted electron temperature, $T\,_e^*$. We find that T_i of C⁺ is lower than its corresponding $T\,_e^*$ for all plasma parameters except for near-detachment conditions in the vicinity of the target. Conversely, T_i of C²⁺ and He⁺ are approximately equal to their corresponding $T\,_e^*$, except near the target in attached conditions. To explain these observations, we present a simple model of T_i evolution that includes the thermalisation between plasma species, and the ionisation state evolution with a source of low temperature neutrals. In the framework of this model we also show that T_i of C²⁺ and He⁺ closely follow T_i of ionized deuterium D⁺ in all our plasma parameters and therefore may be used as an indirect measurement of $T\,_{i, \mathrm{D}^+}$. The results here clearly show the need for a collisional-radiative model that includes local neutral density of deuterium and impurities, to understand T_i of various ion species, and their emission intensities in the divertor plasma.

We review the physics of energetic particles (EPs) in magnetically confined burning fusion plasmas with focus on advances since the last update of the ITER Physics Basis (Fasoli et al 2007 Nucl. Fusion47 S264). Topics include basic EP physics, EP generation, diagnostics of EPs and instabilities, the interaction of EPs and thermal plasma instabilities, EP-driven instabilities, energetic particle modes (EPMs), and turbulence, linear and nonlinear stability and simulation of EP-driven instabilities and EPMs, 3D effects, scenario optimization strategies based on EP phase-space control, EPs in reduced field scenarios in ITER before DT, and the physics of runaway electrons. We describe the simulation and modeling of EPs in fusion plasmas, including instability drive and damping as well as EP transport, with a range of approaches from first-principles to reduced models, including gyrokinetic simulations, kinetic-MHD models, gyrofluid models, reduced models, and semi-analytical approaches.

Since the publication of the review Progress in the ITER Physics Basis (PIPB) in 2007, significant progress has been made in understanding the processes at the plasma-material interface. This review, part of the ITPA Nuclear Fusion Special Issue On the Path to Burning Plasma Operation, presents these developments, focusing on key areas such as the physics of plasma exhaust, plasma-material interactions, and the properties of plasma-facing materials and their evolution under plasma exposure. The coordinated efforts of the ITPA Topical Group on Scrape-Off Layer and Divertor Physics (DivSOL) have been instrumental in identifying and addressing critical research and development issues in numerous collaborative experimental and modelling projects.

Progress in physics understanding and theoretical model development of plasma transport and confinement (TC) in the ITPA TC Topical Group since the publication of the ITER Physics Basis (IPB) document (Doyle et al 2007 Nucl. Fusion47 S18) was summarized focusing on the contributions to ITER and burning plasma prediction and control. This paper provides a general and streamlined overview on the advances that were mainly led by the ITPA TC joint experiments and joint activities for the last 15 years (see JEX/JA table in appendix). This paper starts with the scientific strategy and scope of the ITPA TC Topical group and overall picture of the major progress, followed by the progress of each research field: particle transport, impurity transport, ion and electron thermal turbulent transport, momentum transport, impact of 3D magnetic fields on transport, confinement mode transitions, global confinement, and reduced transport modeling. Cross references with other Topical Groups are given in order to highlight overlapped topics, such as the 3D effect on the plasma transport in the edge and L-H transition physics. The increasing overlap between the topical groups is a reflection of the progress on integrating the known physics into comprehensive models that are better and better able to reproduce the plasma transport. In recent years, such integration has become increasingly prevalent when considering transport from the SOL, through the edge pedestal, and into the plasma core. In the near future, increased collaboration also with the magneto-hydrodynamic and energetic particles community will be important as we approach burning plasma conditions in next-step fusion devices. A summary of remaining challenges and next steps for each research field is given in the Summary section.

Future large tokamaks will operate at high plasma currents and high stored plasma energies. To ensure machine protection in case of a sudden loss of plasma confinement (major disruption), a large fraction of the magnetic and thermal energy must be radiated to reduce thermal loads. The disruption mitigation system for ITER is based on massive material injection in the form of shattered pellet injection (SPI).
To support ITER, a versatile SPI system was installed at the tokamak ASDEX Upgrade (AUG). The AUG SPI features three independent pellet generation cells and guide tubes, and each was equipped with different shatter heads for the 2022 experimental campaign. We dedicated over 200 plasma discharges to the study of SPI plasma termination, and in this manuscript report on the results of bolometry (total radiation) analysis.
We found, that the amount of neon inside the pellets is the dominant factor determining the radiated energy fraction (frad). Large and fast fragments, produced by the 12.5° rectangular shatter head, lead to somewhat higher values of frad compared to the 25° circular or rectangular heads. This effect is strongest for neon content of ≲3×10²⁰ neon atoms (fneon ≲ 1.25% neon) injected, where a lower normal velocity component (larger fragments) seems slightly beneficial.
While full-sized, 8 mm diameter, 100% deuterium (D2) pellets lead to a disruption, the 4 mm or shortened 8 mm pellets of 100% D2 did not. The disruption threshold for 100% D2 is found to be around 1×10²² deuterium molecules inside the pellet.
While the radiated energy fraction of non-disruptive SPI is below 20%, this is increased to 40% during the TQ and VDE phase of the disruptive injections. For deuterium–neon–mix pellets, frad-values of ≤90% are observed, and the curve saturates around 80% already for 10% neon mixed into the 8 mm pellets (2×10²¹ neon atoms).

After installation of tungsten divertor in EAST, impurity accumulation of tungsten ions has been frequently observed in H-mode discharge with internal transport barrier (ITB) due to an enhancement of the impurity confinement inside the ITB. A strong plasma cooling induced by the tungsten impurity ions caused a collapse of the ITB formation. To study the impurity transport in high βN discharges with ITB, temporal behaviors and radial profiles of spectral lines emitted from low- and high-Z impurity ions were analyzed. Line emissions from moderately ionized ions, e.g., O6+, Fe17+ and Mo25+ locating outside the ITB (ρ  0.4), maintain low intensities and remain unchanged during the ITB formation. However, line emissions from highly ionized high-Z impurity ions such as Fe22+, Cu21+, Cu25+, Mo30+ and W26+ - W37+ locating inside the ITB (ρ < 0.4) are strongly influenced by peaking effects of electron density and ion temperature profiles. The impurity screening effect due to the ion temperature peaking is dominant during Ti-ITB phase because the line intensities of high-Z impurity ions are reduced and the radial profiles are flattened. In contrast, during ne-ITB phase accompanied by electron and ion temperature ITB, an increase in the electron density gradient from R/Lne = 3.4 to 4.9 results in a significant increase in the high-Z impurity line intensity, and leads to the impurity accumulation. Statistical analysis on the tungsten impurity density (IW-UTA/ne) with toroidal rotation velocity (Vt0) and ion temperature gradient (R/LTi) suggests that the tungsten impurity accumulation can be effectively mitigated and the IW-UTA/ne can be reduced to below 18 (phs·m·s-1·Sr-1), when R/Lne < 3.4, Vt0 < 150 km/s and R/LTi > 2.5. During two ITB phases, however, low-Z impurity ions like O7+ locating at edge of the ITB appear to be sensitive to only the electron density gradient.

We present NeuralBranch, an interpretable neural network framework. In this work, we use it specifically to predict the pedestal from key engineering parameters in tokamak fusion experiments. The main goal is to uncover intricate relationships that traditional power scalings, with their limited expressive capacity, fail to capture. A secondary objective is to provide a transparent alternative to current opaque, black-box machine learning models used to predict the pedestal in integrated modeling frameworks. By using the proposed method, we obtain a novel global overview of several intricate dependencies in the JET pedestal database. For instance, while both input power and plasma current are positively correlated with pedestal top pressure and temperature, NeuralBranch reveals an attenuating interaction. This means that increasing power weakens the impact that current has on pedestal pressure and temperature, and vice versa. Further investigation of this interaction may be important to avoid overestimating pedestal stored energy at future machines like ITER when using established power scalings. We also identify an amplifying interaction between plasma current and triangularity, where higher triangularity amplifies the effect of plasma current on pedestal density, and vice versa. In addition to these findings, NeuralBranch matches the accuracy of black-box neural networks, with \(R^2\) values as high as 0.88. This demonstrates that interpretability, with its associated benefits, can be achieved without sacrificing accuracy, making NeuralBranch a promising alternative for pedestal predictions.

Stellarator plasmas are known to be very sensitive to perturbations in the magnetic field. The permanent magnet stellarator was in part developed as a solution to high machining tolerances placed on the shape properties of electromagnetic coils in traditional stellarators. However, as a consequence of this high sensitivity to the field structure, sensitivities of permanent magnet stellarator plasmas to perturbations of permanent magnet properties must necessarily be well-understood. The gradient and Hessian matrix methods have been previously demonstrated to be useful sensitivity analysis methods for modular coils. We apply these two methods to the study of island width sensitivities in both the MUSE and PM4STELL permanent magnet stellarator projects. These sensitivity methods were used to determine the relative impacts of permanent magnet parameter perturbations on island widths in the vacuum field approximation of both stellarator equilibria. The square of resonant magnetic field perturbation is used here as a proxy for island width. In particular, gradients of magnetizations of individual magnets were examined in MUSE, as well as gradients of magnet group displacements informed by device design. Three different forms of permanent magnet magnetization perturbations are investigated for MUSE, and the flux surface response to perturbations is demonstrated. The Hessian matrix method is applied to PM4STELL, illustrating the sensitivity of dominant island widths to displacements of toroidal wedge structures. These methods allow for selective direction of experimental resources toward regions of heightened sensitivity, while constraints on less impactful permanent magnet parameters can be relaxed.

The eigen-mode structure and distribution associated with the global dispersion are studied based on linear gyro-kinetic simulations in a global toroidal geometry using parameters and profiles modeled for JT-60U-like discharges with a strongly reversed magnetic shear configuration, which exhibit L-mode characteristics subject to a strong profile constraint. By incorporating the mode mismatch parameter ∆μ, related to the parallel wave number k_∥ (≡Δμ⁄R_0 ), and also the slab-to-toroidal ratio parameter X(≡(k_∥ R_0)⁄(k_θ ρ_i )), we identified two qualitatively distinct unstable branches. One is the density gradient driven trapped electron modes (∇n-TEMs) influenced by the ion temperature gradient with lower toroidal mode numbers n, while transited to weak toroidal-like ion temperature gradient modes (ITG modes) as n increases, in the inner negative magnetic shear region (s o<0). The other is the slab-like ITG modes with higher-n in the outer minimum safety factor region (q~q_min). These dynamics result in the separate radial location of the density and ion/electron temperature gradients, i.e. the former is inner region while the latter is outer region. These two branches are weakly connected through the boundary region inside the q_min surface, which leads to a discontinuity in the quasi-linear flux. Each branch is found to show approximately the similar level of peak growth rate in inner and outer regions, indicating that the constrained profiles are expected to be established such that linearly unstable free energy sources are globally balanced so as to maintain such profile in a quasi-steady state with a self-organized manner without causing unbalanced transport.