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.

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.

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.

Construction of a nuclear weapon requires access to kilogram-scale quantities of fissile material, which can be bred from fertile material like U-238 and Th-232 via neutron capture. Future fusion power plants, with total neutron source rates in excess of 10²⁰ n s⁻¹, could breed weapons-relevant quantities of fissile material on short timescales, posing a breakout proliferation risk. The ARC-class fusion reactor design is characterized by demountable high temperature superconducting magnets, a FLiBe liquid immersion blanket, and a relatively small size (∼4 m major radius, ∼1 m minor radius). We use the open-source Monte Carlo neutronics code OpenMC to perform self-consistent time-dependent simulations of a representative ARC-class blanket to assess the feasibility of a fissile breeding breakout scenario. We find that a significant quantity of fissile material can be bred in less than six months of full power operation for initial fertile inventories ranging from 5 to 50 metric tons, representing a non-negligible proliferation risk. We further study the feasibility of this scenario by examining other consequences of fissile breeding such as reduced tritium breeding ratio, extra heat from fission and decay heat, isotopic purity of bred material, and self-protection time of irradiated blanket material. We also examine the impact of Li-6 enrichment on fissile breeding and find that it substantially reduces breeding rate, motivating its use as a proliferation resistance tool.

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.

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.

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.

An increase in total stored energy correlated with the addition of tritium fuel was observed in supershots during the TFTR DT campaign. This supershot regime had strikingly high, centrally peaked ion and electron temperatures, and the largest neutron emission rates observed in TFTR. This paper presents a study of the causes of this increase in stored energy in supershots. Twenty-six supershots have been recently reanalyzed with the TRANSP plasma analysis code. Early TRANSP simulations did not accurately match the measured magnitude and time evolutions of the neutron emission rates. This mismatch is attributed to neglecting apparent increases of trace amounts of heavy impurities during neutral beam injection. The new TRANSP runs were tuned to accommodate this and match the measured global neutron emission rates. These new runs also had improved fidelity in predicting the time histories and radial dependencies of measured DT neutron emission rates. That in turn adds confidence in the simulated thermal deuterium and tritium density profiles that are needed for calculating the average hydrogenic atomic mass profiles. Six subsets of these supershots had well matched toroidal field $B_{\mathrm{tor}}$, plasma current $I_{\mathrm{p}}$, flux geometry, and total injected neutral beam power. The mix of D and T beam ions was varied for different discharges. The magnitude of the increase of the thermal ion energy $W_{\mathrm{i}}$ with added tritium was relatively small, and the total $W_{\mathrm{tot}}$ increase is dominated by the increase in fast beam ions with T. Analyses at times before the occurrences of deleterious MHD instabilities yielded scaling of $W_{\mathrm{tot}}$ with the volume-average isotopic mass consistent with previous publications. The relative fraction of fast energy ions is expected to be small in practical tokamak reactors. Thus the increase in stored energy $W_{\mathrm{tot}}$ observed in TFTR supershots does not appear likely to be significantly helpful for producing useful fusion energy.

Piecewise omnigenous fields are stellarator magnetic fields that are optimized with respect to radial neoclassical transport thanks to a second adiabatic invariant that is piecewisely constant on the flux-surface. They are qualitatively different from omnigenous fields (including quasi-isodynamic or quasisymmetric fields), for which the second adiabatic invariant is a flux-surface constant. Piecewise omnigenous fields thus open an alternative path towards stellarator reactors. In this work, piecewise omnigenous fields are characterized and parametrized in a systematic manner. This is a step towards including piecewise omnigenity as an explicit design criterion in stellarator optimization, and towards a systematic study of the properties of nearly piecewise omnigenous stellarator configurations.

An experiment was conducted on the Experimental Advanced Superconducting Tokamak (EAST) to investigate the properties of stiff transport in an electron-heated H-mode plasma, using a power deposition scan with electron cyclotron resonance heating (ECRH). During this experiment, a shift in lower hybrid wave heating power and driven current from the plasma core to the outer regions was observed, accompanied by a change in the local magnetic shear. Transport analysis reveals a reduction in the normalized effective electron thermal diffusivity (${\chi _{\text{e}}}$) at larger minor radii when ECRH was applied off-axis, in alignment with the turbulent instability analysis. A threshold for the stiff transport is identified around $R/{L_{{\text{Te}}}}\sim3$ on EAST, above which the electron heat flux (q_e) increases sharply with $R/{L_{{\text{Te}}}}$. Moreover, experimental and simulation results indicate that the change in ECRH power deposition influences local micro-instability turbulence, resulting in the transition of TEM to ITG modes, thereby affecting the plasma performance. These findings provide important insights for optimizing plasma performance, improving confinement, and advancing our understanding of plasma transport in future fusion reactors.

We present a novel framework for quantifying radial impurity transport in the pedestal of ASDEX Upgrade (AUG) discharges. Our method is based on charge-exchange recombination spectroscopy measurements of line radiation from multiple impurity charge states, each along a radially distributed line-of-sight array in steady-state plasmas. Inverse inference based on the diffusive-convective transport solver Aurora combined with a synthetic diagnostic enables us to separate diffusive and convective transport contributions and to derive the impurity density and charge state distribution profiles. Robust uncertainty quantification is provided as the full probability distribution of the parameters is obtained according to Bayesian statistics with the use of a nested sampling algorithm. The approach allows for a high radial resolution and data quality due to the steady-state plasma, but requires data from multiple impurity charge states. It is, therefore, particularly suitable for impurity transport studies in the region of steep edge gradients. In this paper, we present thorough tests of the method based on synthetic data. Furthermore, we show an application to AUG measurement data, inferring the pedestal neon transport in the quasi-continuous exhaust (QCE) regime without large edge-localized modes. The comparison of the transport result with neoclassical simulations shows a clear contribution of turbulent diffusion in the QCE pedestal. This supports the hypothesis of additional transport associated with the predicted high-n ballooning-unstable region and the observed quasi- coherent mode.

In the initial stages of plasma initiation in the Wendelstein7-X stellarator with electron-cyclotron-resonance heating, a downshifted electron cyclotron emission signal is observed. Due to the absence of a corresponding upshifted signal, this signal is believed to come from energetic electrons (∼10 keV). We propose a mechanism for the generation of these fast electron based on the overlap of cyclotron resonances on flux surfaces close to the centre of the plasma. Multiple passages through these resonances lead to the stochastisation of particle trajectories, which ultimately results in the formation of a quasi-steady-state electron distribution function that is predominantly flat in energy space across regions of resonance overlap. The electron cyclotron emission of such a distribution function agrees with the experimental observations.

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.

The efficiency of ion cyclotron resonance heating (ICRH) is highly sensitive to plasma composition, indicating that fusion-born alphas, which have already been observed in deuterium-tritium experiments at JET, will have a non-negligible influence in future fusion reactors. This study aims to investigate the impact of alphas on various ICRH scenarios intended for devices similar to the Chinese Fusion Engineering Testing Reactor (CFETR). An equivalent Maxwellian distribution is employed for a detailed analysis of the potential effects of alphas on ICRH. Preliminary findings indicate that the Doppler broadening mechanism allows alpha particles to absorb ICRH wave energy across a considerably broad spatial area. Furthermore, the relative positioning between the cutoff layer within the plasma and the fundamental resonance layer of alpha particles is crucial for determining absorption. Among the planned ion heating scenarios, alphas are bound to absorb wave energy in both the deuterium minority and three-ion heating scenarios, potentially becoming the dominant absorbers and thereby reducing the heating efficiency for fuel ions. Conversely, the helium-3 minority and second harmonic tritium heating scenarios appear to be less affected by alphas, making them promising candidates for playing a pivotal role in future fusion reactors.

This paper reexamines the linear plasma response to a static resonant error field (EF) in the single-fluid rotating visco-resistive magneto-hydrodinamic (MHD). A tearing-mode stable, rotating plasma shields a resonant static EF by a current sheet at the resonant surface. This response is encapsulated within the delta prime (Δ'), a quantity which measures the magnitude and phase of the current sheet. However, if EF exceeds an amplitude threshold this equilibrium breaks down and a wall-locked tearing mode is formed. Several basic aspects of the problem are addressed. First, we assess the validity of the radial Fourier transform method, commonly used to solve analytically the problem, by comparison with a completely different technique. Second, we derive a new analytical Δ' global formula valid in a wide range of plasma parameters. This formula describes the Δ' features much better than previous asymptotic regimes modelling. Third, we derive the EF amplitude threshold for producing a locked mode, pointing out the crucial role of the neoclassical poloidal flow damping effect. The result is almost identical to recent two-fluids outcomes, showing that the choice between single-fluid and two-fluids MHD is not crucial in this specific problem.

Fusion power reactors will generate intense neutron fluxes into plasma-facing and structural materials. Radiation back-fluxes, generated from neutron-material interactions under these fluxes, can dramatically impact the plasma dynamics, e.g., by seeding runaway electrons during disruptions via Compton scattering of background electrons by wall-emitted gamma radiation. Here, we quantify these back-fluxes, including neutrons, gamma rays, and electrons, using Monte Carlo calculations for a range of structural material candidates and first wall thicknesses. The radiation back-flux magnitudes are remarkably large, with neutron and gamma radiation back-fluxes on the same order of magnitude as the incident fusion neutron flux. Electron back-fluxes are two orders of magnitudes lower, but are emitted at sufficiently high energies to impact the sheath and boundary plasma dynamics. Material configuration plays a key role in determining back-flux magnitudes. The structural material chiefly determines the neutron back-flux magnitude, while the first wall thickness principally attenuates the gamma ray and electron back-fluxes. In addition to prompt back-fluxes, which are emitted immediately after fusion neutrons impact the surface, significant delayed gamma ray and electron back-fluxes arise from nuclear decay processes in the activated materials. These delayed back-flux magnitudes range from 2%-7% of the prompt back-fluxes, and remain present during transients when fusion no longer occurs. During disruptions, build-up of delayed gamma radiation back-flux represents potential runaway electron seeding mechanisms, posing additional challenges for disruption mitigation in a power reactor compared with non-nuclear plasma operations. This work highlights the impact of these radiation back-fluxes plasma performance and demonstrates the importance of considering back-flux generation in materials selection for fusion power reactors.

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 GJ and a plasma duration 364 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-second 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_P, n_e, P_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_e, P_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,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.