We present observations, numerical simulations, and analysis from experiments in the Lithium Tokamak Experiment-Beta (LTX-β) in which the electron temperature profile (Te(r)) shifts from flat to peaked and a tearing mode is also destabilized when the average density (neave) exceeds ∼1019 m−3. Flat Te(r) is obtained routinely in LTX-β, with a lithium coated, low-recycling first wall, once the external fueling is stopped and density decays [Boyle et al 2023 Nucl. Fusion 63 056020]. In the present experiment, flat Te profiles can be sustained while maintaining constant neave below a line averaged density threshold (neaveth) of ∼1019 m−3. Above neaveth, Te(r) shifts from flat to peaked and a tearing mode is destabilized. Due to low recycling, the achieved neave can be controlled precisely by external fueling and hence, a certain threshold of the edge neutral inventory from the external fueling is experimentally manifested through neaveth. The goal of the present work is to investigate the role of edge neutrals in determining Te(r) and MHD stability in the unique low-recycling regime of LTX-β. Our hypothesis is that the peaking of Te(r) beyond neaveth is due ultimately to the edge cooling by the cold neutrals beyond a critical fueling flux. At lower fueling flux, flat Te(r) results in broader pressure profile and lower resistivity, which in turn stabilizes the tearing mode. This hypothesis is supported by edge neutral density estimation by DEGAS 2 code. Mode analysis by singular value decomposition confirms the tearing mode structure to be m/n = 2/1 (m and n being the poloidal and toroidal mode numbers). Linear tearing stability analysis with M3D-C1 predicts that plasmas with neave> 1019 are highly susceptible to a n = 1 tearing mode. ORBIT simulations, however, confirmed that the tearing modes do not contribute to the loss of fast ions from neutral beam injection. This study shows for the first time that the neutral inventory at the edge could be one of the deciding factors for the achievability of the unique operation regime of flat Te(r) and the excitation of tearing activity that could be disruptive for the plasmas.
ISSN: 1741-4326
Nuclear Fusion is the acknowledged world-leading journal specializing in fusion. The journal covers all aspects of research, theoretical and practical, relevant to controlled thermonuclear fusion.
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Santanu Banerjee et al 2024 Nucl. Fusion 64 046026
T. Qian et al 2022 Nucl. Fusion 62 084001
A first-of-a-kind optimized stellarator for confining plasma has been designed and is being constructed with planar circular coils and permanent magnets composed of identical elements. The equilibrium is optimized to be quasi-axisymmetric for good particle confinement. The combination of permanent magnets and planar coils is significantly simpler to construct than fabricating three-dimensionally shaped coils, yet they are able to produce lower helical magnetic ripple than existing devices by two orders of magnitude in , a characteristic neoclassical transport metric.
Vignesh Gopakumar et al 2024 Nucl. Fusion 64 056025
Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier neural operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (Mean Squared Error in the normalised domain ). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations, and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e. cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.
Sehila M. Gonzalez de Vicente et al 2022 Nucl. Fusion 62 085001
In the absence of official standards and guidelines for nuclear fusion plants, fusion designers adopted, as far as possible, well-established standards for fission-based nuclear power plants (NPPs). This often implies interpretation and/or extrapolation, due to differences in structures, systems and components, materials, safety mitigation systems, risks, etc. This approach could result in the consideration of overconservative measures that might lead to an increase in cost and complexity with limited or negligible improvements. One important topic is the generation of radioactive waste in fusion power plants. Fusion waste is significantly different to fission NPP waste, i.e. the quantity of fusion waste is much larger. However, it mostly comprises low-level waste (LLW) and intermediate level waste (ILW). Notably, the waste does not contain many long-lived isotopes, mainly tritium and other activation isotopes but no-transuranic elements. An important benefit of fusion employing reduced-activation materials is the lower decay heat removal and rapid radioactivity decay overall. The dominant fusion wastes are primarily composed of structural materials, such as different types of steel, including reduced activation ferritic martensitic steels, such as EUROFER97 and F82H, AISI 316L, bainitic, and JK2LB. The relevant long-lived radioisotopes come from alloying elements, such as niobium, molybdenum, nickel, carbon, nitrogen, copper and aluminum and also from uncontrolled impurities (of the same elements, but also, e.g. of potassium and cobalt). After irradiation, these isotopes might preclude disposal in LLW repositories. Fusion power should be able to avoid creating high-level waste, while the volume of fusion ILW and LLW will be significant, both in terms of pure volume and volume per unit of electricity produced. Thus, efforts to recycle and clear are essential to support fusion deployment, reclaim resources (through less ore mining) and minimize the radwaste burden for future generations.
Q.M. Hu et al 2024 Nucl. Fusion 64 046027
According to recent DIII-D experiments (Logan et al 2024 Nucl. Fusion64 014003), injecting edge localized electron cyclotron current drive (ECCD) in the counter-plasma-current (counter-Ip) direction reduces the n = 3 resonant magnetic perturbation (RMP) current threshold for edge-localized mode (ELM) suppression, while co-Ip ECCD during the suppressed ELM phase causes a back transition to ELMing. This paper presents nonlinear two-fluid simulations on the ECCD manipulation of edge magnetic islands induced by RMP using the TM1 code. In the presence of a magnetic island chain at the pedestal-top, co-Ip ECCD is found to decrease the island width and restore the initially degraded pedestal pressure when its radial deposition location is close to the rational surface of the island. With a sufficiently strong co-Ip ECCD current, the RMP-driven magnetic island can be healed, and the pedestal pressure fully recovers to its initial ELMing state. On the contrary, counter-Ip ECCD is found to increase the island width and further reduce the pedestal pressure to levels significantly below the peeling-ballooning-mode limited height, leading to even stationary ELM suppression. These simulations align with the results from DIII-D experiments. However, when multiple magnetic island chains are present at the pedestal-top, the ECCD current experiences substantial broadening, and its effects on the island width and pedestal pressure become negligible. Further simulations reveal that counter-Ip ECCD enhances RMP penetration by lowering the penetration threshold, with the degree of reduction proportional to the amplitude of ECCD current. For the ∼1 MW ECCD in DIII-D, the predicted decrease in the RMP penetration threshold for ELM suppression is approximately 20%, consistent with experimental observations. These simulations indicate that edge-localized ECCD can be used to either facilitate RMP-driven ELM suppression or optimize the confinement degradation.
M.S. Islam et al 2024 Nucl. Fusion 64 056036
The SOLPS-ITER code is utilized to analyze the boundary plasma associated with a fast-flow lithium (Li) divertor configuration in the fusion nuclear science facility (FNSF) tokamak and identify operational regimes with acceptable divertor and core conditions. Plasma transport from the SOLPS-ITER code has been coupled with a liquid metal (LM) MHD/heat transfer code to model a Li open-surface divertor design and assess its impact on the scrape-off-layer (SOL) and core plasma performance. Simulations with only Neon (Ne) impurity seeding have been conducted to evaluate its impact on meeting FNSF design demands for the divertor and upstream plasma parameters. Simulation results indicate that Ne seeding significantly mitigates divertor heat flux but potentially reduces both upstream electron and main ion density due to fuel dilution. The combined application of Ne seeding and deuterium (D2) puffing is required to satisfy the FNSF design requirements on upstream density ( ∼1× 1020 m−3) and divertor energy flux (10 MW m−2). D2 puffing plays a role in counteracting upstream density drops and augmenting energy and momentum losses through atomic and molecular processes.
The inlet Li flow velocity is systematically varied across a wide range to identify acceptable flows and corresponding LM surface temperatures. This comprehensive analysis identifies the acceptable Li flow parameters, LM surface temperature, and emitted Li fluxes necessary to meet the major design constraints. The emitted Li fluxes exhibit minimal impact on the main plasma at surface temperatures up to approximately ∼525 ∘C, corresponding emitted Li fluxes of up to φLi ∼2 atoms s−1. Uncertainties in the Li emission processes from the surface are also investigated, primarily influencing Li loss in the lower surface temperature range (C), with simulation results indicating a minor impact on the divertor and upstream plasma. Conversely, evaporation predominantly drives the Li loss processes at higher surface temperature ranges (C), contaminating both the divertor and upstream plasma.
G. Federici et al 2024 Nucl. Fusion 64 036025
High temperature superconductors (HTSs) offer the promise of operating at higher magnetic field and temperature. Recently, the use of high field magnets (by adopting HTS) has been promoted by several groups around the world, including new start-up entries, both to substantially reduce the size of a fusion power reactor system and as a breakthrough innovation that could dramatically accelerate fusion power deployment. This paper describes the results of an assessment to understand the impact of using high field magnets in the design of DEMO in Europe, considering a comprehensive list of physics and engineering limitations together with the interdependencies with other important parameters. Based on the results, it is concluded that increasing the magnetic field does not lead to a reduction in device size with relevant nuclear performance requirements, because (i) large structures are needed to withstand the enormous electromagnetic forces, (ii) thick blanket and n-shield structures are needed to protect the coils from radiation damage effects, and (iii) new divertor solutions with performances well beyond today's concepts are needed. Stronger structural materials allow for more compact tokamaks, but do not change the conclusion that scalability is not favourable when increasing the magnetic field, beyond a certain point, the machine size cannot be further reduced. More advanced structural support concepts for high-field coils have been explored and concluded that these solutions are either unfeasible or provide only marginal size reduction, by far not sufficient to account for the potential of operating at very high field provided by HTS. Additionally, the cost of high field coils is significant at today's price levels and shows to scale roughly with the square of the field. Nevertheless, it is believed that even when not operated at high field and starting within conventional insulated coils, HTS can still offer certain benefits. These include the simplification of the magnet cooling scheme thanks to increased temperature margin (indirect conduction cooling). This in turn can greatly simplify coil construction and minimize high-voltage risks at the terminals.
J. Mailloux et al 2022 Nucl. Fusion 62 042026
The JET 2019–2020 scientific and technological programme exploited the results of years of concerted scientific and engineering work, including the ITER-like wall (ILW: Be wall and W divertor) installed in 2010, improved diagnostic capabilities now fully available, a major neutral beam injection upgrade providing record power in 2019–2020, and tested the technical and procedural preparation for safe operation with tritium. Research along three complementary axes yielded a wealth of new results. Firstly, the JET plasma programme delivered scenarios suitable for high fusion power and alpha particle (α) physics in the coming D–T campaign (DTE2), with record sustained neutron rates, as well as plasmas for clarifying the impact of isotope mass on plasma core, edge and plasma-wall interactions, and for ITER pre-fusion power operation. The efficacy of the newly installed shattered pellet injector for mitigating disruption forces and runaway electrons was demonstrated. Secondly, research on the consequences of long-term exposure to JET-ILW plasma was completed, with emphasis on wall damage and fuel retention, and with analyses of wall materials and dust particles that will help validate assumptions and codes for design and operation of ITER and DEMO. Thirdly, the nuclear technology programme aiming to deliver maximum technological return from operations in D, T and D–T benefited from the highest D–D neutron yield in years, securing results for validating radiation transport and activation codes, and nuclear data for ITER.
Mohamed Abdou et al 2021 Nucl. Fusion 61 013001
The tritium aspects of the DT fuel cycle embody some of the most challenging feasibility and attractiveness issues in the development of fusion systems. The review and analyses in this paper provide important information to understand and quantify these challenges and to define the phase space of plasma physics and fusion technology parameters and features that must guide a serious R&D in the world fusion program. We focus in particular on components, issues and R&D necessary to satisfy three 'principal requirements': (1) achieving tritium self-sufficiency within the fusion system, (2) providing a tritium inventory for the initial start-up of a fusion facility, and (3) managing the safety and biological hazards of tritium. A primary conclusion is that the physics and technology state-of-the-art will not enable DEMO and future power plants to satisfy these principal requirements. We quantify goals and define specific areas and ideas for physics and technology R&D to meet these requirements. A powerful fuel cycle dynamics model was developed to calculate time-dependent tritium inventories and flow rates in all parts and components of the fuel cycle for different ranges of parameters and physics and technology conditions. Dynamics modeling analyses show that the key parameters affecting tritium inventories, tritium start-up inventory, and tritium self-sufficiency are the tritium burn fraction in the plasma (fb), fueling efficiency (ηf), processing time of plasma exhaust in the inner fuel cycle (tp), reactor availability factor (AF), reserve time (tr) which determines the reserve tritium inventory needed in the storage system in order to keep the plant operational for time tr in case of any malfunction of any part of the tritium processing system, and the doubling time (td). Results show that ηffb > 2% and processing time of 1–4 h are required to achieve tritium self-sufficiency with reasonable confidence. For ηffb = 2% and processing time of 4 h, the tritium start-up inventory required for a 3 GW fusion reactor is ∼11 kg, while it is <5 kg if ηffb = 5% and the processing time is 1 h. To achieve these stringent requirements, a serious R&D program in physics and technology is necessary. The EU-DEMO direct internal recycling concept that carries fuel directly from the plasma exhaust gas to the fueling systems without going through the isotope separation system reduces the overall processing time and tritium inventories and has positive effects on the required tritium breeding ratio (TBRR). A significant finding is the strong dependence of tritium self-sufficiency on the reactor availability factor. Simulations show that tritium self-sufficiency is: impossible if AF < 10% for any ηffb, possible if AF > 30% and 1% ⩽ ηffb ⩽ 2%, and achievable with reasonable confidence if AF > 50% and ηffb > 2%. These results are of particular concern in light of the low availability factor predicted for the near-term plasma-based experimental facilities (e.g. FNSF, VNS, CTF), and can have repercussions on tritium economy in DEMO reactors as well, unless significant advancements in RAMI are made. There is a linear dependency between the tritium start-up inventory and the fusion power. The required tritium start-up inventory for a fusion facility of 100 MW fusion power is as small as 1 kg. Since fusion power plants will have large powers for better economics, it is important to maintain a 'reserve' tritium inventory in the tritium storage system to continue to fuel the plasma and avoid plant shutdown in case of malfunctions of some parts of the tritium processing lines. But our results show that a reserve time as short as 24 h leads to unacceptable reserve and start-up inventory requirements. Therefore, high reliability and fast maintainability of all components in the fuel cycle are necessary in order to avoid the need for storing reserve tritium inventory sufficient for continued fusion facility operation for more than a few hours. The physics aspects of plasma fueling, tritium burn fraction, and particle and power exhaust are highly interrelated and complex, and predictions for DEMO and power reactors are highly uncertain because of lack of experiments with burning plasma. Fueling by pellet injection on the high field side of tokamak has evolved to be the preferred method to fuel a burning plasma. Extrapolation from the DIII-D penetration scaling shows fueling efficiency expected in DEMO to be <25%, but such extrapolations are highly uncertain. The fueling efficiency of gas in a reactor relevant regime is expected to be extremely poor and not very useful for getting tritium into the core plasma efficiently. Gas fueling will nonetheless be useful for feedback control of the divertor operating parameters. Extensive modeling has been carried out to predict burn fraction, fueling requirements, and fueling efficiency for ITER, DEMO, and beyond. The fueling rate required to operate Q = 10 ITER plasmas in order to provide the required core fueling, helium exhaust and radiative divertor plasma conditions for acceptable divertor power loads was calculated. If this fueling is performed with a 50–50 DT mix, the tritium burn fraction in ITER would be ∼0.36%, which is too low to satisfy the self-sufficiency conditions derived from the dynamics modeling for fusion reactors. Extrapolation to DEMO using this approach would also yield similarly low burn fraction. Extensive analysis presented shows that specific features of edge neutral dynamics in ITER and fusion reactors, which are different from present experiments, open possibilities for optimization of tritium fueling and thus to improve the burn fraction. Using only tritium in pellet fueling of the plasma core, and only deuterium for edge density, divertor power load and ELM control results in significant increase of the burn fraction to 1.8–3.6%. These estimates are performed with physics models whose results cannot be fully validated for ITER and DEMO plasma conditions since these cannot be achieved in present tokamak experiments. Thus, several uncertainties remain regarding particle transport and scenario requirements in ITER and DEMO. The safety standard requirements for protection of the public and release guidelines for tritium have been reviewed. General safety approaches including minimizing tritium inventories, reducing tritium permeation through materials, and decontaminating material for waste disposal have been suggested.
P. Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 042003
The SPARC tokamak project, currently in engineering design, aims to achieve breakeven and burning plasma conditions in a compact device, thanks to new developments in high-temperature superconductor technology. With a magnetic field of 12.2 T on axis and 8.7 MA of plasma current, SPARC is predicted to produce 140 MW of fusion power with a plasma gain of Q ≈ 11, providing ample margin with respect to its mission of Q > 2. All tokamak systems are being designed to produce this landmark plasma discharge, thus enabling the study of burning plasma physics and tokamak operations in reactor relevant conditions to pave the way for the design and construction of a compact, high-field fusion power plant. Construction of SPARC is planned to begin by mid-2021.
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K.C. Shaing et al 2024 Nucl. Fusion 64 066014
Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.
D. Kim et al 2024 Nucl. Fusion 64 066013
Further investigation of fast ion effects on turbulence and transport in the fast ion regulated enhancement (FIRE) mode discharge (Han et al 2022 Nature609 269–275) was performed in this work as a continuation of a previous study (Kim et al 2023 Nucl. Fusion63 124001) that showed that the dominant turbulence suppression mechanism by fast ions is the dilution effect in the FIRE mode discharge. The current study includes (i) the impact of the fast ion relevant mode observed in the simulation of thermal energy flux, (ii) dilution effects by fast ions compared to dilution effects by other species, and (iii) fast ion effects on electron-scale turbulence. First, nonlinear gyrokinetic simulation results show that turbulence is significantly suppressed even without the fast ion relevant mode, indicating that the impact of this mode on thermal transport is not significant in this discharge. Second, further analysis on the dilution effects shows the three following results: Turbulence is not completely suppressed by the reduced main ion density fraction effect due to impurities; the reduction in energy flux can be limited by a certain impurity mode that is destabilized by a high impurity density gradient from adjusting the main ion density gradient; electrons can contribute to turbulence suppression through the main ion density gradient change, although this effect is less significant compared to other species. Third, we observe that two fast ion effects can influence the linear growth rate of the electron-scale turbulence mode. The growth rate decreases by an increase in and increases by dilution effects, suggesting that fast ion effects on electron-scale turbulence can differ depending on the operation scenario, such as the fast ion fraction. The comprehensive analysis performed in this study can enhance our understanding of fast ion physics, required for burning plasma operation in the future.
A. Wingen et al 2024 Nucl. Fusion 64 066015
In ITER, pellets are calculated to require more than 8 times the mass than currently planned to reliably trigger edge-localized modes (ELMs). Unmitigated heat flux impulses from ELMs are intolerable in ITER at full power and current. Therefore, ITER operation relies on multiple approaches to control ELM heat fluxes. One method is pellet ELM pacing to instigate small rapid ELMs with low heat flux. Predicting the performance of pellet pacing is critical for ITER, which is expected to operate in a regime with a low-collisionality, peeling-limited pedestal. However, to trigger ELMs the local pressure increase in the expanding pellet cloud pushes the equilibrium over the ballooning stability limit. In this work, linear and nonlinear M3D-C1 simulations are used to predict pellet mass thresholds in DIII-D discharges and ITER scenarios with peeling-limited pedestals. It is found that the distance of the equilibrium's operational point from the ballooning branch of the pedestal stability boundary strongly changes thresholds. Linear M3D-C1 simulations find a strong dependence of the pellet mass threshold on the poloidal injection location for ITER's 15 MA, Q = 10 scenario. The required pellet mass at the planned injection locations is 8 to 17 times larger than currently considered. However, such linear simulations do not include pellet ablation physics or time evolution of density and temperature. A new scheme of 2D nonlinear simulations, coupled with linear stability analysis at various steps throughout the nonlinear time evolution, was developed to include such physics and improve on the linear results. These new nonlinear-to-linear simulations confirm previous findings. This result suggests that pellet ELM triggering in ITER could require pellets much larger than those currently planned, which makes ELM-pacing operationally challenging. On the other hand, fueling pellets injected from the high-field side will likely not unintentionally trigger ELMs in an otherwise ELM-stable plasma.
A. Buzás et al 2024 Nucl. Fusion 64 066012
Filaments are studied by examining fast camera images on the Wendelstein 7-X stellarator. Fast cameras offer a unique perspective, revealing the complex 3D structure of filaments in the entire poloidal cross-section of the plasma. By correlating individual pixels, their location, shape, and movement are analyzed in standard and high-ι configurations. The presence of filaments is not uniform poloidally around. The number of active areas matches the number of magnetic islands in both configurations. Filaments are found to extend to multiple toroidal turns in standard configuration. No time delay is observed between the different toroidal sections. Such behavior is not seen in high-ι configuration. Filaments are observed within and without the edge shear layer, indicated by the direction of their poloidal rotation. Inside the shear layer, their velocity scatters around 1.25 km s−1, accompanied by a lifetime between 80 and 120 µs. Outside, their velocity shows greater absolute values and variance, but still in a few km s−1 range. The similarities and differences between the two configurations are discussed and compared to previous results.
Ting Long et al 2024 Nucl. Fusion 64 066011
Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.
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G.D. Conway et al 2022 Nucl. Fusion 62 013001
Geodesic acoustic modes (GAMs) are ubiquitous oscillatory flow phenomena observed in toroidal magnetic confinement fusion plasmas, such as tokamaks and stellarators. They are recognized as the non-stationary branch of the turbulence driven zonal flows which play a critical regulatory role in cross-field turbulent transport. GAMs are supported by the plasma compressibility due to magnetic geodesic curvature—an intrinsic feature of any toroidal confinement device. GAMs impact the plasma confinement via velocity shearing of turbulent eddies, modulation of transport, and by providing additional routes for energy dissipation. GAMs can also be driven by energetic particles (so-called EGAMs) or even pumped by a variety of other mechanisms, both internal and external to the plasma, opening-up possibilities for plasma diagnosis and turbulence control. In recent years there have been major advances in all areas of GAM research: measurements, theory, and numerical simulations. This review assesses the status of these developments and the progress made towards a unified understanding of the GAM behaviour and its role in plasma confinement. The review begins with tutorial-like reviews of the basic concepts and theory, followed by a series of topic orientated sections covering different aspects of the GAM. The approach adopted here is to present and contrast experimental observations alongside the predictions from theory and numerical simulations. The review concludes with a comprehensive summary of the field, highlighting outstanding issues and prospects for future developments.
L. Marrelli et al 2021 Nucl. Fusion 61 023001
This paper reviews the research on the reversed field pinch (RFP) in the last three decades. Substantial experimental and theoretical progress and transformational changes have been achieved since the last review (Bodin 1990 Nucl. Fusion 30 1717–37). The experiments have been performed in devices with different sizes and capabilities. The largest are RFX-mod in Padova (Italy) and MST in Madison (USA). The experimental community includes also EXTRAP-T2R in Sweden, RELAX in Japan and KTX in China. Impressive improvements in the performance are the result of exploration of two lines: the high current operation (up to 2 MA) with the spontaneous occurrence of helical equilibria with good magnetic flux surfaces and the active control of the current profile. A crucial ingredient for the advancements obtained in the experiments has been the development of state-of-art active feedback control systems allowing the control of MHD instabilities in presence of a thin shell. The balance between achievements and still open issues leads us to the conclusion that the RFP can be a valuable and diverse contributor in the quest for fusion electricity.
Mohamed Abdou et al 2021 Nucl. Fusion 61 013001
The tritium aspects of the DT fuel cycle embody some of the most challenging feasibility and attractiveness issues in the development of fusion systems. The review and analyses in this paper provide important information to understand and quantify these challenges and to define the phase space of plasma physics and fusion technology parameters and features that must guide a serious R&D in the world fusion program. We focus in particular on components, issues and R&D necessary to satisfy three 'principal requirements': (1) achieving tritium self-sufficiency within the fusion system, (2) providing a tritium inventory for the initial start-up of a fusion facility, and (3) managing the safety and biological hazards of tritium. A primary conclusion is that the physics and technology state-of-the-art will not enable DEMO and future power plants to satisfy these principal requirements. We quantify goals and define specific areas and ideas for physics and technology R&D to meet these requirements. A powerful fuel cycle dynamics model was developed to calculate time-dependent tritium inventories and flow rates in all parts and components of the fuel cycle for different ranges of parameters and physics and technology conditions. Dynamics modeling analyses show that the key parameters affecting tritium inventories, tritium start-up inventory, and tritium self-sufficiency are the tritium burn fraction in the plasma (fb), fueling efficiency (ηf), processing time of plasma exhaust in the inner fuel cycle (tp), reactor availability factor (AF), reserve time (tr) which determines the reserve tritium inventory needed in the storage system in order to keep the plant operational for time tr in case of any malfunction of any part of the tritium processing system, and the doubling time (td). Results show that ηffb > 2% and processing time of 1–4 h are required to achieve tritium self-sufficiency with reasonable confidence. For ηffb = 2% and processing time of 4 h, the tritium start-up inventory required for a 3 GW fusion reactor is ∼11 kg, while it is <5 kg if ηffb = 5% and the processing time is 1 h. To achieve these stringent requirements, a serious R&D program in physics and technology is necessary. The EU-DEMO direct internal recycling concept that carries fuel directly from the plasma exhaust gas to the fueling systems without going through the isotope separation system reduces the overall processing time and tritium inventories and has positive effects on the required tritium breeding ratio (TBRR). A significant finding is the strong dependence of tritium self-sufficiency on the reactor availability factor. Simulations show that tritium self-sufficiency is: impossible if AF < 10% for any ηffb, possible if AF > 30% and 1% ⩽ ηffb ⩽ 2%, and achievable with reasonable confidence if AF > 50% and ηffb > 2%. These results are of particular concern in light of the low availability factor predicted for the near-term plasma-based experimental facilities (e.g. FNSF, VNS, CTF), and can have repercussions on tritium economy in DEMO reactors as well, unless significant advancements in RAMI are made. There is a linear dependency between the tritium start-up inventory and the fusion power. The required tritium start-up inventory for a fusion facility of 100 MW fusion power is as small as 1 kg. Since fusion power plants will have large powers for better economics, it is important to maintain a 'reserve' tritium inventory in the tritium storage system to continue to fuel the plasma and avoid plant shutdown in case of malfunctions of some parts of the tritium processing lines. But our results show that a reserve time as short as 24 h leads to unacceptable reserve and start-up inventory requirements. Therefore, high reliability and fast maintainability of all components in the fuel cycle are necessary in order to avoid the need for storing reserve tritium inventory sufficient for continued fusion facility operation for more than a few hours. The physics aspects of plasma fueling, tritium burn fraction, and particle and power exhaust are highly interrelated and complex, and predictions for DEMO and power reactors are highly uncertain because of lack of experiments with burning plasma. Fueling by pellet injection on the high field side of tokamak has evolved to be the preferred method to fuel a burning plasma. Extrapolation from the DIII-D penetration scaling shows fueling efficiency expected in DEMO to be <25%, but such extrapolations are highly uncertain. The fueling efficiency of gas in a reactor relevant regime is expected to be extremely poor and not very useful for getting tritium into the core plasma efficiently. Gas fueling will nonetheless be useful for feedback control of the divertor operating parameters. Extensive modeling has been carried out to predict burn fraction, fueling requirements, and fueling efficiency for ITER, DEMO, and beyond. The fueling rate required to operate Q = 10 ITER plasmas in order to provide the required core fueling, helium exhaust and radiative divertor plasma conditions for acceptable divertor power loads was calculated. If this fueling is performed with a 50–50 DT mix, the tritium burn fraction in ITER would be ∼0.36%, which is too low to satisfy the self-sufficiency conditions derived from the dynamics modeling for fusion reactors. Extrapolation to DEMO using this approach would also yield similarly low burn fraction. Extensive analysis presented shows that specific features of edge neutral dynamics in ITER and fusion reactors, which are different from present experiments, open possibilities for optimization of tritium fueling and thus to improve the burn fraction. Using only tritium in pellet fueling of the plasma core, and only deuterium for edge density, divertor power load and ELM control results in significant increase of the burn fraction to 1.8–3.6%. These estimates are performed with physics models whose results cannot be fully validated for ITER and DEMO plasma conditions since these cannot be achieved in present tokamak experiments. Thus, several uncertainties remain regarding particle transport and scenario requirements in ITER and DEMO. The safety standard requirements for protection of the public and release guidelines for tritium have been reviewed. General safety approaches including minimizing tritium inventories, reducing tritium permeation through materials, and decontaminating material for waste disposal have been suggested.
Boris N. Breizman et al 2019 Nucl. Fusion 59 083001
Of all electrons, runaway electrons have long been recognized in the fusion community as a distinctive population. They now attract special attention as a part of ITER mission considerations. This review covers basic physics ingredients of the runaway phenomenon and the ongoing efforts (experimental and theoretical) aimed at runaway electron (RE) taming in the next generation tokamaks. We emphasize the prevailing physics themes of the last 20 years: the hot-tail mechanism of runaway production, RE interaction with impurity ions, the role of synchrotron radiation in runaway kinetics, RE transport in presence of magnetic fluctuations, micro-instabilities driven by REs in magnetized plasmas, and vertical stability of the plasma with REs. The review also discusses implications of the runaway phenomenon for ITER and the current strategy of RE mitigation.
M.K.A. Thumm et al 2019 Nucl. Fusion 59 073001
In many tokamak and stellarator experiments around the globe that are investigating energy production via controlled thermonuclear fusion, electron cyclotron heating and current drive (ECH&CD) are used for plasma start-up, heating, non-inductive current drive and magnetohydrodynamic stability control. ECH will be the first auxiliary heating method used on ITER. Megawatt-class, continuous wave gyrotrons are employed as high-power millimeter (mm)-wave sources. The present review reports on the worldwide state-of-the-art of high-power gyrotrons. Their successful development during recent years changed ECH from a minor to a major heating method. After a general introduction of the various functions of ECH&CD in fusion physics, especially for ITER, section 2 will explain the fast-wave gyrotron interaction principle. Section 3 discusses innovations on the components of modern long-pulse fusion gyrotrons (magnetron injection electron gun, beam tunnel, cavity, quasi-optical output coupler, synthetic diamond output window, single-stage depressed collector) and auxiliary components (superconducting magnets, gyrotron diagnostics, high-power calorimetric dummy loads). Section 4 deals with present megawatt-class gyrotrons for ITER, W7-X, LHD, EAST, KSTAR and JT-60SA, and also includes tubes for moderate pulse length machines such as ASDEX-U, DIII-D, HL-2A, TCV, QUEST and GAMMA-10. In section 5 the development of future advanced fusion gyrotrons is discussed. These are tubes with higher frequencies for DEMO, multi-frequency (multi-purpose) gyrotrons, stepwise frequency tunable tubes for plasma stabilization, injection-locked and coaxial-cavity multi-megawatt gyrotrons, as well as sub-THz gyrotrons for collective Thomson scattering. Efficiency enhancement via multi-stage depressed collectors, fast oscillation recovery methods and reliability, availability, maintainability and inspectability will be discussed at the end of this section.
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Jiang et al
Four Test Blanket Systems (TBS) will be tested in the International Thermonuclear Experimental Reactor (ITER) equatorial ports #16 and #18 to verify tritium breeding and heat extraction technology. A significant quantity of tritium would be produced in TBM, and partly released into the port cell from the pipework of TBS or other high-temperature components due to its strong mobility and high permeation. The port cell should be accessible during equipment maintenance and human intervention. This work built a multi-dimensional geometric model to characterize HTO transport in the port cell, absorption/desorption, and diffusion in walls and discussed the effect of paint thickness, ventilation rate, source term, and epoxy properties on detritiation efficiency. The results suggest that a 0.1-0.16 mm paint with the lowest HTO solubility is optimal from the compromise between quick cleanup and tritiated waste decommission. A higher ventilation rate could accelerate detritiation while minimizing the radioactive source by a tritium-resisting layer is the most direct method. The optimized design options for reducing the time required to reach 1 DAC in 12 h still need further discussion because of the delayed HTO source from epoxy paint and dead zone of the flow field.
Joung et al
A neural network, BES-ELMnet, predicting a quasi-periodic disruptive eruption of the plasma energy and particles known as edge localized mode (ELM) onset is developed with observed pedestal turbulence from the beam emission spectroscopy system in D\rom{3}-D. BES-ELMnet has convolutional and fully-connected layers, taking two-dimensional plasma fluctuations with a temporal window of size 128\:$\mu$s and generating a scalar output which can be interpreted as a probability of the upcoming ELM onset. As approximately labelled inter-ELM broadband (15\:kHz\:$\leq f\leq$\:150\:kHz) fluctuations are given to the network, BES-ELMnet learns by itself ELM-related precursors arising before the onsets through supervised learning scheme. BES-ELMnet achieves the gradually increasing ELM onset probabilities between two consecutive ELMs during the inter-ELM phases and can forecast the first ELM onsets which occur after the high confinement mode transition. We further investigate the network generality in terms of the selected frequency band to ensure the use of BES-ELMnet for various operation regimes without changing the trained architecture. Therefore, our novel prediction method will enhance a proactive high confinement mode control of fusion-grade plasmas.
Cheng et al
The parametric decay of toroidal Alfvén eigenmode (TAE) in nonuniform plasmas is investigated using nonlinear gyrokinetic equation. It is found that, the plasma nonuniformity not only significantly enhances the nonlinear coupling cross-section, but also qualitatively modifies the decay process. Specifically, the condition for spontaneous decay becomes the toroidal mode number of the sideband TAE being higher than that of the pump TAE, instead of the frequency of the sideband TAE being lower than the pump TAE in uniform plasmas. The consequences on TAE saturation and energetic particle transport are also discussed.
Rui et al
Vertical position control is essential for stabilizing plasma with elongated configurations. Currently, a PD controller with fixed parameters is used for the vertical position control of EAST plasma. However, the response of the plasma in the vertical position changes with changes in plasma configuration, which can result in different control parameter requirements. It is essential to develop a model-based fast-tuning control algorithm for ensuring stability in the vertical position under different configurations. In this study, a model-based vertical position controller tuning method based on a linear quadratic regulator algorithm (LQR) is proposed. Compared with contemporary PD controllers, the proposed model-based LQR controller can enable adjusting controller parameters based on the response of the system, achieving stable control under different vertical position responses. In the EAST experiment, the model-based LQR controller achieved stable control under a shot with a continuously increasing growth rate and reached a maximum controllable vertical displacement growth rate of 968 s-1. The robustness of the system was also demonstrated in a free drift experiment. The new vertical displacement control method can be adapted to different system states and plasma configurations and improve the controllability and safety of future devices.
Rueda-Rueda et al
Alfvén Eigenmodes-driven fast-ion flows have been measured for the first time at the ASDEX Upgrade tokamak using an imaging neutral particle analyzer. The flow is such that particles are expelled from the mode location, losing energy as they move outwards. This flow aligns well with the projection of the lines of constant magnetic moment and constant $E'$ ($E' = E - \omega P_\phi/n$, with $E$ being the particle energy, $\omega, n$ the mode frequency and toroidal number and $P_\phi$ the toroidal canonical angular momentum). The observed redistributions are consistent with full-orbit simulations performed with the ASCOT5 code, using the mode structure predicted by the linear gyro-kinetic code LIGKA.

This article corresponds to the new material presented by the authors at the FEC 2023
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K.C. Shaing et al 2024 Nucl. Fusion 64 066014
Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.
D. Kim et al 2024 Nucl. Fusion 64 066013
Further investigation of fast ion effects on turbulence and transport in the fast ion regulated enhancement (FIRE) mode discharge (Han et al 2022 Nature609 269–275) was performed in this work as a continuation of a previous study (Kim et al 2023 Nucl. Fusion63 124001) that showed that the dominant turbulence suppression mechanism by fast ions is the dilution effect in the FIRE mode discharge. The current study includes (i) the impact of the fast ion relevant mode observed in the simulation of thermal energy flux, (ii) dilution effects by fast ions compared to dilution effects by other species, and (iii) fast ion effects on electron-scale turbulence. First, nonlinear gyrokinetic simulation results show that turbulence is significantly suppressed even without the fast ion relevant mode, indicating that the impact of this mode on thermal transport is not significant in this discharge. Second, further analysis on the dilution effects shows the three following results: Turbulence is not completely suppressed by the reduced main ion density fraction effect due to impurities; the reduction in energy flux can be limited by a certain impurity mode that is destabilized by a high impurity density gradient from adjusting the main ion density gradient; electrons can contribute to turbulence suppression through the main ion density gradient change, although this effect is less significant compared to other species. Third, we observe that two fast ion effects can influence the linear growth rate of the electron-scale turbulence mode. The growth rate decreases by an increase in and increases by dilution effects, suggesting that fast ion effects on electron-scale turbulence can differ depending on the operation scenario, such as the fast ion fraction. The comprehensive analysis performed in this study can enhance our understanding of fast ion physics, required for burning plasma operation in the future.
A. Wingen et al 2024 Nucl. Fusion 64 066015
In ITER, pellets are calculated to require more than 8 times the mass than currently planned to reliably trigger edge-localized modes (ELMs). Unmitigated heat flux impulses from ELMs are intolerable in ITER at full power and current. Therefore, ITER operation relies on multiple approaches to control ELM heat fluxes. One method is pellet ELM pacing to instigate small rapid ELMs with low heat flux. Predicting the performance of pellet pacing is critical for ITER, which is expected to operate in a regime with a low-collisionality, peeling-limited pedestal. However, to trigger ELMs the local pressure increase in the expanding pellet cloud pushes the equilibrium over the ballooning stability limit. In this work, linear and nonlinear M3D-C1 simulations are used to predict pellet mass thresholds in DIII-D discharges and ITER scenarios with peeling-limited pedestals. It is found that the distance of the equilibrium's operational point from the ballooning branch of the pedestal stability boundary strongly changes thresholds. Linear M3D-C1 simulations find a strong dependence of the pellet mass threshold on the poloidal injection location for ITER's 15 MA, Q = 10 scenario. The required pellet mass at the planned injection locations is 8 to 17 times larger than currently considered. However, such linear simulations do not include pellet ablation physics or time evolution of density and temperature. A new scheme of 2D nonlinear simulations, coupled with linear stability analysis at various steps throughout the nonlinear time evolution, was developed to include such physics and improve on the linear results. These new nonlinear-to-linear simulations confirm previous findings. This result suggests that pellet ELM triggering in ITER could require pellets much larger than those currently planned, which makes ELM-pacing operationally challenging. On the other hand, fueling pellets injected from the high-field side will likely not unintentionally trigger ELMs in an otherwise ELM-stable plasma.
A. Buzás et al 2024 Nucl. Fusion 64 066012
Filaments are studied by examining fast camera images on the Wendelstein 7-X stellarator. Fast cameras offer a unique perspective, revealing the complex 3D structure of filaments in the entire poloidal cross-section of the plasma. By correlating individual pixels, their location, shape, and movement are analyzed in standard and high-ι configurations. The presence of filaments is not uniform poloidally around. The number of active areas matches the number of magnetic islands in both configurations. Filaments are found to extend to multiple toroidal turns in standard configuration. No time delay is observed between the different toroidal sections. Such behavior is not seen in high-ι configuration. Filaments are observed within and without the edge shear layer, indicated by the direction of their poloidal rotation. Inside the shear layer, their velocity scatters around 1.25 km s−1, accompanied by a lifetime between 80 and 120 µs. Outside, their velocity shows greater absolute values and variance, but still in a few km s−1 range. The similarities and differences between the two configurations are discussed and compared to previous results.
Yingwu Jiang et al 2024 Nucl. Fusion
Four Test Blanket Systems (TBS) will be tested in the International Thermonuclear Experimental Reactor (ITER) equatorial ports #16 and #18 to verify tritium breeding and heat extraction technology. A significant quantity of tritium would be produced in TBM, and partly released into the port cell from the pipework of TBS or other high-temperature components due to its strong mobility and high permeation. The port cell should be accessible during equipment maintenance and human intervention. This work built a multi-dimensional geometric model to characterize HTO transport in the port cell, absorption/desorption, and diffusion in walls and discussed the effect of paint thickness, ventilation rate, source term, and epoxy properties on detritiation efficiency. The results suggest that a 0.1-0.16 mm paint with the lowest HTO solubility is optimal from the compromise between quick cleanup and tritiated waste decommission. A higher ventilation rate could accelerate detritiation while minimizing the radioactive source by a tritium-resisting layer is the most direct method. The optimized design options for reducing the time required to reach 1 DAC in 12 h still need further discussion because of the delayed HTO source from epoxy paint and dead zone of the flow field.
Semin Joung et al 2024 Nucl. Fusion
A neural network, BES-ELMnet, predicting a quasi-periodic disruptive eruption of the plasma energy and particles known as edge localized mode (ELM) onset is developed with observed pedestal turbulence from the beam emission spectroscopy system in D\rom{3}-D. BES-ELMnet has convolutional and fully-connected layers, taking two-dimensional plasma fluctuations with a temporal window of size 128\:$\mu$s and generating a scalar output which can be interpreted as a probability of the upcoming ELM onset. As approximately labelled inter-ELM broadband (15\:kHz\:$\leq f\leq$\:150\:kHz) fluctuations are given to the network, BES-ELMnet learns by itself ELM-related precursors arising before the onsets through supervised learning scheme. BES-ELMnet achieves the gradually increasing ELM onset probabilities between two consecutive ELMs during the inter-ELM phases and can forecast the first ELM onsets which occur after the high confinement mode transition. We further investigate the network generality in terms of the selected frequency band to ensure the use of BES-ELMnet for various operation regimes without changing the trained architecture. Therefore, our novel prediction method will enhance a proactive high confinement mode control of fusion-grade plasmas.
Zhiwen Cheng et al 2024 Nucl. Fusion
The parametric decay of toroidal Alfvén eigenmode (TAE) in nonuniform plasmas is investigated using nonlinear gyrokinetic equation. It is found that, the plasma nonuniformity not only significantly enhances the nonlinear coupling cross-section, but also qualitatively modifies the decay process. Specifically, the condition for spontaneous decay becomes the toroidal mode number of the sideband TAE being higher than that of the pump TAE, instead of the frequency of the sideband TAE being lower than the pump TAE in uniform plasmas. The consequences on TAE saturation and energetic particle transport are also discussed.
Wangyi Rui et al 2024 Nucl. Fusion
Vertical position control is essential for stabilizing plasma with elongated configurations. Currently, a PD controller with fixed parameters is used for the vertical position control of EAST plasma. However, the response of the plasma in the vertical position changes with changes in plasma configuration, which can result in different control parameter requirements. It is essential to develop a model-based fast-tuning control algorithm for ensuring stability in the vertical position under different configurations. In this study, a model-based vertical position controller tuning method based on a linear quadratic regulator algorithm (LQR) is proposed. Compared with contemporary PD controllers, the proposed model-based LQR controller can enable adjusting controller parameters based on the response of the system, achieving stable control under different vertical position responses. In the EAST experiment, the model-based LQR controller achieved stable control under a shot with a continuously increasing growth rate and reached a maximum controllable vertical displacement growth rate of 968 s-1. The robustness of the system was also demonstrated in a free drift experiment. The new vertical displacement control method can be adapted to different system states and plasma configurations and improve the controllability and safety of future devices.
Jose Rueda-Rueda et al 2024 Nucl. Fusion
Alfvén Eigenmodes-driven fast-ion flows have been measured for the first time at the ASDEX Upgrade tokamak using an imaging neutral particle analyzer. The flow is such that particles are expelled from the mode location, losing energy as they move outwards. This flow aligns well with the projection of the lines of constant magnetic moment and constant $E'$ ($E' = E - \omega P_\phi/n$, with $E$ being the particle energy, $\omega, n$ the mode frequency and toroidal number and $P_\phi$ the toroidal canonical angular momentum). The observed redistributions are consistent with full-orbit simulations performed with the ASCOT5 code, using the mode structure predicted by the linear gyro-kinetic code LIGKA.

This article corresponds to the new material presented by the authors at the FEC 2023
Ting Long et al 2024 Nucl. Fusion 64 066011
Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.