A theoretical model is presented that for the first time matches experimental measurements of the pedestal width-height Diallo scaling in the low-aspect-ratio high-β tokamak NSTX. Combining linear gyrokinetics with self-consistent pedestal equilibrium variation, kinetic-ballooning, rather than ideal-ballooning plasma instability, is shown to limit achievable confinement in spherical tokamak pedestals. Simulations are used to find the novel Gyrokinetic Critical Pedestal constraint, which determines the steepest pressure profile a pedestal can sustain subject to gyrokinetic instability. Gyrokinetic width-height scaling expressions for NSTX pedestals with varying density and temperature profiles are obtained. These scalings for STs depart significantly from that of conventional aspect ratio tokamaks.
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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J.F. Parisi et al 2024 Nucl. Fusion 64 054002
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.
J. Elbez-Uzan et al 2024 Nucl. Fusion 64 037001
The discussion in the international community on how fusion power plants (FPPs) will be licenced and regulated is ongoing. As such, there is a concerted drive from the European stakeholders to understand the requirements from such a framework and how to best establish it with the aim of easing the licensing process of FPPs. Initiated by the EUROfusion consortium, a group of European experts were convened to produce a set of recommendations on the regulatory framework for the safety and licensing of FPPs. To do so effectively, the group assessed lessons learned from existing fusion facilities, reports by International Atomic Energy Agency and European Commission on FPP safety and the on-going work by the UK government, US Nuclear Regulatory Commission and Canadian Nuclear Safety Commission, as well as the licensing process of ITER. As a result, commonalities between fusion and fission were identified in terms of fundamental safety objectives which could facilitate parity in certain framework aspects. However, significant differences to any such implementation were also identified, particularly with respect to the lower hazard potential inherent to FPPs and how to remain proportionate to the associated safety challenges and the physical principles behind these two types of reactors together with their associated technologies. The recognition of the differences in the safety challenges in FPPs and fission-based nuclear power plants (NPPs) is paramount to future regulatory framework development. Ultimately, regulatory frameworks depend upon a country's legal framework, therefore it is apparent that a common global regulatory framework for FPPs is not possible. However, as with present-day NPP regulation, efforts could be made to develop harmonised approaches to FPP regulation to provide common levels of protection. In view of this objective, 12 recommendations are presented across 4 topics: regulations, international databases, codes and standards, safety demonstration rules and regulatory approaches. These recommendations are provided to inform and advise potential future actions on FPP regulatory framework and licencing process principles.
Semin Joung et al 2024 Nucl. Fusion 64 066038
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 DIII-D. BES-ELMnet has convolutional and fully-connected layers, taking two-dimensional plasma fluctuations with a temporal window of size 128 µs and generating a scalar output which can be interpreted as a probability of the upcoming ELM onset. As approximately labeled inter-ELM broadband () 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.
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.
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.
I.A.M. Datta et al 2024 Nucl. Fusion 64 066016
The FuZE sheared-flow-stabilized Z pinch at Zap Energy is simulated using whole-device modeling employing an axisymmetric resistive magnetohydrodynamic formulation implemented within the discontinuous Galerkin WARPXM framework. Simulations show formation of Z pinches with densities of approximately 1022 m−3 and total DD fusion neutron rate of 107 per µs for approximately 2 µs. Simulation-derived synthetic diagnostics show peak currents and voltages within 10% and total yield within approximately 30% of experiment for similar plasma mass. The simulations provide insight into the plasma dynamics in the experiment and enable a predictive capability for exploring design changes on devices built at Zap Energy.
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.
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T. Lyytinen et al 2024 Nucl. Fusion 64 076042
This contribution presents neutron transport studies for the 5-period helical-axis advanced stellarator stellarator using the Serpent2 code. These studies utilize a parametric geometry model, enabling scans in neutronics modeling by varying the thickness of the reactor layers. For example, the tritium breeding ratio (TBR) can be determined by exploring various blanket material options and thicknesses to identify the threshold configuration that meets the TBR design criterion of 1.15. We found out that with the helium-cooled pebble ped candidate option, the TBR criterion is met with a breeding zone thickness of 26 cm, while with the dual-coolant lithium lead the threshold is exceeded at a thickness of 46 cm. Furthermore, the geometry includes non-planar field coils, allowing to study the fast neutron flux in these superconducting coils with a technological limit of . It is shown that the neutron fast flux is not constant at the coils, necessitating a neutron transport simulation to determine the distribution of the fast-flux at the coils. We show that the peak fast flux can be more than a factor of 2 higher than the average flux, and that the peak flux location rotates helically.
Vijay Shankar et al 2024 Nucl. Fusion 64 076041
We present an improved model for the study of edge biasing in a tokamak plasma that incorporates electron and ion mobility contributions. The non-ambipolar nature of the drifts due to the electron/ion mobility terms influences the space charge separation due to edge biasing and affects plasma dynamics in the edge and SOL regions in a significant manner. In contrast to earlier studies, the present model enables simulation studies at higher biasing voltages. The inclusion of mobility enhances/decreases the effect of negative/positive biasing. The radial profiles of plasma density, electron temperature, radial electric field, and its shear for positive as well as negative biasing are investigated as a function of mobility.
P. Arena et al 2024 Nucl. Fusion 64 076043
In the framework of the activities coordinated by the EUROfusion consortium, the Water thermal-HYDRAulic (W-HYDRA) experimental platform is being built at the ENEA Brasimone Research Centre in order to support the development of the Water-Cooled Lead Lithium (WCLL) Breeding Blanket (BB). In particular, this infrastructure will make possible the installation and testing of prototypical mock-ups under relevant working conditions, such as the First Wall (FW), the manifold and the Steam Generator (SG). Moreover, it will represent an integral test facility for the investigation of phenomena characteristic of WCLL BB concept, such as the PbLi/water interaction. Finally, the collection of data coming from the different planned experimental campaigns will allow to qualify and validate numerical models and codes currently adopted for the design of components, as well as for the modelling of complex phenomena typical of the WCLL BB. In order to come to a definitive design of the different facilities constituting the experimental platform, several design analyses assessing the thermal, hydraulic and structural performances of the different facilities and components are necessary. The paper reports a highlight of the W-HYDRA platform with a general description of the facilities. Some of the most relevant design studies carried out so far are reported as well, highlighting their impact on the evolution of the design.
Allen H. Boozer 2024 Nucl. Fusion 64 074004
A stellarator design is described with the purpose of achieving three goals: (1) enhance the confinement time of tritium. (2) Have a sufficient density of high-Z impurities to radiate the thermal power escaping from the core while having an extremely low impurity density in the core. (3) Maintain a large fraction of the plasma in a burning plasma state with an optimal tritium fraction. Some features of this design could be used in tokamaks. Although having three confinement zones is natural for stellarators, it is not for tokamaks.
M.T. Beidler et al 2024 Nucl. Fusion 64 076038
Subcritical energetic electrons (SEEs) produced by the runaway electron (RE) avalanche source at energies below the runaway threshold are found to be the primary contributor to surface heating of plasma-facing components (PFCs) during final loss events. This finding is supported by theoretical analysis, computational modeling with the Kinetic Orbit Runaway electrons Code (KORC), and qualitative agreement with DIII-D experimental observations. The avalanche source generates significantly more secondary electrons below the runaway threshold, which thermalize rapidly when well-confined. However, during a final loss event, the RE beam impacts the first wall, and SEEs are deconfined before they can thermalize. Additionally, because the energy deposition length decreases faster than energy, the deposited energy density, and thus the maximum PFC surface temperature change, is larger for SEEs than REs. KORC simulations employ an analytic first wall to model particle deconfinement onto a non-axisymmetric wall composed of individual tiles. PFC surface heating is calculated using a 1D model extended to include an energy-dependent deposition length scale. Simulations of DIII-D qualitatively agree with infrared (IR) imaging only when SEEs from the avalanche source are included. These results demonstrate that SEEs are the dominant contributor to PFC surface heating and indicate that the avalanche source plays a critical role in the PFC damage caused during final loss events. The prominence of SEEs also has important implications for interpreting IR imaging, one of the primary diagnostics for RE-wall interaction diagnosis, despite REs dominating the energy and current density. This result improves predictions of wall damage due to post-disruption REs to estimate material lifetime and design RE mitigation systems for ITER and future reactors.
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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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Zheng et al
It was found previously that the negative triangularity (NT) configuration is more MHD-unstable for low n modes than the positive triangularity (PT) case, although the situation is reversed for intermediate n modes and the NT configuration becomes more stable for intermediate n modes (n = 3 − 10) [Nucl. Fusion 61 116014 (2021)]. In this work, we extend the studies to include the rotation effects, as well as the diamagnetic drift effects, to see how the resistive wall modes in the NT configuration are affected as compared with the PT configuration. This is particularly motivated by noting that the wall interface with the plasma is quite different between the NT
and PT configurations. It affects the plasma rotation and diamagnetic drift effects on the low n resistive wall modes (RWMs). We consider the DIII-D-NT-experiment equilibrium reconstructed by the EFIT code. Based on the equilibrium g-file, the extended equilibria are constructed with the VMEC code by varying the beta values while keeping the pressure and poloidal current flux profiles basically unchanged. The bootstrap current contribution to the equilibria is taken into account with the Sauter formula. The MHD stability is then computed using the AEGIS code with the rotation and diamagnetic drift effects taken into account. We found that, although the negative triangularity configuration is less stable for n = 1 MHD modes, the rotation and diamagnetic drift stabilization effects on RWMs are more effective in the negative triangularity configuration than in the positive triangularity one. Note that even in the PT case, the stabilization of RWMs by the rotation and kinetic effects is critical. Because the low-n RWMs in the regular NT case are more unstable, the rotation and diamagnetic drift stabilization effects found in this research are important for the NT tokamak concept.
Ko et al
Using a global gyrofluid code, we conduct comprehensive flux-driven simulations incorporating external heat and momentum sources/sinks. They involve an external torque ramp keeping a heating power constant. Simulations show the formation of internal transport barriers (ITBs) in ion heat and parallel momentum in weak magnetic shear configuration. The ITB formation is attributed to the reduction of turbulent transport accompanied by strong E × B flow shear generation, where the majority of E × B shear arises from plasma rotation shear. In contrast, only a minor confinement improvement is observed in strong magnetic shear configuration. There exists a substantial difference in the rotation shear between the weak and strong magnetic shear cases at the same amount of external torque. Transport analysis implies that the difference comes from intrinsic rotation generated by residual stress. Global linear simulations demonstrate that the effect of E×B shear on k∥ symmetry breaking is enhanced in weak magnetic shear configuration, explaining the origin of the difference in intrinsic rotation. The ITB is not achieved when the external torque is injected in counter-direction to intrinsic rotation. It is also shown that threshold torque for the ITB formation depends on power and the ratio of external torque to heating power should exceed a critical value to attain an ITB.
Puchmayr et al
We demonstrate for the first time that symmetry-breaking in tokamak plasmas reduces the window of stable edge operational space, leading to a lower achievable edge pressure gradient. Predictive simulations with the linear magnetohydrodynamic stability code CASTOR3D show a reduction of the critical pressure gradient by up to 30%, in agreement with experimental observations. The analysis has been extended to experimental plasmas considering, for the first time, ion diamagnetic drift effects in realistic non-axisymmetric (3D) tokamak geometry. The 3D geometry in plasmas with edge localised modes (ELMs) increases the growth rate of edge instabilities compared to the axisymmetric case. Further reducing the edge pressure gradient eliminates the instabilities corresponding to an experiment with suppressed ELMs, reproducing the empirically observed threshold for ELM suppression. Our findings highlight the importance of predictions of the ELM occurrence in full 3D geometry for future tokamak devices with intentionally and unintentionally broken axisymmetry.
Vallhagen et al
This study systematically explores the parameter space of disruption mitigation through shattered pellet injection in ITER with a focus on runaway electron dynamics, using the disruption modelling tool DREAM. The physics fidelity is considerably increased compared to previous studies, by e.g., using realistic magnetic geometry, resistive wall configuration, thermal quench onset criteria, as well as including additional effects, such as ion transport and enhanced runaway electron transport during the thermal quench. The work aims to provide a fairly comprehensive coverage of experimentally feasible scenarios, considering plasmas representative of both non-activated and high-performance DT operation, different thermal quench onset criteria and transport levels, a wide range of hydrogen and neon quantities injected in one or two stages, and pellets with various characteristic shard sizes. Using a staggered injection scheme, with a pure hydrogen injection preceding a mixed hydrogen-neon injection, we find injection parameters leading to acceptable runaway electron currents in all investigated discharges without activated runaway sources. Dividing the injection into two stages is found to significantly enhance the assimilation and minimize runaway electron generation due to the hot-tail mechanism. However, while a staggered injection outperforms a single stage injection also in cases with radioactive runaway electron sources, no cases with acceptable runaway electron currents are found for a DT-plasma with a 15 MA plasma current.
Li et al
A BOUT ++ three-field MHD model is employed to study the triggering and evolution of ELM by Li pellet injected along the outer mid-plane in the EAST configuration. The linear simulation shows that compared with a big deposition on the pedestal top (scenario I), a smaller deposition within the steep-gradient pedestal region (scenario II) can stimulate much larger linear growth rates of all-n peeling-ballooning modes (PBMs). The nonlinear simulation shows that there exists a pellet size threshold for ELM triggering for two deposition locations; the threshold for scenario I predicted in the present work matches EAST observation well. In comparison of the two scenarios, a smaller deposition is sufficient to trigger an ELM in a much shorter time in scenario II, whose ELM size is comparable to that in scenario I. The conclusion confirms the previous DIII-D and ASDEX-Upgrade observations, suggesting that the steep-gradient pedestal region be a favorable deposition location for ELM triggering with minimum pellet size. Simulation analyses also find that the positive radial gradient of the hump-like pressure profile in the outer mid-plane induced by the pellet deposition plays a different role in the two scenarios: in scenario I, the force resulting from the gradient hinders the outflow of core plasmas and in return, the perturbation is suppressed from spreading inward after ELM crashes; in scenario II, with a sizable deposition, the gradient results in another competitive perturbation growth region during the linear phase, thus dispersing the free energy and reducing the efficiency of destabilizing PBMs by pellet injection. The suppressing effect of saturated zonal flow on other modes, the short ELM fast crash phase, and the restricting transport effect of the positive radial pressure gradient work together to constrain the pedestal energy loss, especially when the pellet deposition amount is high.
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T. Lyytinen et al 2024 Nucl. Fusion 64 076042
This contribution presents neutron transport studies for the 5-period helical-axis advanced stellarator stellarator using the Serpent2 code. These studies utilize a parametric geometry model, enabling scans in neutronics modeling by varying the thickness of the reactor layers. For example, the tritium breeding ratio (TBR) can be determined by exploring various blanket material options and thicknesses to identify the threshold configuration that meets the TBR design criterion of 1.15. We found out that with the helium-cooled pebble ped candidate option, the TBR criterion is met with a breeding zone thickness of 26 cm, while with the dual-coolant lithium lead the threshold is exceeded at a thickness of 46 cm. Furthermore, the geometry includes non-planar field coils, allowing to study the fast neutron flux in these superconducting coils with a technological limit of . It is shown that the neutron fast flux is not constant at the coils, necessitating a neutron transport simulation to determine the distribution of the fast-flux at the coils. We show that the peak fast flux can be more than a factor of 2 higher than the average flux, and that the peak flux location rotates helically.
Vijay Shankar et al 2024 Nucl. Fusion 64 076041
We present an improved model for the study of edge biasing in a tokamak plasma that incorporates electron and ion mobility contributions. The non-ambipolar nature of the drifts due to the electron/ion mobility terms influences the space charge separation due to edge biasing and affects plasma dynamics in the edge and SOL regions in a significant manner. In contrast to earlier studies, the present model enables simulation studies at higher biasing voltages. The inclusion of mobility enhances/decreases the effect of negative/positive biasing. The radial profiles of plasma density, electron temperature, radial electric field, and its shear for positive as well as negative biasing are investigated as a function of mobility.
P. Arena et al 2024 Nucl. Fusion 64 076043
In the framework of the activities coordinated by the EUROfusion consortium, the Water thermal-HYDRAulic (W-HYDRA) experimental platform is being built at the ENEA Brasimone Research Centre in order to support the development of the Water-Cooled Lead Lithium (WCLL) Breeding Blanket (BB). In particular, this infrastructure will make possible the installation and testing of prototypical mock-ups under relevant working conditions, such as the First Wall (FW), the manifold and the Steam Generator (SG). Moreover, it will represent an integral test facility for the investigation of phenomena characteristic of WCLL BB concept, such as the PbLi/water interaction. Finally, the collection of data coming from the different planned experimental campaigns will allow to qualify and validate numerical models and codes currently adopted for the design of components, as well as for the modelling of complex phenomena typical of the WCLL BB. In order to come to a definitive design of the different facilities constituting the experimental platform, several design analyses assessing the thermal, hydraulic and structural performances of the different facilities and components are necessary. The paper reports a highlight of the W-HYDRA platform with a general description of the facilities. Some of the most relevant design studies carried out so far are reported as well, highlighting their impact on the evolution of the design.
Allen H. Boozer 2024 Nucl. Fusion 64 074004
A stellarator design is described with the purpose of achieving three goals: (1) enhance the confinement time of tritium. (2) Have a sufficient density of high-Z impurities to radiate the thermal power escaping from the core while having an extremely low impurity density in the core. (3) Maintain a large fraction of the plasma in a burning plasma state with an optimal tritium fraction. Some features of this design could be used in tokamaks. Although having three confinement zones is natural for stellarators, it is not for tokamaks.
M.T. Beidler et al 2024 Nucl. Fusion 64 076038
Subcritical energetic electrons (SEEs) produced by the runaway electron (RE) avalanche source at energies below the runaway threshold are found to be the primary contributor to surface heating of plasma-facing components (PFCs) during final loss events. This finding is supported by theoretical analysis, computational modeling with the Kinetic Orbit Runaway electrons Code (KORC), and qualitative agreement with DIII-D experimental observations. The avalanche source generates significantly more secondary electrons below the runaway threshold, which thermalize rapidly when well-confined. However, during a final loss event, the RE beam impacts the first wall, and SEEs are deconfined before they can thermalize. Additionally, because the energy deposition length decreases faster than energy, the deposited energy density, and thus the maximum PFC surface temperature change, is larger for SEEs than REs. KORC simulations employ an analytic first wall to model particle deconfinement onto a non-axisymmetric wall composed of individual tiles. PFC surface heating is calculated using a 1D model extended to include an energy-dependent deposition length scale. Simulations of DIII-D qualitatively agree with infrared (IR) imaging only when SEEs from the avalanche source are included. These results demonstrate that SEEs are the dominant contributor to PFC surface heating and indicate that the avalanche source plays a critical role in the PFC damage caused during final loss events. The prominence of SEEs also has important implications for interpreting IR imaging, one of the primary diagnostics for RE-wall interaction diagnosis, despite REs dominating the energy and current density. This result improves predictions of wall damage due to post-disruption REs to estimate material lifetime and design RE mitigation systems for ITER and future reactors.
Andrej Žohar et al 2024 Nucl. Fusion 64 076040
To computationally support hydrogen and helium plasma discharges in the early stages of tokamak operation and to support the commissioning of the neutron detectors during these operational phases, creation of a realistic neutron and gamma ray particle source for Monte Carlo simulations will be needed. One of the most important parts of creating the particle source is calculating the reaction rates of the particle-emitting reactions to determine the emission profile in the plasma and the energy spectra of the emitted particles. In this paper the analysis and evaluation of cross sections for important neutron-emitting reactions, namely, 9Be(p,nγ)9B, 9Be(3He,nγ)11C, and charged-particle emission reactions 9Be(p,d)2α and 9Be(p,α)6Li that cause neutron emission in the next step of interactions are presented. The reaction cross sections were evaluated based on experimental measurements and empirical models describing the interaction of two charged particles. Evaluation of the associated uncertainties was also performed. The main goal of the work is to propose the newly evaluated cross sections for inclusion in the FENDL nuclear data library, thus making the cross section available to other researchers studying the above listed reactions.
C. Marini et al 2024 Nucl. Fusion 64 076039
Current profile reconstructions are obtained for high current ( kA) post-disruption runaway electron (RE) plateau plasmas in DIII-D. Two novel methods of measuring the RE current profile in high-current RE plateaus are introduced and compared: localization of the q = 2 rational surface using visible synchrotron emission (SE) imaging and the measurement of the polarization angle of line-integrated Ar-II line emission. The two methods are found to be consistent with each other within the data uncertainties. Different simulations of the RE current profile are compared with the measurements: the toroidal fluid RE model is found to best fit the data, within the measurement uncertainties. In addition to introducing two novel methods to measure the RE current profile and validating present simulation capabilities, this work demonstrates that instabilities can grow at q = 2 and q = 1 surfaces without necessarily causing a RE final loss instability. Numerical simulations are also presented to elucidate the role of these instabilities on synchrotron emission.
A.C.C. Sips et al 2024 Nucl. Fusion 64 076037
Experiments in DIII-D document the ITER Baseline Scenario (IBS) at q95 ∼ 3 and PIN/PLH ∼ 1–2, in both deuterium and hydrogen utilizing Kr and Xe as Tungsten-equivalent radiators. The power threshold for H-mode operation (PLH) was determined experimentally without added impurities and found to be about a factor of two higher than the scaling law. In recent IBS experiments in deuterium, intrinsic levels of metals such as Tungsten (W) or molybdenum and inconel are present that reduce the pedestal pressure by 20%–25%. A complete radiative collapse of deuterium IBS plasmas occurs at W core concentrations CW = 10−5. Simulations show that for core temperatures expected for ITER, the plasmas would not have a radiative collapse at CW = 1 × 10−5, moreover Q = 8–10 would still be achieved for CW up to 3 × 10−5. In contrast to deuterium, the IBS in hydrogen is not affected by intrinsic high-Z impurities, indicating that hydrogen H-modes in ITER may not inform the D-T phase with respect to W accumulation and discharge survival. Compared to deuterium, the pedestal pressure in hydrogen is ∼25% lower, with much higher ELM frequency of 150 Hz, decreasing with input power. Krypton was injected in a matrix scan of input power and impurity flow in IBS hydrogen discharges. Krypton impurity density profiles in hydrogen are similar to deuterium plasmas, but at Kr flows that are 2–3 times higher for the same input power. Krypton is transported into the core and affects the whole radius; at the highest injection rates a radiative collapse occurs at core radiation fractions of 0.3–0.35, consistent with the expected maximum W radiation fraction for ITER core plasmas. Comparing the results with previous International Tokamak Physics Activity database studies of the IBS confirms that at higher radiation fraction due to high-Z impurities, a drop in H98 of >10% is observed. On the other hand, the results using Kr as a W-equivalent radiator indicate that metal (W) devices at lower core temperatures than ITER may provide overly pessimistic performance extrapolations to ITER for deuterium-tritium operation. The new DIII-D results support a more attractive option for the ITER Research Plan with a short hydrogen phase for system commissioning, transitioning to deuterium operations as soon as possible to provide relevant conditions for deuterium-tritium operations.
Jae-Sun Park et al 2024 Nucl. Fusion 64 076036
This paper presents the application of full time-dependent SOLPS-ITER simulations for actuator design in the SPARC tokamak. This study employs both the EIRENE module, a neutral solver, and the B2.5 plasma module in a time-dependent mode. This is in contrast to most SOLPS simulations, which focus on steady-state solutions, where the neutral distribution is evolved without any time limit or for a time step of 1 second, which is several orders of magnitude larger than the fluid plasma time step. The time-dependent EIRENE was tested with a fixed B2.5 background and compared with a simple conductance based model in a simplified pump chamber geometry. This comparison aimed to verify the reliability of the neutral relaxation timescale derived from the time-dependent EIRENE. Subsequently, a full time-dependent simulation was performed in a realistic geometry, with the Monte-Carlo neutral time step synchronized with the plasma fluid time step. The numerical setup of the code, including relative time steps and the size of the census data used to store Monte-Carlo particle information is considered. The full-time dependent simulations are then applied to inform the design of the SPARC louver structure, which affects divertor plasma parameters by regulating the neutral conductance from the divertor to the pump. The response of the plasma and neutral parameters was captured on a timescale that enables the design of the actuator to consider time-dependent control capability. It was found that changing the louver opacity has an equivalent effect as varying the gas throughput via puff actuation. Therefore, equivalent divertor plasma conditions can be obtained from both actuators, while the neutral pressure distribution in the pump and divertor differs for each actuator.
Linjin Zheng et al 2024 Nucl. Fusion
It was found previously that the negative triangularity (NT) configuration is more MHD-unstable for low n modes than the positive triangularity (PT) case, although the situation is reversed for intermediate n modes and the NT configuration becomes more stable for intermediate n modes (n = 3 − 10) [Nucl. Fusion 61 116014 (2021)]. In this work, we extend the studies to include the rotation effects, as well as the diamagnetic drift effects, to see how the resistive wall modes in the NT configuration are affected as compared with the PT configuration. This is particularly motivated by noting that the wall interface with the plasma is quite different between the NT
and PT configurations. It affects the plasma rotation and diamagnetic drift effects on the low n resistive wall modes (RWMs). We consider the DIII-D-NT-experiment equilibrium reconstructed by the EFIT code. Based on the equilibrium g-file, the extended equilibria are constructed with the VMEC code by varying the beta values while keeping the pressure and poloidal current flux profiles basically unchanged. The bootstrap current contribution to the equilibria is taken into account with the Sauter formula. The MHD stability is then computed using the AEGIS code with the rotation and diamagnetic drift effects taken into account. We found that, although the negative triangularity configuration is less stable for n = 1 MHD modes, the rotation and diamagnetic drift stabilization effects on RWMs are more effective in the negative triangularity configuration than in the positive triangularity one. Note that even in the PT case, the stabilization of RWMs by the rotation and kinetic effects is critical. Because the low-n RWMs in the regular NT case are more unstable, the rotation and diamagnetic drift stabilization effects found in this research are important for the NT tokamak concept.