Plasma Physics and Controlled Fusion

The first stellarator design was a simple tube of plasma twisted and closed on itself in the form of a figure-8. The line of such devices, however, was quickly ended over concerns related to plasma stability. We revisit the figure-8 concept, re-imagined as a modern optimized stellarator, and find the potential for a high degree of stability, as well as exceptionally simple construction. In particular, the design that we find admits planar coils, and is the first quasi-isodynamic stellarator design to have this property. Our work is made possible by recent theoretical progress in the near-axis theory of quasi-isodynamic stellarators, combined with fundamental progress in the numerical solution of three-dimensional magnetohydrodynamic equilibria that cannot be well represented using traditional cylindrical coordinates.

Micro-cones so far mainly used for high energy density physics research have been proven to have an effective control on the fast electrons in the context of fast ignition research. In this paper we demonstrate by performing three-dimensional particle-in-cell simulations that an ultra-high intensity laser pulse can be intensified 28 times at the interaction with plastic micro-cones. The extreme intensities of the focused laser which are reached at the interaction with the plastic micro-cones are important in the plasma and nuclear physics investigations of dark matter, non-linear quantum electrodynamics, and fission–fusion experiments to study the N = 126 waiting point for better understanding of the Universe. Furthermore, we observe that micro-cones can shorten ultra-high intensity laser pulses both in time and space. The highest intensification of the incident laser pulse varies in time but not in position being localized very close to the rear side of the micro-cone tip. Therefore, the micro-cone can be a useful device in relativistic plasma optics.

Being three-dimensional, stellarators have the advantage that plasma currents are not essential for creating rotational-transform; however, the external current-carrying coils in stellarators can have strong geometrical shaping, which can complicate the construction. Reducing the inter-coil electromagnetic forces acting on strongly shaped 3D coils and the stress on the support structure while preserving the favorable properties of the magnetic field is a design challenge. In this work, we recognize that the inter-coil forces are the gradient of the vacuum magnetic energy. We introduce an objective functional built on the usual quadratic flux on a prescribed target surface together with a weighed penalty on the vacuum energy. The Euler–Lagrange equation for stationary states is derived, and numerical illustrations are computed using a modern stellarator optimization framework. A study of the effect of the energy functional on the inter-coil forces is conducted and the energy is shown to be a promising quantity in producing coils with low forces.

Turbulent full-f simulations in a linear plasma device are presented. Extending the work of Frei et al (2024 Phys. Plasmas 31 012301), the simulations are based on a drift-kinetic (DK) model that includes corrections associated with higher-order drifts and finite Larmor radius (FLR) effects, while avoiding the Boussinesq approximation. To solve the DK equation, the ion distribution function is expanded on a Hermite-Laguerre basis and the expansion coefficients, denoted as the gyro-moments (GMs), are evolved. Convergence is demonstrated with a small number of GMs and the ion distribution function is shown to be, approximately, a bi-Maxwellian distribution. The simulations reveal significantly reduced cross-field transport with respect to standard DK simulations. Turbulent structures are observed, predominantly elongated in the parallel direction, and largely unaffected by the number of GMs. Linear investigations of the unstable turbulent modes reveal the presence of a long-wavelength Kelvin–Helmholtz mode and a short-wavelength mode driven unstable by finite FLR corrections. The role of these modes in the nonlinear simulations is discussed.

Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.

During its 40 years of operations, the Joint European Torus (JET) tokamak has consistently pushed the physics and engineering boundaries of fusion research, providing the scientific community with a unique testing ground for theories and innovative ideas. This paper covers a selection of remarkable contributions of JET to various fields of tokamak science, from transport and plasma heating studies to plasma-wall interaction and D-T experiments, and their impact on the fusion research progress.

High-Z plasma facing components redeposit within the sheath through a combination of two distinct mechanisms: prompt (or geometric-driven) and local (or sheath-driven) redeposition. Experimental efforts are needed to determine the leading-order parameters influencing prompt-vs-local trade-off, which sets the fraction of material entering the scrape-off layer. In preparation for such experiments, leading-order parameters are isolated within the PYEAD-RustBCA-GITR coupled net erosion code using Sobol' sensitivity analysis. Then, experiments resolving prompt-vs-local trade-off under variation of these leading-order parameters are proposed using an isotopic coupon design with multifaceted diagnostic coverage. The measurability of these experiments is evaluated using synthetic diagnostics.

This article reviews applications of Bayesian inference and machine learning (ML) in nuclear fusion research. Current and next-generation nuclear fusion experiments require analysis and modelling efforts that integrate different models consistently and exploit information found across heterogeneous data sources in an efficient manner. Model-based Bayesian inference provides a framework well suited for the interpretation of observed data given physics and probabilistic assumptions, also for very complex systems, thanks to its rigorous and straightforward treatment of uncertainties and modelling hypothesis. On the other hand, ML, in particular neural networks and deep learning models, are based on black-box statistical models and allow the handling of large volumes of data and computation very efficiently. For this reason, approaches which make use of ML and Bayesian inference separately and also in conjunction are of particular interest for today's experiments and are the main topic of this review. This article also presents an approach where physics-based Bayesian inference and black-box ML play along, mitigating each other's drawbacks: the former is made more efficient, the latter more interpretable.

Resilient divertor features connected to open chaotic edge structures in the Helically Symmetric eXperiment are investigated. For the first time, an expanded vessel wall was considered that would give space for implementation of a physical divertor target structure. The analysis was done for four different magnetic configurations with very different chaotic plasma edges. A resilient plasma wall interaction pattern was identified across all configurations. This manifests as qualitatively very similar footprint behavior across the different plasma equilibria. Overall, the resilient field lines of interest with high connection length L_C lie within a helical band along the wall for all configurations. This resiliency can be used to identify the best location of a divertor. The details of the magnetic footprint's resilient helical band is subject to specific field line structures which are linked to the penetration depth of field lines into the plasma and directly influence the heat and particle flux patterns. The differences arising from these details are characterized by introducing a new metric, the minimum radial connection min$(\delta_N)$ of a field line from the last closed flux surface. The relationship, namely the deviation from a scaling law, between min$(\delta_N)$ and L_C of the field lines in the plasma edge field line behavior suggests that the field lines are associated with structures such as resonant islands, cantori, and turnstiles. This helps determine the relevant magnetic flux channels based on the radial location of these chaotic edge structures and the divertor target footprint. These details will need to be taken into account for resilient divertor design.

Generation of zonal flows (ZF) by drift wave turbulence in numerical simulations based on the modified Hasegawa–Wakatani model is investigated using probability density functions (PDFs) and information rate which quantifies the number of statistically distinct states generated per unit time in the non-equilibrium system. The evolution of time-dependent PDFs of the electrostatic potential, density, and vorticity is quantified by the information rate and is directly compared. We examine this evolution for the system dominated by the isotropic turbulence as well as the system dominated by anisotropic ZF. Impact of ZF on turbulence is captured by a narrower PDF of fluctuating velocity perpendicular to ZF. The information rates of the turbulent potential and density, which are coupled via fast electron parallel transport, are similar confirming the strong coupling between these quantities during their evolution. In contrast, zonal parts of these fields exhibit a distinct information rate evolution. This suggests that the zonal density structure may develop independently of ZF, consistent with recent finding in gyrokinetic simulations.

An adequate modelling of the electromagnetic (EM) interaction of the plasma with the surrounding conductors is paramount for the correct reproduction of 3D plasma dynamics. Simulations of the latter provide in turn useful predictions regarding the plasma evolution, the related MHD modes leading to disruptions and the EM forces acting on the vacuum vessel's components when said disruptions occur. The latest modelling efforts with the 3D FEM non-linear JOREK code have been directed towards the eddy current coupling of a reduced magnetohydrodynamic (MHD) plasma model with thin and volumetric wall codes (STARWALL and CARIDDI). In this contribution, we present an eddy current coupling between the full MHD model of JOREK and the STARWALL code; this new coupling scheme describes the full three-dimensional interactions of the plasma with the vacuum region and external conductors, modeled by natural boundary conditions linking the magnetic vector potential A to the magnetic field B. The consistency of the new coupling scheme is validated via benchmarks for axisymmetric Vertical Displacement Events and multi-harmonics simulations of MHD modes.

A primary objective of the experimental advanced super-conducting tokamak (EAST) is to demonstrate steady-state long-pulse high-performance plasma operation for future large-scale devices like ITER and CFETR (Wan et al 2017 Nucl. Fusion57 102019). The formation of internal transport barriers (ITBs) is one of the key issues to achieve high-performance plasma operation. Optimizing the current density profile is a promising way to improve plasma confinement, which is beneficial to the formation of ITBs. A lot of effort has been dedicated to optimizing the current density profile at EAST over recent years. In this paper, the authors discuss the formation of ITBs leading to a significant improvement of plasma confinement by optimizing the injection time of electron cyclotron resonance heating (ECRH) power at EAST. After ECRH delayed injection, poloidal beta and thermal energy confinement (${H_{98y2}}$) was observed to increase. The current density distribution and the power deposition distribution were changed. The analysis of the soft x-ray (Xu et al 2020 Phys. Scr.95 055603) and electron cyclotron emission (Liu et al 2016 Plasma Sci. Technol.18 1148–54) diagnostics data showed that the structural strength of magnetohydrodynamics was significantly decreased in the core region in this case. The turbulence growth rate calculated by the tokamak global linearized fusion code (Kinsey et al 2008 Phys. Plasmas15 055908) also shows that trapped electron mode turbulence is stabilized.

Lead–lithium flows are key features in the design of tokamak breeding blanket concepts such as the dual-coolant lead–lithium (DCLL). Since they flow under magnetic fields, they are affected by magnetohydrodynamic (MHD) effects. The neutron flux originating in the tokamak plasma heats the breeding blanket channels in a non-uniform manner, inducing buoyancy forces in the liquid metal. Buoyancy may become a source of quasi-two-dimensional (Q2D) turbulence, and the appearance of eddies may affect the transport of heat and tritium across the blanket. Blankets characterized by high-speed liquid metal flows (such as DCLL) will need ceramic insulating walls to reduce the MHD-related pressure drop in the channels. In our simulations, we have used the Q2D model proposed by Sommeria and Moreau (SM82) which is especially suitable for modeling electrically insulating channel flows. On top of that, we have modelled buoyancy forces in the momentum equation using the Oberbeck–Boussinesq approximation. In this work, we include a validation of the implemented Q2D model in buoyancy-driven cases and identify a thermohydraulic configuration that promotes the generation of eddies and the accumulation of tritium. We also show the results provided by our post-processing tool based on the bi-dimensional fast Fourier transform for eddy detection and characterization. We complete our investigation by performing an initial assessment of how eddies can accumulate tritium in the breeding blanket. We conclude by discussing the relevance of preventing accumulation of tritium within the blanket and suggest a possible solution.

Simulating plasma turbulence presents significant computational challenges due to the complex interplay of multi-scale dynamics. In this work, we investigate the use of convolutional neural networks to improve the efficiency of plasma turbulence simulations, focusing on the Hasegawa–Wakatani model. The networks are trained to learn the closure terms in large eddy simulations, providing a computationally cheaper alternative to the high-resolution numerical solvers for capturing the effects of high-frequency components. This study is the first to successfully apply machine learning to predict plasma behavior for adiabatic coefficients beyond the training range for the Hasegawa–Wakatani equations. We generate ground truth simulations for three values of the adiabatic coefficient ($C\in\{0.2, 1.0, 5.0\}$), and train our models on one, or two. The evaluation is then performed on the remaining values. The models generalize well and accurately predict the particle flux up to a factor 5 outside the training range. Finally, we address a key challenge in machine-learning-accelerated plasma simulations—initialization—by starting simulations for previously unseen adiabatic coefficients C with states from existing simulations at other known C values. This approach removes the need for expensive direct numerical simulations for initialization while maintaining physical accuracy and a fast convergence rate. Overall, the results highlight the model's strong generalization capabilities and its potential for accelerating plasma turbulence simulations with more complex sets of parameters.

The primary purpose of the ITER Radial Neutron Camera (RNC) is the real-time control of plasma burn. It requires neutron emissivity profile reconstruction with an accuracy better than 10% and a time resolution of 10 ms. Algorithms based on the Tikhonov Regularization, Minimum Fisher Information, Maximum Entropy and Maximum Likelihood methods were compared for the 1D deconvolution of the neutron emissivity profile from RNC measurements. The reconstruction performance was evaluated using the baseline RNC architecture and two ITER DT 15 MA scenarios of inductive operation. The reconstruction was carried out assuming constant neutron emissivity on the magnetic flux surfaces: in this case, the neutron profile can be represented as a normalized poloidal magnetic flux function. The number of the used flux surfaces was about twice the number of lines of sight in the RNC. All methods (except Maximum Entropy) achieved a reconstruction accuracy better than 10%. The two Tikhonov Regularization algorithms provide in general a good reconstruction, with the second-order derivative regularization matrix giving a better accuracy than 10% in a wider range of the normalized poloidal magnetic flux (Ψ) but a higher standard deviation than the first-order derivative regularization matrix. At the same time, the Minimum Fisher Information proved to be the most stable method. The performance of these two best methods was validated with actual experimental data using the JET neutron camera measurements collected in the second deuterium-tritium campaign.

During its 40 years of operations, the Joint European Torus (JET) tokamak has consistently pushed the physics and engineering boundaries of fusion research, providing the scientific community with a unique testing ground for theories and innovative ideas. This paper covers a selection of remarkable contributions of JET to various fields of tokamak science, from transport and plasma heating studies to plasma-wall interaction and D-T experiments, and their impact on the fusion research progress.

Turbulence, a fascinating and intricate phenomenon, has captivated scientists over different domains, mainly for its complex cross-scale nature spanning a wide range of temporal and spatial scales. Despite significant advances in theories and observations in the last decades, some aspects of turbulence still remain unsolved, motivating new efforts to understand its underlying physical mechanisms and refine mathematical theories along with numerical models. This topical review explores recent findings from the Parker Solar Probe mission, providing a distinctive opportunity to characterize solar wind features at varying heliocentric distances. Analyzing the radial evolution of magnetic and velocity field fluctuations across the inertial range, a transition has been evidenced from local to global self-similarity as proximity to the Sun increases. This behavior has been reconciled with magnetohydrodynamic theory revising an old concept by emphasizing the evolving nature of the coupling between fields. This offers inspiration for novel modeling approaches to understand open challenges in interplanetary plasma physics as the heating and acceleration of the solar wind, as well as, its evolution within the inner Heliosphere.

This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling–ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.

This article reviews applications of Bayesian inference and machine learning (ML) in nuclear fusion research. Current and next-generation nuclear fusion experiments require analysis and modelling efforts that integrate different models consistently and exploit information found across heterogeneous data sources in an efficient manner. Model-based Bayesian inference provides a framework well suited for the interpretation of observed data given physics and probabilistic assumptions, also for very complex systems, thanks to its rigorous and straightforward treatment of uncertainties and modelling hypothesis. On the other hand, ML, in particular neural networks and deep learning models, are based on black-box statistical models and allow the handling of large volumes of data and computation very efficiently. For this reason, approaches which make use of ML and Bayesian inference separately and also in conjunction are of particular interest for today's experiments and are the main topic of this review. This article also presents an approach where physics-based Bayesian inference and black-box ML play along, mitigating each other's drawbacks: the former is made more efficient, the latter more interpretable.

Nonlinear phenomena and turbulence are central to our understanding and modeling of the dynamics of fluids and plasmas, and yet they still resist analytical resolution in many instances. However, progress has been made recently, displaying a richness of phenomena, which was somewhat unexpected a few years back, such as double constant-flux cascades of the same invariant for both large and small scales, or the presence of non-Gaussian wings in large-scale fields, for fluids and plasmas. Here, I will concentrate on the direct measurement of the magnitude of dissipation and the evaluation of intermittency in a turbulent plasma using exact laws stemming from invariance principles and involving cross-correlation tensors with both the velocity and the magnetic fields. I will illustrate these points through scaling laws, together with data analysis from existing experiments, observations and numerical simulations. Finally, I will also briefly explore the possible implications for the validity and use of several modeling strategies.

In tokamak plasmas, a nonlinear interplay between transport and sources/sinks takes place for all transported quantities (current, heat, particle and momentum). Thanks to integrated modelling frameworks, we can iterate physics based quasilinear turbulent transport models over multiple confinement times. Such modelling allows predicting current, temperature, density and rotation profiles and disentangle the causality at play behind the modeled time evolution.
An intense validation effort of such modelling against experimental measurements has been on-going and has progressed our understanding. In dynamical phases, the so called 'cold pulse' physics has been explained in the AUG tokamak, the isotope impact in plasma current ramp up understood in the JET tokamak, the impact of the particle source (from neutral beam injection) on tungsten core accumulation clarified in JET and AUG. In stationary phases, the saturation of the ion temperature in electron heated WEST plasmas has been understood, the energy content has been predicted with higher accuracy than empirical scaling laws with respect to plasma current, magnetic field, plasma size and gas fueling; both in L and H modes on AUG.
Validation of physics based integrated modelling allows control optimisation in preparation of ITER operation as well as risk reduction for future reactors design. However, despite the reported progresses, physics gaps remain on this path. For example, unlike today's devices, ITER-class devices will be opaque to neutrals and fueled by pellets. In absence of physics understanding of the transport in the pedestal, extrapolation is uncertain. Moreover, in burning plasmas, the non-linear coupling between the central core profiles and the fusion power is very strong. The uncertainties on profile predictions due to unverified and unvalidated reduced transport models in such high pressure plasmas lead to uncertain fusion power predictions. Routes on how to address these challenges within integrated modelling will be proposed.

Neoclassical Tearing Modes (NTMs) have been identified as the most deleterious perturbations in high-performance plasmas at Mega-Amp Spherical Tokamak Upgrade (MAST-U). They produce magnetic islands that flatten the electron temperature profile and enhance the fast-ion transport. Understanding the NTM-induced losses can reveal paths to mitigate them, thus increasing the energy available to heat up the plasma. The MAST-U fast-ion loss detector (FILD) is equipped with a high-resolution camera and a high-speed camera that simultaneously measure the fast-ion losses in MAST-U. The combination of both systems makes it possible to infer the velocity-space of the losses fluctuating at the frequency of the NTMs. The FILDSIM code is used to infer the velocity space of the fast-ion losses from the strike position in a scintillator plate. Eulerian video magnification (EVM) is employed to identify the losses that oscillate at the frequencies of the NTMs. NTMs produce fast-ion losses across a broad range of velocity space, with pitch angles ranging from 35° to 54°. Non-linear interactions between the fast-ion orbits and different magnetic islands have been observed. The lost fast-ion orbits meet the stringent conditions that makes it possible to measure these effects.

During the operation of a fusion device, plasma instability can trigger various electromagnetic interferences and thermal radiation, potentially leading to a quench. A quench protection system is crucial to ensure stable plasma confinement and the safe operation of the entire device. Given the extreme requirements for vacuum circuit breaker(VCB) in fusion applications—such as interrupting super-large currents and withstanding harsh electromagnetic and thermal environments—traditional operating mechanism designs may not be directly applicable. To meet the rapidity and reliability demands of the operating mechanism, this paper conducts a kinematic and dynamic analysis of the VCB. By integrating the characteristics of large-capacity vacuum interrupters and electromagnetic repulsion mechanisms, the optimal transmission ratio of the indirect-acting VCB is derived. Through comparisons of initial acceleration, it is validated that indirect-acting operating mechanisms are more suitable for fusion device VCBs. Dynamic tests were performed on the developed prototype. The experimental results show that the operating mechanism designed with the optimal transmission ratio achieves the required opening time for fusion devices. Meanwhile, the high consistency of mechanical actions during repeated operations demonstrates stable and reliable breaking performance. This work provides a theoretical foundation and technical reference for the design of high-current DC VCBs in extreme environments.

A novel approach for efficient representation of three-dimensional (3D) tokamak equilibria is investigated, where a set of helical current filaments occupying the plasma region are employed to resolve deviations from the two-dimensional (2D) axi-symmetric state. A discrete set of 3D filaments, located at rational surfaces for a given toroidal mode number $n$ and following the 2D equilibrium field lines (thus forming closed current loops), are found to provide a surrogate model of 3D equilibria with reasonable accuracy. Specifically, application of the filament model to 3D perturbed equilibria, due to the resonant magnetic perturbation (RMP) in DIII-D and MAST-U discharges, reveals that (1) a single helical filament per rational surface is sufficient; (2) 21 such helical filaments are capable of representing the $n=2$ 3D response field in MAST-U with less than 10\% relative error as compared to that computed by a full magnetohydrodynamic (MHD) code; (3) optimizing currents (both amplitude and phase) flowing in 3D filaments with fixed geometry, the highest accuracy fitting is found to depend on the characteristics of the 3D equilibria such as the coil current phasing of the RMP coils in our case studies. This filament approach is also applicable for generating surrogate models of other type of 3D tokamak equilibria, including those during the initial phase of the plasma disruption.

The phenomena of island healing and configuration transition induced by high-power electron cyclotron resonance heating (ECRH) have been investigated in the island divertor configuration on the J-TEXT tokamak. Experimental results reveal that the size of the edge open magnetic island with mode number m/n = 3/1 decreases substantially under specific ECRH conditions. This process, referred to as island healing, occurs when ECRH with a power of 500~600 kW is deposited in the plasma core or when 250 kW of ECRH is deposited at r_EC = 0.5 a, where a is the minor radius. The reduction of the island width makes the island divertor ineffective and transition into the limiter configuration. A model incorporating the influence of ECRH on the scrape-off layer (SOL) thermoelectric current is proposed to explain the observed changes in the edge magnetic topology of the island divertor configuration. These findings suggest that ECRH should be deposited at the plasma core with carefully controlled power to ensure the stable and compatible operation of ECRH and the island divertor configuration in tokamaks. The results can provide insights into achieving robust operation of an island divertor in tokamaks.

An adequate modelling of the electromagnetic (EM) interaction of the plasma with the surrounding conductors is paramount for the correct reproduction of 3D plasma dynamics. Simulations of the latter provide in turn useful predictions regarding the plasma evolution, the related MHD modes leading to disruptions and the EM forces acting on the vacuum vessel's components when said disruptions occur. The latest modelling efforts with the 3D FEM non-linear JOREK code have been directed towards the eddy current coupling of a reduced magnetohydrodynamic (MHD) plasma model with thin and volumetric wall codes (STARWALL and CARIDDI). In this contribution, we present an eddy current coupling between the full MHD model of JOREK and the STARWALL code; this new coupling scheme describes the full three-dimensional interactions of the plasma with the vacuum region and external conductors, modeled by natural boundary conditions linking the magnetic vector potential A to the magnetic field B. The consistency of the new coupling scheme is validated via benchmarks for axisymmetric Vertical Displacement Events and multi-harmonics simulations of MHD modes.

Neoclassical Tearing Modes (NTMs) have been identified as the most deleterious perturbations in high-performance plasmas at Mega-Amp Spherical Tokamak Upgrade (MAST-U). They produce magnetic islands that flatten the electron temperature profile and enhance the fast-ion transport. Understanding the NTM-induced losses can reveal paths to mitigate them, thus increasing the energy available to heat up the plasma. The MAST-U fast-ion loss detector (FILD) is equipped with a high-resolution camera and a high-speed camera that simultaneously measure the fast-ion losses in MAST-U. The combination of both systems makes it possible to infer the velocity-space of the losses fluctuating at the frequency of the NTMs. The FILDSIM code is used to infer the velocity space of the fast-ion losses from the strike position in a scintillator plate. Eulerian video magnification (EVM) is employed to identify the losses that oscillate at the frequencies of the NTMs. NTMs produce fast-ion losses across a broad range of velocity space, with pitch angles ranging from 35° to 54°. Non-linear interactions between the fast-ion orbits and different magnetic islands have been observed. The lost fast-ion orbits meet the stringent conditions that makes it possible to measure these effects.

During the operation of a fusion device, plasma instability can trigger various electromagnetic interferences and thermal radiation, potentially leading to a quench. A quench protection system is crucial to ensure stable plasma confinement and the safe operation of the entire device. Given the extreme requirements for vacuum circuit breaker(VCB) in fusion applications—such as interrupting super-large currents and withstanding harsh electromagnetic and thermal environments—traditional operating mechanism designs may not be directly applicable. To meet the rapidity and reliability demands of the operating mechanism, this paper conducts a kinematic and dynamic analysis of the VCB. By integrating the characteristics of large-capacity vacuum interrupters and electromagnetic repulsion mechanisms, the optimal transmission ratio of the indirect-acting VCB is derived. Through comparisons of initial acceleration, it is validated that indirect-acting operating mechanisms are more suitable for fusion device VCBs. Dynamic tests were performed on the developed prototype. The experimental results show that the operating mechanism designed with the optimal transmission ratio achieves the required opening time for fusion devices. Meanwhile, the high consistency of mechanical actions during repeated operations demonstrates stable and reliable breaking performance. This work provides a theoretical foundation and technical reference for the design of high-current DC VCBs in extreme environments.

Plasma-impurity reaction rates are a crucial part of modelling tokamak scrape-off layer (SOL) plasmas. To avoid calculating the full set of rates for the large number of important processes involved, a set of effective rates are typically derived which assume Maxwellian electrons. However, non-local parallel electron transport may result in non-Maxwellian electrons, particularly close to divertor targets. Here, the validity of using Maxwellian-averaged rates in this context is investigated by computing the full set of rate equations for a fixed plasma background from kinetic and fluid SOL simulations. We consider the effect of the electron distribution as well as the impact of the electron transport model on plasma profiles. Results are presented for lithium, beryllium, carbon, nitrogen, neon and argon. It is found that electron distributions with enhanced high-energy tails can result in significant modifications to the ionisation balance and radiative power loss rates from excitation, on the order of 50-75% for the latter. Fluid electron models with Spitzer-Härm or flux-limited Spitzer-Härm thermal conductivity, combined with Maxwellian electrons for rate calculations, can increase or decrease this error, depending on the impurity species and plasma conditions. Based on these results, we also discuss some approaches to experimentally observing non-local electron transport in SOL plasmas.

Lead–lithium flows are key features in the design of tokamak breeding blanket concepts such as the dual-coolant lead–lithium (DCLL). Since they flow under magnetic fields, they are affected by magnetohydrodynamic (MHD) effects. The neutron flux originating in the tokamak plasma heats the breeding blanket channels in a non-uniform manner, inducing buoyancy forces in the liquid metal. Buoyancy may become a source of quasi-two-dimensional (Q2D) turbulence, and the appearance of eddies may affect the transport of heat and tritium across the blanket. Blankets characterized by high-speed liquid metal flows (such as DCLL) will need ceramic insulating walls to reduce the MHD-related pressure drop in the channels. In our simulations, we have used the Q2D model proposed by Sommeria and Moreau (SM82) which is especially suitable for modeling electrically insulating channel flows. On top of that, we have modelled buoyancy forces in the momentum equation using the Oberbeck–Boussinesq approximation. In this work, we include a validation of the implemented Q2D model in buoyancy-driven cases and identify a thermohydraulic configuration that promotes the generation of eddies and the accumulation of tritium. We also show the results provided by our post-processing tool based on the bi-dimensional fast Fourier transform for eddy detection and characterization. We complete our investigation by performing an initial assessment of how eddies can accumulate tritium in the breeding blanket. We conclude by discussing the relevance of preventing accumulation of tritium within the blanket and suggest a possible solution.

Energetic ions (EIs) are responsible for driving most meso-scale Alfvenic instabilities, and can also couple with micro-scale turbulence and macro-scale MHD modes driven by bulk plasmas. In this work, we demonstrate the extension of gyrokinetic EI capability for MAS code (Bao et al 2023 Nucl. Fusion 63 076021) that treats bulk plasma instabilities of different temporal-spatial scales and polarizations on the same footing by 5-field Landau-fluid model, which then form a comprehensive Landau fluid-gyrokinetic hy- brid model for analyzing the linear interactions between EIs and unstable/damped bulk plasma modes with a non-perturbative manner in general geometry. An efficient numerical scheme is proposed for evaluating EI moments in MAS formulation that greatly decreases computational cost, which numerically integrates the EI distribution function in phase space with adopting well-circulating and deeply-trapped approximations for passing and trapped particle species respectively, so that the effects of finite Larmor radius (FLR) and finite orbit width (FOW) can be accurately retained for arbitrary wavelength electromagnetic fluctuations together with dominant wave-particle resonances. In the long wavelength limit, the EI moments in MAS formulation can recover early theory on the response functions. These EI upgrades in MAS code has been verified by simulating EI-excited reversed shear Alfven eigenmode (RSAE) based on a well-benchmarked DIII-D equilibrium case, which exhibits good agreements with other codes on the mode structure and dis- persion relation, and the FOW stabilization on RSAE is found to be important in the regime of k⊥ρd ≥ 1 (where ρd is the magnetic drift orbit size).

Ion cyclotron resonance heating (ICRH) has the potential of providing efficient ion heating of reactor grade fusion plasmas especially during the start-up phase. In order to assess such heating scenarios, ICRH modelling is required. However, the physics is complex and certain elements are not universally taken into account in ICRH modelling. In this paper we discuss the importance of including Doppler shift displacements of resonance points away from the cold resonance (i.e. where $\omega = n \Omega_{c}$) in Fokker-Planck calculations of the distribution function of resonating ions. In particular, the effective wave-particle interaction time and the wave electric field varies with the local Doppler shifted resonance positions. The importance of accounting for these variations in Fokker-Planck modelling is investigated. Furthermore , it is shown how they can be included in a simplified Fokker-Planck treatment that is sufficiently quick to be included in integrated modelling frameworks of fusion plasmas. 
Because 2D effects in velocity space play a crucial role in determining Doppler shifts, we employ a model of the anisotropy of the non-thermal distribution function. 
Simulation results show that taking the Doppler effects into account in Fokker-Planck modelling can have a significant impact on the distribution functions of fast ions and important quantities, such as the collisional power transfer to the background plasma. 
This is especially important in cases where the poloidal variation of the left-hand component of the wave electric field is strong.

Simulating plasma turbulence presents significant computational challenges due to the complex interplay of multi-scale dynamics. In this work, we investigate the use of convolutional neural networks to improve the efficiency of plasma turbulence simulations, focusing on the Hasegawa–Wakatani model. The networks are trained to learn the closure terms in large eddy simulations, providing a computationally cheaper alternative to the high-resolution numerical solvers for capturing the effects of high-frequency components. This study is the first to successfully apply machine learning to predict plasma behavior for adiabatic coefficients beyond the training range for the Hasegawa–Wakatani equations. We generate ground truth simulations for three values of the adiabatic coefficient ($C\in\{0.2, 1.0, 5.0\}$), and train our models on one, or two. The evaluation is then performed on the remaining values. The models generalize well and accurately predict the particle flux up to a factor 5 outside the training range. Finally, we address a key challenge in machine-learning-accelerated plasma simulations—initialization—by starting simulations for previously unseen adiabatic coefficients C with states from existing simulations at other known C values. This approach removes the need for expensive direct numerical simulations for initialization while maintaining physical accuracy and a fast convergence rate. Overall, the results highlight the model's strong generalization capabilities and its potential for accelerating plasma turbulence simulations with more complex sets of parameters.

The primary purpose of the ITER Radial Neutron Camera (RNC) is the real-time control of plasma burn. It requires neutron emissivity profile reconstruction with an accuracy better than 10% and a time resolution of 10 ms. Algorithms based on the Tikhonov Regularization, Minimum Fisher Information, Maximum Entropy and Maximum Likelihood methods were compared for the 1D deconvolution of the neutron emissivity profile from RNC measurements. The reconstruction performance was evaluated using the baseline RNC architecture and two ITER DT 15 MA scenarios of inductive operation. The reconstruction was carried out assuming constant neutron emissivity on the magnetic flux surfaces: in this case, the neutron profile can be represented as a normalized poloidal magnetic flux function. The number of the used flux surfaces was about twice the number of lines of sight in the RNC. All methods (except Maximum Entropy) achieved a reconstruction accuracy better than 10%. The two Tikhonov Regularization algorithms provide in general a good reconstruction, with the second-order derivative regularization matrix giving a better accuracy than 10% in a wider range of the normalized poloidal magnetic flux (Ψ) but a higher standard deviation than the first-order derivative regularization matrix. At the same time, the Minimum Fisher Information proved to be the most stable method. The performance of these two best methods was validated with actual experimental data using the JET neutron camera measurements collected in the second deuterium-tritium campaign.

Tearing modes are a signifcant challenge for the operation of large tokamak devices as they cause confinement degradation, can lead to a disruption and are part of the disruption process itself. Detecting and characterising tearing modes is basis for both, improved understanding of their evolution as well as adequate countermeasures. 

The most harmful tearing mode has the toroidal mode number n = 1, which, due to toroidal coupling, usually consists of different helicities, referred to as poloidal harmonics. Determining the poloidal harmonics requires modelling the magnetic measurements with different challenges for rotating and locked modes. Rotating modes produce frequency-dependent shielding currents in conducting structures that modify the perturbation field. Locked modes require pick-up coils measuring mainly the radial perturbation field Br, of which there are far fewer than Mirnov coils in ASDEX Upgrade. The agreement between Br coils and Mirnov coils in a model description can be validated in the low frequency range, where all coils observe the modes and shielding currents are important.

We employ a three-dimensional FEM model to calculate the expected magnetic measurements of the perturbation field produced by an n = 1 tearing mode with a single helicity and frequency. The TMs are represented by helical perturbation currents at the corresponding resonant surfaces while the rest of the plasma is treated as vacuum. We show that, besides the vacuum vessel and the Passive Stabilisation Loop, it is crucial to include other in-vessel components of ASDEX Upgrade. The poloidal composition of an n = 1 TM is determined by the linear superposition of modelled TMs with single helicities that best matches the measurements by a poloidal array of Mirnov coils. The resulting amplitudes and phases of the poloidal harmonics give simulated measurements that are found to be in agreement with their measured values for all coil types.