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A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element basis, called current potential patches. Current potential patches leverage the relationship between distributions of magnetic dipoles and current potentials to explore limits of the access properties of stellarator coil sets. An example calculation is shown using the Helically Symmetric Experiment (HSX) equilibrium, demonstrating the method's use in coil design and understanding the limits of the access properties of coil sets. Current potential patches have additional desirable properties such as of promoting sparse current sheet solutions and identifying crucial locations of shaping current placement. A result is found for the HSX equilibrium that shaping currents covering only 22% of the winding surface are sufficient to produce the equilibrium to a good accuracy, provided a toroidal field is generated by an exterior coil set. [ABSTRACT FROM AUTHOR]

This paper presents a first implementation of gradient, divergence, and particle tracing schemes for the EMC3 code, a stochastic 3D plasma fluid code widely employed for edge plasma and impurity transport modeling in tokamaks and stellarators. These schemes are essential to accommodate plasma drift computations, which are currently absent in the code. Plasma drifts have been recognized to significantly influence transport of particles and energy, and their inclusion in future code upgrades will substantially enhance the code's predictive capabilities. For gradient and divergence calculations, we introduce a second‐order least‐squares gradient scheme. We confirm the second‐order convergence properties and assess the accuracy of several analytical test cases in the presence of synthetic noise. In the second part of this paper, we employ the validated gradient scheme in a fourth‐order Runge–Kutta particle tracing scheme to trace a particle through a generic drift velocity field. The impact of synthetic noise on the scheme's performance is investigated by evaluating various error metrics. We find that the implemented schemes function as intended and exhibit sufficient accuracy to enable drift computations. [ABSTRACT FROM AUTHOR]

A review of recent advances in simulations of turbulent filaments with relevance to stellarators is presented. Progress in performing global edge turbulence simulations is discussed as well as results from seeded filament simulations with applications to the unique environment of a stellarator island divertor-including abrupt changes in connection length and highly-nonuniform curvature drive. It is determined that the motion of filaments generally follows the average curvature, but strong nonuniform perturbations can shear a filament and reduce the overall transport. The coherence of filament transport is also determined to be influenced by the collisionality and electron plasma beta. By simplifying the simulation geometries, large parameter scans can be performed which accurately reflect the macroscopic transport of filaments observed in Wendelstein 7-X. Comparisons to experiments are discussed, and a the develeopment of a synthetic diagnostic has been able to inform experimental measurements by quantifying potential sources of error in filament propagation measurements. A discussion of the necessary extension to more complex multifluid models, and the scope for near-term filament simulations in stellarators, is provided. [ABSTRACT FROM AUTHOR]

We investigate the core confinement properties of two recently devised quasi-helically symmetric stellarator configurations, HSK and QSTK. Both have been optimized for large critical gradients of the ion temperature gradient mode, which is an important driver of turbulent transport in magnetic confinement fusion devices. To predict the resulting core plasma profiles, assuming a fixed edge temperature, we utilize an advanced theoretical framework based on the gyrokinetic codes GENE and GENE-3D, coupled to the transport code TANGO. Compared to the HSX stellarator, both HSK and QSTK achieve significantly higher core-to-edge temperature ratios, partly thanks to their smaller aspect ratios, with the other part due to more detailed shaping of the magnetic geometry achieved during optimization. The computed core confinement time, however, is less sensitive to core temperature than the fixed edge temperature, simply due to the disproportionate influence, the edge has on stored plasma energy. We, therefore, emphasize the possible benefits of further optimizing turbulence in the outer core region, and the need to include accurate modeling of confinement in the edge region in order to assess overall plasma performance of turbulence optimized stellarators. [ABSTRACT FROM AUTHOR]

Stellarator plasmas are externally controlled to a degree unparalleled by any other fusion concept, magnetic or inertial. This control is largely through the magnetic fields produced by external coils. The development of fusion energy could be expedited by carrying out remarkably straight-forward computations to define strategies for exploiting this external control. In addition to these computations, which have a reliability limited only by competence, certain physics areas that affect the development of stellarator power plants should have a more intense study. The low cost and speed with which computations can be carried out relative to experiments have implications for the development of fusion. Computations should be used to develop a strategy that to the extent possible allows major issues to be circumvented. Required computations for this strategy are the subject of this paper. [ABSTRACT FROM AUTHOR]

Many stellarator coil design problems are plagued by multiple minima, where the locally optimal coil sets can sometimes vary substantially in performance. As a result, solving a coil design problem a single time with a local optimization algorithm is usually insufficient and better optima likely do exist. To address this problem, we propose a global optimization algorithm for the design of stellarator coils and outline how to apply box constraints to the physical positions of the coils. The algorithm has a global exploration phase that searches for interesting regions of design space and is followed by three local optimization algorithms that search in these interesting regions (a 'global-to-local' approach). The first local algorithm (phase I), following the globalization phase, is based on near-axis expansions and finds stellarator coils that optimize for quasisymmetry in the neighbourhood of a magnetic axis. The second local algorithm (phase II) takes these coil sets and optimizes them for nested flux surfaces and quasisymmetry on a toroidal volume. The final local algorithm (phase III) polishes these configurations for an accurate approximation of quasisymmetry. Using our global algorithm, we study the trade-off between coil length, aspect ratio, rotational transform and quality of quasi-axisymmetry. The database of stellarators, which comprises approximately 200 000 coil sets, is available online and is called QUASR, for 'quasi-symmetric stellarator repository'. [ABSTRACT FROM AUTHOR]

This paper extends a 1D dynamic physics-based model of the scrape-off layer (SOL) plasma, DIV1D, to include the core SOL and possibly a second target. The extended model is benchmarked on 1D mapped SOLPS-ITER simulations to find input settings for DIV1D that allow it to describe SOL plasmas from upstream to target—calibrating it on a scenario and device basis. The benchmark shows a quantitative match between DIV1D and 1D mapped SOLPS-ITER profiles for the heat flux, electron temperature, and electron density within roughly 50% on: (1) the Tokamak Configuration Variable (TCV) for a gas puff scan; (2) a single SOLPS-ITER simulation of the Upgraded Mega Ampere Spherical Tokamak; and (3) the Upgraded Axially Symmetric Divertor EXperiment in Garching Tokamak (AUG) for a simultaneous scan in heating power and gas puff. Once calibrated, DIV1D self-consistently describes dependencies of the SOL solution on core fluxes and external neutral gas densities for a density scan on TCV whereas a varying SOL width is used in DIV1D for AUG to match a simultaneous change in power and density. The ability to calibrate DIV1D on a scenario and device basis is enabled by accounting for cross field transport with an effective flux expansion factor and by allowing neutrals to be exchanged between SOL and adjacent domains. [ABSTRACT FROM AUTHOR]

The influence of collisions on the growth rate of trapped-electron modes (TEMs) in core plasmas is assessed through both analytical linear gyrokinetics and linear gyrokinetic simulations. Both methods are applied to the magnetic geometry of the DIII-D tokamak, as well as the Helically Symmetric eXperiment (HSX) and Wendelstein 7-X (W7-X) stellarators, in the absence of temperature gradients. Here we analytically investigate the influence of collisions on the TEM eigenmode frequency by a perturbative approach in the response of trapped particles to the mode, using an energy-dependent Krook operator to model collisions. Although the resulting growth rates exceed perturbative thresholds, they reveal important qualitative dependencies: a geometry-dependent stabilization rate occurs for all wavenumbers at high collisionality, while at low collisionality, a geometry-sensitive mixture of collisionless, resonantly driven, and collisionally destabilized modes is found. Additionally, linear gyrokinetic simulations have been performed with a rigorous pitch-angle scattering operator for the same geometries. In the case of DIII-D and large wavenumber modes in HSX, the trends predicted by analytical theory are reproduced. Dissimilarities are, however, obtained in W7-X geometry and for low wavenumber modes in HSX, which are shown to be due to a collision-induced transition to the Universal Instability as the dominant instability at marginal collisionality. [ABSTRACT FROM AUTHOR]

Using a novel optimization procedure, it has been shown that the Helically Symmetric eXperiment stellarator can be optimized for reduced trapped-electron-mode (TEM) instability [Gerard et al., Nucl. Fusion 63, (2023) 056004]. Presently, with a set of 563 experimental candidate configurations, gyrokinetic simulations are performed to investigate the efficacy of available energy E A , quasi-helical symmetry, and flux-surface shaping parameters as metrics for TEM stabilization. It is found that lower values of E A correlate with reduced growth rates, but only when separate flux-surface shaping regimes are considered. Moreover, configurations with improved quasi-helical symmetry demonstrate a similar reduction in growth rates and less scatter compared to E A . Regarding flux-surface shaping, a set of helical shaping parameters is introduced that show increased elongation is strongly correlated with reduced TEM growth rates, however, only when the quasi-helical symmetry is preserved. Using a newly derived velocity-space-averaged TEM resonance operator, these trends are analyzed to provide insights into the physical mechanism of the observed stabilization. For elongation, stabilization is attributed to geometric effects that reduce the destabilizing particle drifts across the magnetic field. Regarding quasi-helical symmetry, the TEM resonance in the maximally resonant trapping well is shown to increase as the quasi-helical symmetry is broken, and breaking quasi-helical symmetry increases the prevalence of highly resonant trapping wells. While these results demonstrate the limitations of using any single metric as a linear TEM proxy, it is shown that quasi-helical symmetry and plasma elongation are highly effective metrics for reducing TEM growth rates in helical equilibria. [ABSTRACT FROM AUTHOR]

The design, development, and successful implementation of pop-up Langmuir probes installed in the water-cooled divertor of W7-X are described. The probes are controlled by drive coils (actuators) installed behind the divertor plates. These drive coils make use of the magnetic field in W7-X to move the probe tips into and out of the plasma. The drive coils were installed in the vacuum vessel after extensively testing the durability of the coils and analyzing the criteria for safe operation. The probe design is carefully tailored for each of the 36 probe tips in order to be suitable for the different magnetic field configurations used in W7-X and ensure that the probes do not present leading edges to the magnetic flux tubes. An electronic bridge circuit is used for measurement to compensate for the effects of signal propagation time on the long cable lengths used. The diagnostic is integrated with the segment control of W7-X for automated operation and control of the diagnostic. The evaluation of the results from the plasma operation is presented after accounting for appropriate sheath expansion for negative bias voltage on the probes. [ABSTRACT FROM AUTHOR]

Some stellarators tend to benefit from favourable average magnetic curvature for trapped particles when the plasma pressure is sufficiently high. This so-called maximum- $J$ property has several positive implications, such as good fast-particle confinement, magnetohydrodynamic stability and suppression of certain trapped-particle instabilities. This property cannot be attained in quasisymmetric stellarators, in which deeply trapped particles experience average bad curvature and therefore precess in the diamagnetic direction close to the magnetic axis. However, quasi-isodynamic stellarators offer greater flexibility and allow the average curvature to be favourable and the precession to be reversed. We find that it is possible to design such stellarators so that the maximum- $J$ condition is satisfied for the great majority of all particles, even when the plasma pressure vanishes. The qualitative properties of such a stellarator field can be derived analytically by examining the most deeply and the most shallowly trapped particles, although some small fraction of the latter will inevitably not behave as desired. However, through numerical optimisation, we construct a vacuum field in which 99.6 % of all trapped particles satisfy the maximum- $J$ condition. [ABSTRACT FROM AUTHOR]

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles. [ABSTRACT FROM AUTHOR]

The gyrokinetic theory of the residual flow, in the electrostatic limit, is revisited, with optimized stellarators in mind. We consider general initial conditions for the problem, and identify cases that lead to a non-zonal residual electrostatic potential, i.e. one having a significant component that varies within a flux surface. We investigate the behaviour of the 'intermediate residual' in stellarators, a measure of the flow that remains after geodesic acoustic modes have damped away, but before the action of the slower damping that is caused by unconfined particle orbits. The case of a quasi-isodynamic stellarator is identified as having a particularly large such residual, owing to the small orbit width achieved by optimization. [ABSTRACT FROM AUTHOR]

This document is a correction notice for a paper titled "Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators" by E. Rodriguez. The erratum addresses typographical errors in the equations of the paper, specifically in Figure 5 and Table 1. The errors have been rectified, and supplementary computational and numerical materials are provided for thoroughness and precision. The corrections do not impact the conclusions and discussions presented in the original work. The paper discusses the dependence of the Mercier criterion on lower-order near-axis quantities and the Shafranov shift, and it also provides the correct expression for the geometry at the stellarator symmetric point. [Extracted from the article]

Recently, stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor was observed numerically. This validated the theoretical predictions that (i) the stochastic diffusion represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators and (ii) it is possible to prevent the escape of particles to the wall by closing the separatrix between the locally trapped and passing states. It was concluded that, in principle, the separatrix could be made closed, resulting in a reduction of fast ion losses, by compensating for the effect of the helical component of the magnetic field $(1, 1)$ with an enhanced 'anti-helical' harmonic $(1, -1)$ ; the enlargement of this harmonic was proposed previously for other reasons. This possibility is explored in this work. Equations of previous relevant works were generalised to include the $(1, -1)$ harmonic. Calculations were carried out for several magnitudes of the ratio of anti-helical to helical magnetic field harmonics. Positive effects were found already at the smallest anti-helical harmonic considered: when the latter ratio is 0.25, transitioning particles with the smallest and intermediate pitch parameters are confined and, moreover, their fraction decreased. When the ratio is 0.85, almost all transitioning particles are confined and their fraction is minimal; well-confined localised orbits dominate at the smallest pitch parameters. [ABSTRACT FROM AUTHOR]

Combined high-fusion performance and long-pulse operation is one of the key integration challenges for fusion energy development in magnetic devices. Addressing these challenges requires an integrated vision of physics and engineering aspects with the purpose of simultaneously increasing time duration and fusion performance. Significant progress has been made in tokamaks and stellarators, including very recent achievement in duration and/or performance. This progress is reviewed by analyzing the experimental data (109 plasma pulses with a total of 3200 data points, i.e. on average 29 data per pulse) provided by ten tokamaks (in alphabetical order: Axially Symmetric Divertor Experiment Upgrade, DIII-D, Experimental Advanced Superconducting Tokamak, Joint European Torus, JT-60 Upgrade, Korea Superconducting Tokamak Advanced Research, tokamak à configuration variable, Tokamak Fusion Test Reactor, Tore Supra, W Environment in Steady-State Tokamak) and two stellarators (Large Helical Device and Wendelstein 7-X) expanding the pioneering work of Kikuchi (Kikuchi M. and Azumi M. 2015 Frontiers in Fusion Research II: Introduction to Modern Tokamak Physics (Springer)). Data have been gathered up to January 2022 and coordination has been provided by the recently created International Energy Agency-International Atomic Energy Agency international C oordination on I nternational C hallenges on L ong duration OP eration group. By exploiting the multi-machine international database, recent progress in terms of injected energies (e.g. 1730 MJ in L-mode, 425 MJ in H-mode), durations (1056 s in L-mode, 101 s in H-mode), injected powers, and sustained performance will be reviewed. Progress has been made to sustain long-pulse operation in tokamaks and stellarators with superconducting coils, actively cooled components, and/or with metallic walls. The graph of the fusion triple products as a function of duration shows a dramatic reduction of, at least two orders of magnitude when increasing the plasma duration from less than 1 s to 100 s. Indeed, long-pulse operation is usually reached in dominant electron-heating modes at reduced density (current drive optimization) but with low ion temperatures ranging from 1 to 3 keV for discharges above 100 s. Difficulties in extending the duration may arise from coupling high heating powers over long durations and the evolving plasma-wall interaction towards an unstable operational domain. Possible causes limiting the duration and critical issues to be addressed prior to ITER operation and DEMO design are reported and analyzed. [ABSTRACT FROM AUTHOR]

We present a new analytical model for the expansion of a thin slab of plasma into vacuum. By considering the rising plasma scale length during the initial heating phase, we were able to give the plasma a smooth quadratic behavior at the origin while describing its exponentially falling density at a large distance. We show this functional form to be a solution to the plasma equations and validate its predictions against numerical simulations and experimental measurements. We demonstrate the applicability of the model to experimental scenarios in which solid foils are turned into tens of micrometer-scale plasmas, to serve as targets for direct laser acceleration of electrons. [ABSTRACT FROM AUTHOR]

The effect of considerable broadening of the power deposition profile in on-axis X2 electron cyclotron resonance heating experiments observed in the L-2M stellarator is interpreted in the paper as one of the consequences of the low-threshold parametric decay instability of the pump wave, resulting in excitation of ion and electron Bernstein daughter waves. The instability is considered under the specific L-2M experimental conditions and shown to be absolute. The threshold of this instability is exceeded in the experiment. This finally allows explaining, at least qualitatively, the effect of nonlocal microwave power deposition detected in L-2M. [ABSTRACT FROM AUTHOR]

Measurements are taken using a helicon plasma device to analyze the spatial distribution of plasma properties as the throat of the magnetic nozzle is axially shifted with respect to the antenna center. Krypton plasma is generated in the sub-kilowatt range and probed using a suite of diagnostics including a rf-compensated Langmuir probe, a planar probe, and laser-induced fluorescence. It is found that larger ion currents and increased plasma confinement are achieved when the throat of the magnetic nozzle is located downstream the antenna center, at a distance that equals or exceeds two times the antenna length. The ions, although being accelerated, retain subsonic velocities even beyond the magnetic throat. [ABSTRACT FROM AUTHOR]

The benefits of operating fusion devices, such as tokamaks and stellarators, at high fields make high-temperature superconducting magnets necessary to realize a compact fusion power system. Superconducting stellarators, such as W7-X, have used standard low-temperature superconductor technology niobium-titanium. ARPA-E has recently funded a two-year project led by the startup Type One Energy and involving the Fusion Technology Institute at the University of Wisconsin-Madison, the Plasma Science to design and fabricate the first non-planar high-temperature superconductor (HTS) rare-earth barium copper oxide (REBCO) coil for a high-field stellarator based on the SPARC tokamak's VIPER cable concept. The design consists of a 1.5-turn non-planar REBCO coil supported by a pair of 3D printed stainless steel radial plates. The ultimate goals of the project are to determine if commercial REBCO tapes and additive manufacturing can be used to fabricate high field ( ⩾ 10 T ) non-planar coils with tight bending radii ( ≃ 100 m m ) and with a degradation of the critical current smaller than 20% with respect to the expected performance. In this work we present numerical analysis for non-planar coils (critical current, magnetic field map, Lorentz forces and quench aspects) at the operating conditions of 77 K and 20 K and the fabrication and testing in liquid nitrogen (77 K) of the first two non-planar demonstrators for stellarators based on a VIPER cable. The first demonstrator is a short NO n-planar V IP E R cab L e (cable demonstrator at which we will refer to as NOVEL) equipped with 100 HTS REBCO tapes and with a critical current of 5700 A at 77 K (self-field); the second is a M ult I ple turns (1.5-turns) NO n-pl AN ar coil (coil demonstrator at which we will refer to as MINOAN) equipped with 30 HTS tapes and with a critical current of 2100 A at 77 K (self-field). Both demonstrators were tested at 77 K (liquid nitrogen bath) and the results showed that—even after being bent into non-planar shapes with bend radii ≃ 100 m m —the degradation of the critical current I c was within 15%, meeting the expected goals of the project. [ABSTRACT FROM AUTHOR]

While it is important to design stellarators with high magnetohydrodynamic stability $\beta$ -limit, it is also crucial to ensure that good magnetic surfaces exist in a large range of $\beta$ values. As $\beta$ increases, pressure-driven currents perturb the vacuum magnetic field and often lead to the emergence of magnetic field line chaos, which can worsen the confinement and is the cause of another kind of $\beta$ -limit, the so-called equilibrium $\beta$ -limit. In this paper, we explore numerically the dependence of the equilibrium $\beta$ -limit on the bootstrap current strength in a classical stellarator geometry using the stepped pressure equilibrium code. We develop a diagnostic to determine whether or not magnetic islands are expected to participate significantly to radial transport, and we build an analytical model to predict the expected equilibrium $\beta$ -limit, which recovers the main features of the numerical results. This research opens the possibility to include additional targets in stellarator optimization functions, provides additional understanding on the existence of magnetic surfaces at large $\beta$ , and is a step forward in the understanding of the equilibrium $\beta$ -limit. [ABSTRACT FROM AUTHOR]

This paper documents the design and construction of MUSE, the world's first permanent magnet (PM) stellarator and the first quasi-axisymmetric experiment. The purpose of MUSE is to develop and assess a new way of building optimised stellarators that uses simple planar coils PMs. Our PM optimisation algorithm consists of initialising a geometry to pack dipoles densely, running the FAMUS code to minimise surface field error subject to PM constraints and applying discrete jumps to reach a physically realisable solution. FAMUS treats the PM system as a set of ideal point dipoles. From there we construct finite-volume magnet towers to be housed in 3D-printed PM holders. We describe the design of the PM holders, which were validated by laser metrology. We analyse the effects of finite permeability, sensitivity to perturbations and magnetostatic forces. An exact analytic formula for the magnetic field from a finite-volume PM tower is presented to compute PM–PM forces and stress on the PM holder. Stellarator construction is complete and experiments are underway. [ABSTRACT FROM AUTHOR]

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering and financial criteria. In this study, we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium and the total length of the electromagnetic coils. [ABSTRACT FROM AUTHOR]

We study the microwave absorption during electron cyclotron resonance heating (ECRH) by the extraordinary wave at second harmonic (X2 mode) in the T-10 tokamak and TJ-II stellarator in a wide range of plasma densities, and compare experiments with the classical formulas for the absorption of the injected ECR power. Empirical relations for the absorption efficiency and for the critical plasma density , which separates the regions with full and partial absorption of the injected ECR power, are obtained using the numerical simulation of the heat transport with the transport model of canonical profiles. It is shown that in both devices, the range of densities exists, where the absorption predicted by the classical formulas is almost full, while according with the empirical formula, only a small fraction of the power is absorbed. The obtained relations allow ones to optimize the conditions of ECRH in toroidal systems for magnetic plasma confinement. [ABSTRACT FROM AUTHOR]

In tokamaks and neoclassically optimised stellarators, like Wendelstein 7-X (W7-X) and the Helically Symmetric Experiment, turbulent transport is expected to be the dominant transport mechanism. Among the electrostatic instabilities that drive turbulence, the trapped-electron mode (TEM) has been shown both analytically and in simulations to be absent over large ranges of parameter space in quasi-isodynamic stellarator configurations with the maximum- $J$ property. It has been proposed that the reduction of the linear TEM growth rate in such configurations may lead to the passing-electron-driven universal instability, which is often subdominant to the TEM, becoming the fastest-growing instability over some range of parameter space. Here, we show through gyrokinetic simulations using the Gene code, that the universal instability is dominant in a variety of stellarator geometries over a range of parameter space typically occupied by the TEM, but most consequentially in devices which possess beneficial TEM stability properties like W7-X, which locally satisfies the maximum- $J$ property for deeply trapped particles in the regions of worst curvature. We find that the universal instability exists at long perpendicular wavelengths and, as a result, dominates the potential fluctuation amplitude in nonlinear simulations. In W7-X, universal modes are found to differ in parallel mode structure from trapped-particle modes, which may impact turbulence localisation in experiments. [ABSTRACT FROM AUTHOR]

In this work, two new profiles at the leading-edge tubercles of the tidal turbine have been proposed to predict the hydrodynamic performance and obtain more power production than the original blade with a smooth leading edge. A computational method based on the Reynolds-Averaged Navier-Stokes (RANS) is employed for predicting the hydrodynamic performance of the tidal turbine. The turbulent model of the k − ω S S T (shear stress transport) has been used. A three-bladed tidal turbine with the NREL's S814 foil section is selected. The numerical results of the power coefficient against tip speed ratio (TSR) show a good agreement in comparison with the experimental data. Then, two new profiles of tubercles, namely zigzag (ZZ) and absolute sinus (AS), at the leading-edge with 0.1 chord length height at each section, are proposed. The results of the power and torque coefficients are significantly increased, especially at higher TSRs. [ABSTRACT FROM AUTHOR]

The impurity transport at Wendelstein 7-X during its most recent campaign is characterized and documented for a variety of different plasma scenarios. An overview of its dependence on several quantities is given, which allows identification of transport regimes and the major driver for impurity transport. Beyond this, a comparison with the impurity behavior in other fusion devices is now possible. In contrast to other stellarators, no density dependence of the impurity transport has been found. Additionally, the influence of the turbulence contribution to the overall transport is reflected in the dependence on various parameters, e.g. turbulent diffusion and density fluctuation amplitudes. With this database approach, one can now also apply scaling laws to make extrapolations about the impurity confinement in future plasma scenarios. [ABSTRACT FROM AUTHOR]

We propose a theoretical scheme for the study of the nonlinear interaction of drift-wave-like turbulence and energetic particles in stellarators. The approach is based on gyrokinetics, and features a separation of time and scales, for electromagnetic fluctuations, inspired by linear ballooning theory. Two specific moments of the gyrokinetic equation constitute the main equations of the system, which requires a full kinetic nonlinear solution. This is found iteratively, expanding in the smallness of the bounce-average radial drift frequency, and nonlinear $\boldsymbol {E}\times \boldsymbol {B}$ drift frequency, compared with the inverse time scales of the resonantly interacting energetic particles. Our analysis is therefore valid for neoclassically optimised stellators. The resummation of all iterative and perturbative nonlinear kinetic solutions is discussed in terms of Feynman diagrams. Particular emphasis is put on the role of collisionlessly undamped large-scale structures in phase space, the kinetic equivalent of zonal flows, i.e. phase-space zonal structures, and on wave-like fluctuations generated by energetic particles. [ABSTRACT FROM AUTHOR]

The equilibrium code, VMEC, is used to study external kinks in low β tokamaks and l = 2 stellarators. The applicability of the code when modeling nonlinear MHD effects is explored in an attempt to understand and predict how the initial saturation of the MHD mode depends on the external rotational transform. It is shown that helicity preserving, free boundary VMEC computations do not converge to a single perturbed solution with increasing spectral resolution. Additional constraints are applied to narrow down the numerical resolution parameters appropriate for physical scans. The dependence of the modeled (4, 1) kink mode on the external rotational transform and field periodicity is then studied. While saturated states can be identified which decrease in amplitude with increasing external rotational transform, alternative bifurcated states are found, which contradict this trend. As a result, it was not possible to use VMEC alone to identify the physical dependency of the nonlinear mode amplitude on the magnetic geometry. Nevertheless, the accuracy of VMEC solutions is demonstrated by showing that the expected toroidal mode coupling is captured in the magnetic energy spectrum for stellarator cases. Comparing with the initial value code, JOREK, the predicted redistribution of poloidal magnetic energy from the vacuum to plasma region in VMEC is shown to be physical. This work is a first step toward using VMEC to study MHD modes in stellarator geometry. [ABSTRACT FROM AUTHOR]

The condition of quasi-isodynamicity is derived to second order in the distance from the magnetic axis. We do so using a formulation of omnigenity that explicitly requires the balance between radial particle drifts at opposite bounce points of a magnetic well. This is a physically intuitive alternative to the integrated condition involving distances between bounce points, used in previous works. We investigate the appearance of topological defects in the magnetic field strength (puddles). A hallmark of quasi-isodynamic fields, the curved contour of minimum field strength, is found to be inextricably linked to these defects. Our results pave the way to construct solutions that satisfy omnigenity to a higher degree of precision and also to simultaneously consider other physical properties, like shaping and stability. [ABSTRACT FROM AUTHOR]

The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m − n q = 0 , with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M ≥ 1. The corresponding matrix eigenvalue problem involves a 2 M × 2 M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics. [ABSTRACT FROM AUTHOR]

We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two-stage coil design process, as well as coils from a near-axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. The last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization. [ABSTRACT FROM AUTHOR]

Due to stringent emission regulations, it is of practical significance to understand cycle-to-cycle variations in the combustion of fossil or renewable fuels to reach future emission regulations. The present study aims to conduct a parametric investigation to analyse the influence of the valve lift and different mass flows of an inlet valve of the test engine "Flex-OeCoS" on the flow structures. To gain a deeper understanding of the flow behaviour, an optical test bench for 2D Particle Image Velocimetry (PIV) and a Large Eddy Simulation (LES) are used. Turbulence phenomena are investigated using Proper Orthogonal Decomposition (POD) with a quadruple decomposition and the Reynolds stress transport equation. The results show good agreement between the PIV and LES. Moreover, the main flow structures are primarily affected by valve lift while being unaffected by mass flow variation. The turbulent kinetic energy within the flow field increases quadratically to the mass flow and to the decreasing valve lift, where large high-energetic flow structures are observed in the vicinity of the jet and small low-energetic structures are homogeneously distributed within the flow field. Furthermore, the convective flux, the turbulent diffusive flux, the rate of change, and the production of specific Reynolds stress are the dominant terms within the specific Reynolds stress transport equation. [ABSTRACT FROM AUTHOR]

We describe a magnetic mirror device, namely, the Keda Mirror with AXisymmetricity (KMAX), which aims to study new approaches to confine and stabilize the mirror plasma as well as basic plasma research. KMAX consists of one central cell, two side cells, and two end chambers at two ends of the device. For the central cell, the mirror-to-mirror distance is 5.2 m, while the central cylinder is 2.5 m in length and 1.2 m in diameter. The plasmas are generated by two washer guns located in the end chambers, which subsequently flow into the central cell and merge there. The density in the central cell is usually adjusted by changing the magnetic field strength inside the side cell, and it ranges from 1017 to 1019 m−3, depending on the experimental requirement. Ion cyclotron frequency heating with two 100 kW transmitters is routinely used to heat up the ions. Plasma controls mainly rely on configuring the magnetic geometry and rotating magnetic fields to improve the confinement and suppress instability. Routine diagnostics, such as probes, interferometers, spectrometers, diamagnetic loops, and bolometers, are also reported in this paper. [ABSTRACT FROM AUTHOR]

Since the first H-mode transitions were observed in TJ-II plasmas in 2008, an extensive experimental effort has been done aiming at better physics understanding of confinement transitions. In this article, an overview of the main findings related to the L-H transition in TJ-II is presented including how the radial electric field is driven, what are the possible mechanisms for turbulence suppression and what are the related temporal and spatial scales that can impact the transition. The trigger of the L-H transition in TJII plasmas is found to be more correlated with the development of fluctuating E x B flows than with steady-state Er effects, pointing to the role played by zonal flows in mediating the transition. Experimental evidence supporting the predator–prey relationship between turbulence and flows as the basis for the LH transition, found for the first time in TJ-II, reinforces this conclusion. Besides, the reduction in the turbulent transport at the transition is detected at the barrier region but also in a wider radial range with weak or even zero E x B flow shear, which points to other mechanisms beyond the turbulence suppression by local sheared flows. [ABSTRACT FROM AUTHOR]

Laser peening is a promising surface treatment technique for enhancing the mechanical performance of metals. In laser peening, the plasma confinement layer contributes to the generation of high-pressure shockwaves by suppressing the expansion of laser-induced plasma. Therefore, the choice of a plasma confinement layer is important for improving laser peening effectiveness. For laser peening in environments where liquid materials cannot be used as a plasma confinement layer, alginate gel, which is a pliable material with shape-following capabilities, has been proposed to reduce the acoustic impedance mismatch caused by surface roughness when using solid materials. In this study, the feasibility of alginate gel as a plasma confinement layer and an appropriate process window for laser irradiation were investigated. The results of this study are then presented. [ABSTRACT FROM AUTHOR]

Alpha particle confinement is one of the most demanding issues for stellarators. It now seems clear that it is possible to design optimized stellarators that confine the background plasma at near tokamak radial transport levels. Moreover, adequate collisionless alpha particle confinement is possible in the core of a highly optimized stellarator. Here, the collisional confinement of barely trapped alphas in an optimized stellarator is considered by accounting for the resonance due to the reversal in direction of the drift within a flux surface and investigating the sensitive role of magnetic shear in keeping this resonance close to the passing boundary in some nearly quasisymmetric stellarator configurations. The treatment relies on a narrow collisional boundary layer formulation that combines the responses of both these resonant pitch angle alphas and the remaining barely trapped alphas. A novel merged regime treatment leads to explicit expressions for the energy diffusivity for both superbanana plateau (or resonant plateau) and $\sqrt \nu$ transport in the large aspect ratio limit for a slowing down tail alpha distribution function, where $\nu$ is the effective pitch angle scattering collision frequency of the trapped alphas off the background ions. Depending on the details of the optimization scheme and the sign of the magnetic shear, modest magnetic shear can be used to reduce superbanana (or resonant) plateau transport to below the $\sqrt \nu$ transport level. In addition, a quasilinear equation retaining spatial diffusion is derived for a general alpha distribution function that allows the radial alpha transport to modify the distribution so it is no longer isotropic in velocity space. [ABSTRACT FROM AUTHOR]

We present a technique that can be used to design stellarators with a high degree of experimental flexibility. For our purposes, flexibility is defined by the range of values the rotational transform can take on the magnetic axis of the vacuum field while maintaining satisfactory quasisymmetry. We show that accounting for configuration flexibility during the modular coil design improves flexibility beyond that attained by previous methods. Careful placement of planar control coils and the incorporation of an integrability objective enhance the quasisymmetry and nested flux surface volume of each configuration. We show that it is possible to achieve flexibility, quasisymmetry, and nested flux surface volume to reasonable degrees with a relatively simple coil set through an NCSX-like example. This example coil design is optimized to achieve three rotational transform targets and nested flux surface volumes in each magnetic configuration larger than the NCSX design plasma volume. Our work suggests that there is a tradeoff between flexibility, quasisymmetry, and volume of nested flux surfaces. [ABSTRACT FROM AUTHOR]

In a symmetric plasma confinement device, a perturbation such as an Alfvén mode produces a resonance island which flattens the local energy gradient due to induced rotation about the elliptic points of the resonance. The location of the resonance is mode frequency and particle energy dependent, and particles away from the resonance are not affected. A projection onto the Poincaré subspace allows the evaluation of resonance widths and internal rotation rates. In a stellarator without symmetry because of the toroidal dependence of the equilibrium magnetic field, a mode instead produces chaos in all orbits passing where the amplitude is large and is, thus, much more effective in producing radial transport and loss. The mode growth rate and saturation are also affected by the local chaos. [ABSTRACT FROM AUTHOR]

A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and quasisymmetry, expanded in the small distance from the magnetic axis, as formulated by Garren & Boozer [ Phys. Fluids B, vol. 3, 1991, p. 2805]. Due to the reduction of the equations by the expansion, the computational cost is significantly reduced, to times of the order of 1 cpu second, enabling wide and high-resolution scans over parameter space. In contrast to traditional stellarator optimization, here, the cost function serves to maximize the volume in which the expansion is accurate. A key term in the cost function is $\| \boldsymbol {\nabla }\boldsymbol B \|$ , the norm of the magnetic field gradient, to maximize scale lengths in the field. Using this method, a database of $5\times 10^5$ optimized configurations is calculated and presented. Quasisymmetric configurations are observed to exist in continuous bands, varying in the ratio of the magnetic axis length to average major radius. Several qualitatively new types of configuration are found, including quasi-helically symmetric fields in which the number of field periods is two or more than six. [ABSTRACT FROM AUTHOR]

Power-transfer and fixed-point analysis of previous NIMROD simulations (Roberds et al. , Phys. Plasmas , vol. 23, issue 9, 2016, 092513) improved the understanding of the effect of 3D (non-axisymmetric equilibrium) magnetic fields on sawtooth oscillations in the Compact Toroidal Hybrid (CTH) experiment. Computing the locations of order-1 fixed points, their Greene's residues, and local values for the rotational transform results in a description of CTH sawteeth consistent with Kadomtsev's model. A power-transfer analysis quantifies the distribution of energy among toroidal Fourier modes and their nonlinear interactions. The Lorentz power transfer drives sawtooth growth, and it is unambiguously interpreted as the flow of energy from toroidal mode $n'$ to mode $n$ , catalysed by $\boldsymbol {B}_{n-n'}$. It has been reported previously that the CTH sawtooth frequency increases with the 3D field strength. This is attributed to an increased growth rate of the internal kink that drives sawtooth oscillations. Here, 3D fields remove energy from the kink, eliminating the possibility that these fields are an additional energy source that drives growth. Instead, 3D fields catalyse energy transfer from large-to-small scales, where magnetic reconnection is stronger. It is proposed that this energy transfer increases the reconnection rate at small scales, which is consistent with the increased growth rate observed at higher 3D field strengths. [ABSTRACT FROM AUTHOR]

The optical thickness of plasma is often insufficient to absorb completely electromagnetic waves when heated at the second harmonic of the electron-cyclotron frequency. The analysis of experiments at the T-10 tokamak allowed us to find the criterion of complete absorption and to provide a transport model for complete and incomplete absorption of waves. The conditions for the equivalence of discharges in different tokamaks, as well as in a pair of tokamak–stellarator W7-X are formulated. For equivalent discharges, calculations using the model for the T-15MD tokamak meet the measurements of electron and ion temperatures in the W7-X in a wide range of plasma densities. The confirmed model is used to analyze future T-15MD pulses. [ABSTRACT FROM AUTHOR]

Wendelstein 7-X (W7-X) is currently the largest optimized stellarator in operation in the world. Its main objective is to demonstrate long pulse operation and to investigate the suitability of this type of fusion device for a power plant. Maintaining the safety of the first wall is critical to achieving the desired discharge times of approximately 30 min while keeping a steady-state condition. We present a deep learning-based solution to detect the unexpected plasma-wall and plasma-object interactions, so-called hot-spots, in the images of the Event Detection Intelligent Camera (EDICAM) system. These events can pose a serious threat to the safety of the first wall, therefore, to the operation of the device. We show that sufficiently training a neural network with relatively small amounts of data is possible using our approach of mixing the experimental dataset with new images containing so-called synthetic hot-spots generated by us. Diversifying the dataset with synthetic hot-spots increases performance and can make up for the lack of data. The best performing YOLOv5 Small model processes images in 168 ms on average during inference, making it a good candidate for real-time operation. To our knowledge, we are the first ones to be able to detect events in the visible spectrum in stellarators with high accuracy, using neural networks trained on small amounts of data while achieving near-real-time inference times. [ABSTRACT FROM AUTHOR]

• An External Rotational Transform (ERT) coil has been designed on J-TEXT to explore innovative approaches for optimizing tokamak configurations and combining the advantages of both tokamaks and stellarators. • To cope with the complex vacuum vessel environment, a new coil design approach with a modular rail structure has been put forward. • The ERT coil system has been successfully applied to the experiments in J-TEXT, preliminary experimental results indicate that the ERT coils have achieved the expected goals. To explore innovative approaches for optimizing tokamak configurations and combining the advantages of both tokamaks and stellarators, the J-TEXT tokamak recently underwent an upgrade by installing the External Rotational Transform (ERT) coil system. This system consists of two rings for producing a helical magnetic field. Due to space limitations, the ERT coil system is installed inside the vacuum vessel. The ERT coils feature a modular rail structure designed to navigate the intricate vacuum vessel environment. The successful installation of the ERT coil system on J-TEXT has yielded preliminary experimental results that align with the design objectives. [ABSTRACT FROM AUTHOR]

Stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor is observed numerically for the first time. This validates theory prediction that the collisionless stochastic diffusion of these particles represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators [Beidler et al., Phys. Plasmas 8, 2731 (2001)]. The numerical calculation has also demonstrated a possibility to prevent the escape of particles to the wall by making the separatrix between the locally trapped and passing states closed, as was proposed in Tykhyy et al. [Plasma Phys. Control. Fusion 49, 703 (2007)]. It is found that stochastic regions can vary from very narrow to very wide that occupy almost the whole plasma cross section. It is shown that the fraction of alpha particles with closed separatrix in the population of transition alphas can be considerable. Potentially, this fraction can be increased, and the number of transitioning particles can be reduced by a special optimization of the magnetic configuration, which decreases delayed losses of alphas by means of reducing the separatrix maximum radius. [ABSTRACT FROM AUTHOR]

Particle resonances in stellarators can produce islands in the space of passing particle orbits without the presence of an unstable Alfvén mode, provided the period of the resonance matches the period of the equilibrium magnetic field. In this case, the equilibrium itself plays the role of a mode amplitude, and the islands appear on surfaces where the orbital helicity matches the field period. At low energy, these surfaces are given by the field line helicity, but at higher energy, cross field drift causes them to move. The resonances are also felt by trapped particles bouncing back and forth on surfaces with matching helicity. The periodic variation of B along these orbits produces local wells, giving loss due to drift while trapped in a well. Stellarator designs that have equilibrium-induced resonance islands exhibit anomalous alpha particle loss and are unsuitable for reactors. [ABSTRACT FROM AUTHOR]

A first-of-a-kind optimized stellarator for confining plasma has been designed and is being constructed with planar circular coils and permanent magnets composed of identical elements. The equilibrium is optimized to be quasi-axisymmetric for good particle confinement. The combination of permanent magnets and planar coils is significantly simpler to construct than fabricating three-dimensionally shaped coils, yet they are able to produce lower helical magnetic ripple than existing devices by two orders of magnitude in ϵ eff 3 / 2 , a characteristic neoclassical transport metric. [ABSTRACT FROM AUTHOR]