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The magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long. [ABSTRACT FROM AUTHOR]

In studies of impurity transport in quasi-stationary hot plasma, the initial kinetic equation and the diffusive-convective transport model take into account ionization and recombination as "sources and sinks" of particles. Due to the incompatible representation of the radial dynamics and charge kinetics of impurity charge states, this approach and the results obtained appear to be out of system. The basis for their systematic criticism is the ideas of the theory of random processes proposed by M.A. Leontovich in 1935 as a theoretical alternative to the gas-kinetic equation. In this case, the charge-radial transport of an impurity in a quasi-stationary plasma is defined as a syncretic vector random Markov process of charge state transport. Its coupling (ergodicity) in a two-dimensional Markov system excludes "sources and sinks" from it in principle, and the relaxation convergence is directed to the formation of equilibrium invariant density profiles. The impurity equilibrium and density profiles are specified by a system of invariant functions that provide analysis of any types of density profiles observed in experiments. Modeling of radial profiles of helium, boron and carbon impurities allows us to find variants of their transformation from accumulation in the center to concentration near the plasma edge, transport coefficients and systematic connection with plasma parameters. [ABSTRACT FROM AUTHOR]

The linear and nonlinear effects of hydrogen isotope species on ion temperature gradient (ITG) instability in the Large Helical Device (LHD) stellarator are studied using radially global gyrokinetic simulation. We found that the coupling range of linear toroidal harmonics depends on the ion mass of the hydrogen isotope. The growth rates of ITG mode are almost the same for H, D, and T plasmas, indicating a gyro-Bohm scaling of ion-mass dependence. The nonlinear electrostatic simulations show that the zonal flow breaks the radially elongated eigenmode structures and reduces the size of the turbulence eddies, which suppresses the turbulence and the ion heat transport in the LHD. The turbulence amplitude without the zonal flow is almost the same for H, D, and T plasmas, while it decreases with increasing ion mass of the hydrogen isotope when the zonal flow is present. The reduction of the turbulent transport with larger ion mass is mostly due to the enhancement of zonal flows by larger ion mass. The ion heat conductivity deviates from the gyro-Bohm scaling for both cases with and without the zonal flow. [ABSTRACT FROM AUTHOR]

We study the effect of the rotational transform profile on the L–H confinement transitions in the neutral beam-heated plasmas in the TJ-II stellarator. The rotational transform profile in the vacuum is determined by the external coil currents but is modified by the plasma current, Ip. We find that L–H confinement transitions systematically occur when the configuration and plasma current are such that a low-order rational is placed in the plasma edge region, with a distribution centered around ρ=0.8±0.05. It is suggested that magnetohydrodynamic turbulence plays an important role in triggering the L–H transitions at TJ-II.

[Introduction] Fusion energy has the characteristics of large energy released through reactions, safe and reliable operation, abundant fuel sources, and low environmental pollution. Therefore, it is expected to become a commercial energy source that can be supplied in the market on a large scale, providing stable energy output and power supply in the future. To popularize the development path of magnetic confined fusion energy in China, the article reviews the discovery and realization path of fusion energy. [Method] The article provided an overview of the early research and development process of magnetic confined fusion energy in China by the method of literature review. The paper took the development of magnetic confined fusion energy as an example to provide a preliminary overview of the construction of typical research devices in China, such as tokamak, stellarator, spherical tokamak, reversed field pinch, magnetic mirror field, linear plasma, and dipole magnetic field devices. [Result] Based on the construction and researches of these devices, China has cultivated a group of scientific and technological talents in the field of magnetic confined fusion research, achieving significant progress. In addition, the article provides an overview of international cooperation in fusion energy research, as well as the International Thermonuclear Experimental Reactor (ITER) project that China is participating in construction. [Conclusion] Although the current research on fusion energy still needs to overcome significant challenges from various aspects, such as fusion plasma physics, fusion reactor materials, and tritium self-sustaining technology, it is believed that the magnetic confined fusion energy in China will turn from a blueprint into a reality in the future thanks to the urgent need for energy structure transformation and the strong support for fusion researches in China.

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]

Plasma was heated at the second harmonic of electron cyclotron resonance (ECR) in the L-2M stellarator and the T-10 tokamak. The concept of equivalent tokamak and stellarator discharges was extended to the case of both full and partial absorption of EC power. Comparison of experimental electron temperature profiles with profiles calculated using the canonical profiles transport model allows us to estimate the efficiency of ECR heating in the L-2M discharges without suprathermal electrons, which distort the distribution function, preventing reliable measurements of temperature. The dependence of the ECR heating efficiency on the plasma density was obtained, describing experiments on the L-2M and TJ-II stellarators, and on the T-10 tokamak. The energy characteristics (the stored energy and the confinement time) for L-2M discharges were calculated. Predictions for ECR heating in the T-15MD tokamak are considered. The features of solving the ill-posed transport problem for the L-2M are discussed. [ABSTRACT FROM AUTHOR]

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The three-dimensional variation inherent to stellarator geometries and fusion sources motivates three-dimensional modeling to obtain accurate results from computational modeling in support of design and analysis of first wall, blanket, and shield (FWBS) systems. Manually constructing stellarator fusion power plant geometries in computer-aided design (CAD) and defining the corresponding fusion source can be cumbersome and challenging. The open-source parametric modeling toolset ParaStell has been developed to automate construction of such geometries in low-fidelity. Low-fidelity modeling is useful during the conceptual phase of engineering design as a means of rapidly exploring the design space of a given device. The modeling capability of ParaStell includes in-vessel components and magnets, for any given stellarator configuration, using a parametric definition and plasma equilibrium data. Furthermore, the toolset automates the generation of detailed, tetrahedral neutron source definitions and DAGMC geometries for use in neutronics modeling. ParaStell assists rapid design iteration, parametric study, and design optimization of stellarator fusion cores. As a demonstration of the design iteration capability, the effect of the three-dimensional parameter space on tritium breeding and magnet shielding is investigated, using the WISTELL-D configuration as a design basis. Blanket and shield thicknesses are varied in three dimensions, using the space available between the plasma edge and magnet coils as a constraint. The corresponding effects on tritium breeding ratio and magnet heating are tallied using the open-source Monte Carlo particle transport code OpenMC. The inclusion of additional and higher-fidelity modeling capabilities is planned for ParaStell's future, as well as its implementation in machine-driven optimization. [ABSTRACT FROM AUTHOR]

Electricity generation will need to reach net zero emissions globally in 2050. This will require an increase in share of renewable energy and the implementation of a controllable carbon-free base-load source. Nuclear fusion is a promising option to decarbonize base-load electricity production but its capital cost still doubles the one of technologically more mature alternatives such as large photovoltaic fields or off-shore wind installations. Within this framework, the retrofit of a dismissed power-plant could allow significant cost savings, thus facilitating the realization of a fusion electricity demonstrator. Among fusion reactors, stellarators are a valid alternative to tokamaks thanks to the higher blanket temperature and inherent continuous operation. In this scenario, we posit the challenge to use a nuclear fusion stellarator-based reactor to retrofit conventional power plants (PPs). Specifically, we select a nuclear fission plant in France and a supercritical coal fired site in Italy, by constructing 4 different retrofit scenarios as a function of the re-used components. We compare each option with a greenfield and optimized plant with the same reactor thermal power. through a thermodynamic, economic, and investment analysis.The results proves significant savings by retrofitting an existing plant, with a CapEx reduction up to 50% compared to the greenfield plants. Specifically, the most convenient retrofit strategy is to select a site that already implements cutting edge thermodynamic parameters while reusing the most existing systems (i.e. buildings, steam cycle, electricity generation, and heat rejection). This is the case of the 2 x 660 MWe supercritical coal-fired plant in Italy. Therein, the LCOEs are 39 $/MWh and 51 $/MWh, calculated with an interest rate of 2.7% and 6%, respectively, and compare with the conventional energy technologies. Moreover, such costs are competitive in the current European energy markets and yield significant net present values at the plant end of life.

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.

Modelling of the plasma transport for inherently three-dimensional (3D) problems as in stellarators requires dedicated complex codes. FINDIF is a 3D multifluid plasma edge transport code that has been previously successfully used for the analysis of energy transport in the TEXTOR-DED tokamak [1], where 3D perturbations led to an ergodic structure of field lines in the plasma edge. The ongoing efforts to apply it meaningfully to Wendelstein 7-X (W7-X) plasma problems resulted in advancements in the main model and accompanying tools for mesh generation and post-processing. In order to verify the applicability of the code and to compare with the reported simulation (EMC3-EIRENE) and experimental (OP1.1) results, a series of simulations for varying plasma density, temperature and anomalous transport coefficients as well as for fixed input power were performed. The connection length pattern of FINDIF traced magnetic field lines on the limiter was reproduced and its impact on heat loads was confirmed. An increase in the peak heat load on the limiter with a rise in plasma density, temperature and anomalous plasma transport coefficients was observed. The decay lengths of density, electron temperature and heat flux did not change with density, and were decreasing with temperature and increasing with anomalous plasma transport coefficient, which was compared to the simple scrape-off layer (SOL) model. [ABSTRACT FROM AUTHOR]

Results of experiments carried out with a quasi-stationary L-2M stellarator in the regime of electron cyclotron resonance heating by means of two gyrotrons are presented. The data on increase in the plasma energy lifetime by means of modulation (profiling) of the microwave pulse are obtained. The first gyrotron operating at fixed power was used for ionization and initial heating of plasma, while the second gyrotron initiated a stationary discharge with a duration of 10 ms. It is demonstrated that the lifetime can be increased by varying the second-gyrotron power in the range of 50–200 kW. A fourfold increase in the lifetime was obtained when the second-gyrotron power was reduced to 50 kW. This work is of interest as a method of studying hot plasma confined in the toroidal magnetic system of a stellarator. [ABSTRACT FROM AUTHOR]

The three-dimensional variation inherent to stellarator geometries and fusion sources motivates three-dimensional modeling to obtain accurate results from computational modeling in support of design and analysis of first wall, blanket, and shield (FWBS) systems. Manually constructing stellarator fusion power plant geometries in computer-aided design (CAD) and defining the corresponding fusion source can be cumbersome and challenging. The open-source parametric modeling toolset ParaStell has been developed to automate construction of such geometries in low-fidelity. Low-fidelity modeling is useful during the conceptual phase of engineering design as a means of rapidly exploring the design space of a given device. The modeling capability of ParaStell includes in-vessel components and magnets, for any given stellarator configuration, using a parametric definition and plasma equilibrium data. Furthermore, the toolset automates the generation of detailed, tetrahedral neutron source definitions and DAGMC geometries for use in neutronics modeling. ParaStell assists rapid design iteration, parametric study, and design optimization of stellarator fusion cores. As a demonstration of the design iteration capability, the effect of the three-dimensional parameter space on tritium breeding and magnet shielding is investigated, using the WISTELL-D configuration as a design basis. Blanket and shield thicknesses are varied in three dimensions, using the space available between the plasma edge and magnet coils as a constraint. The corresponding effects on tritium breeding ratio and magnet heating are tallied using the open-source Monte Carlo particle transport code OpenMC. The inclusion of additional and higher-fidelity modeling capabilities is planned for ParaStell’s future, as well as its implementation in machine-driven optimization.

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]

The evolution of fluctuating signals from electrostatic and magnetic probes and reflectometry on the L-2M stellarator is presented. The L-2M facility is a quasi-stationary toroidal magnetic trap in which plasma is generated and heated by high-power pulsed microwave radiation. Pulses with transitions to improved confinement modes accompanied by an increase in energy, increase in plasma density, and restructuring of the peripheral electric field, were analyzed. Spectral analysis of signals is carried out using Fourier analysis and various wavelets. The possible influence of magnetohydrodynamic and kinetic instabilities on the development of transient processes is considered. [ABSTRACT FROM AUTHOR]

Recently an improved confinement regime, characterized by reduced turbulent fluctuations has been observed in the Large Helical Device upon the injection of boron powder into the plasma (Nespoli et al 2022 Nat. Phys. 18 350–56). In this article, we report in more detail the experimental observations of increased plasma temperature and the decrease of turbulent fluctuations across the plasma cross section, on an extended database. In particular, we compare powders of different materials (B, C, BN), finding similar temperature improvement and turbulence response for the three cases. Modeling of the powder penetration into the plasma and of neoclassical electric field and fluxes support the interpretation of the experimental results. Additionally, we report evidence of the temperature improvement increasing with powder injection rates and decreasing for both increasing density and heating power. Though, plasma turbulence response varies depending on the initial conditions of the plasma, making it difficult to draw an inclusive description of the phenomenon. [ABSTRACT FROM AUTHOR]

Alfvén eigenmodes are of great interest in any fusion device as they can be excited by fast ions in the plasma. If the modes grow to large amplitudes, they can cause transport and redistribution of the fast ions, thus limiting fusion performance. To save computational resources, the resonant kinetic interaction between the fast-particle species and the modes is often modeled by MHD-kinetic hybrid codes. Here, we present such a hybrid model which is applicable to three-dimensional magnetic fields, accounts for a finite parallel electric field and multiple MHD modes present at the same time. The model extends the one previously implemented in the CKA-EUTERPE code allowing for a better estimate of the damping due to the parallel electric field and nonlinear mode-mode interaction. The capabilities of our model are illustrated by applying the code to model nonlinear frequency chirping and fast-ion profile flattening.

In the Large Helical Device (LHD) a low temperature mode (LTM) of the helical divertor was discovered. It combines particle detachment and very large sub-divertor pressures up to 1.4 Pa. During the LTM, the electron temperature in the divertor was in the range from 0.25 to 0.42 eV so that volume recombination occurred. This result is remarkable because in the stellarators LHD and Wendelstein 7-X only low sub-divertor pressures (0.03–0.3 Pa) were expected and measured up to now due the loss of pressure conservation along flux tubes by an enhanced cross-field transport. It demonstrates that the more complex, three-dimensional divertors of stellarators can achieve a similar performance with respect to particle exhaust and detachment like the geometrically simpler poloidal divertors in tokamaks even if the favorable effect of flux amplification is absent. The LTM of the helical divertor depends, however, on the magnetic configuration, i.e. on geometry. It was only observed in the inward shifted configuration with $R_\mathrm{ax} = 3.55$ m, but not in the more frequently studied configuration with $R_\mathrm{ax} = 3.6$ m. A nuclear fusion reactor based on the heliotron concept (DEMO) would benefit from the LTM by the very compact divertor configuration and the excellent performance.

After a long device enhancement phase, scientific operation resumed in 2022. The main new device components are the water cooling of all plasma facing components and the new water-cooled high heat flux divertor units. Water cooling allowed for the first long-pulse operation campaign. A maximum discharge length of 8 min was achieved with a total heating energy of 1.3 GJ. Safe divertor operation was demonstrated in attached and detached mode. Stable detachment is readily achieved in some magnetic configurations but requires impurity seeding in configurations with small magnetic pitch angle within the edge islands. Progress was made in the characterization of transport mechanisms across edge magnetic islands: Measurement of the potential distribution and flow pattern reveals that the islands are associated with a strong poloidal drift, which leads to rapid convection of energy and particles from the last closed flux surface into the scrape-off layer. Using the upgraded plasma heating systems, advanced heating scenarios were developed, which provide improved energy confinement comparable to the scenario, in which the record triple product for stellarators was achieved in the previous operation campaign. However, a magnetic configuration-dependent critical heating power limit of the electron cyclotron resonance heating was observed. Exceeding the respective power limit leads to a degradation of the confinement.

Filaments are studied by examining fast camera images on the Wendelstein 7-X stellarator. Fast cameras offer a unique perspective, revealing the complex 3D structure of filaments in the entire poloidal cross-section of the plasma. By correlating individual pixels, their location, shape, and movement are analyzed in standard and high- ι configurations. The presence of filaments is not uniform poloidally around. The number of active areas matches the number of magnetic islands in both configurations. Filaments are found to extend to multiple toroidal turns in standard configuration. No time delay is observed between the different toroidal sections. Such behavior is not seen in high- ι configuration. Filaments are observed within and without the edge shear layer, indicated by the direction of their poloidal rotation. Inside the shear layer, their velocity scatters around 1.25 km s ^−1 , accompanied by a lifetime between 80 and 120 µ s. Outside, their velocity shows greater absolute values and variance, but still in a few km s ^−1 range. The similarities and differences between the two configurations are discussed and compared to previous results.

The EMC3-Eirene code was used to study the main impurity leakage mechanism for the island divertor in the standard magnetic field configuration. It was found that under experimentally accessible plasma scenarios in the last experimental campaign, the majority of the island scrape-off layer was friction-force dominated. The impurity force balance was only thermal force dominated for upstream locations closed to the last closed flux surface, beyond the island X-point. No impurity neutral ionization was found in this location and hence the parallel impurity transport provides excellent impurity retention. It was found that impurities approach the confinement region nonetheless via perpendicular transport across the island O-point near the parallel flow stagnation region. This finding points out the specific role of the parallel flow stagnation region in providing lower parallel convective transport and long impurity residence times, which makes non-parallel transport channels more important or even the dominant driver of impurity leakage. In line with the relevance of the particle build-up in the flow stagnation region, different retention behavior as a function of density is seen for various species, which is shown to be due to ionization length changes as the plasma background density is increased.

Measurements of ion cyclotron emission (ICE) are planned for magnetically confined fusion plasmas heated by neutral beam injection (NBI) in the Wendelstein 7-X stellarator (W7-X). Freshly injected NBI ions in the edge region, whose velocity-space distribution function approximates a delta-function, are potentially unstable against the magnetoacoustic cyclotron instability (MCI), which could drive a detectable ICE signal. Prediction of ICE from NBI protons in W7-X hydrogen plasmas is challenging, owing to the low ratio of the ions’ perpendicular velocity to the local Alfvén speed, $v_{\perp (\textrm{NBI})}/V_A \simeq 0.14$ . We address this from first principles, using the particle-in-cell kinetic code EPOCH. This self-consistently solves the Lorentz force equation and Maxwell’s equations for tens of millions of computational ions (both thermal majority and energetic NBI minority) and electrons, fully resolving gyromotion and hence capturing the cyclotron resonant phenomenology which gives rise to ICE. Our simulations predict an ICE signal which is predominantly electrostatic while incorporating a significant electromagnetic component. Its frequency power spectrum reflects novel MCI physics, reported here for the first time. The NBI ions relaxing under the MCI first drive broadband field energy at frequencies a little below the lower hybrid frequency $\omega_\textrm{LH},$ across the wavenumber range $k\omega_{c}/V_A = 40$ –60, where ω _c and V _A denote ion cyclotron frequency and Alfvén velocity. Nonlinear coupling between these waves then excites spectrally structured ICE with narrow peaks, at much lower frequencies, typically the proton cyclotron frequency and its lower harmonics. The relative strength of these peaks depends on the specifics of the NBI ion velocity-space distribution and of the local plasma conditions, implying diagnostic potential for the predicted ICE signal from W7-X.

A pellet-induced enhanced confinement (PiEC) phase, with general characteristics similar to those reported for the stellarator W7-X, is observed after single pellet injection (>10 ^19 H atoms) into the neutral beam injection heated phase of plasmas in the mid-sized heliac-type stellarator TJ-II. In addition to a step-like increase in density, plasma diamagnetic energy content rises significantly with respect to that of reference discharges, energy confinement time is similarly enhanced when compared to International Stellarator Scaling law predictions (Yamada et al 2005 Nucl. Fusion 45 1684) renormalized for TJ-II, and the triple product, n _e · T _i · τ _E , exhibits a clear bifurcation towards an improved confinement branch when compared to the branch product predicted by the same law. In this work, multiple pellets are injected in series into NBI-heated plasmas in the TJ-II and post-injection plasma performance is reported and discussed. For instance, a charge-exchange recombination spectroscopy diagnostic reveals significantly increased core ion temperatures after pellet injection compared to temperatures achieved in comparable reference plasmas, this pointing to increased ion energy content and improved ion energy confinement during a PiEC phase. It is also found that enhanced performance is independent of whether co- or counter-NBI heating beam is employed. Finally, record stored diamagnetic energy content and plasma beta values are achieved when the largest available pellets are employed. The results indicate that pellet injections extend the operational regime well beyond limits previously achieved in TJ-II without pellets.

Sawtooth oscillations in tokamaks frequently lead to the redistribution of energetic ions, mainly on passing orbits, causing their expulsion from the core. This paper discusses the first measurements of the interaction of fast ions and sawteeth in the Large Helical Device. The crashes were caused by the plasma current induced by Electron Cyclotron Current Drive and Neutral Beam Current Drive. Despite these crashes, there was no detectable redistribution effect on fast ions in either the core or at the edge of the plasma.

The first experimental campaigns of Wendelstein 7-X (W7-X) have shown that turbulence plays a decisive role in the performance of neoclassically optimized stellarators. This stresses the importance of understanding microturbulence from the theoretical and experimental points of view. To this end, this paper addresses a comprehensive characterization of the turbulent fluctuations by means of nonlinear gyrokinetic simulations performed with the code stella in two W7-X scenarios. In the first part of the paper, the amplitude of the density fluctuations is calculated and compared with measurements obtained by Doppler reflectometry (DR) in the OP1 experimental campaigns. It is found that the trend of the fluctuations along the radius is explained by the access of the DR system to different regions of the turbulence wavenumber spectrum. In the second part of the article, frequency spectra of the density fluctuations and the zonal component of the turbulent flow are numerically characterized for comparisons against future experimental analyses. Both quantities feature broad frequency spectra with dominant frequencies of O(1)–O(10) kHz.

The present work presents a 2D and 3D modeling of the neutral gas flow in the sub-divertor region of the W7-X. The investigations have been done using the DIVGAS code. The complex 2D and 3D geometries of the divertor components in the sub-divertor region have been considered and the Standard and High-Iota magnetic configurations have been numerically simulated. The main objective of this study is to investigate the dynamics of neutral particles in the sub-divertor region including the effects due to geometry and toroidal and poloidal leakages located at the divertor targets and baffles on the achieved pumping efficiency. A sensitivity analysis has been performed for the effect of various geometrical and flow parameters on the pumping performance, under different plasma scenarios. The considered incoming fluxes in the sub-divertor range between 10 ^20 to 10 ^22 (H _2 s ^−1 ). The main conclusions, which can be extracted from the present numerical analysis could be summarized as follows; a large fraction of incoming neutral particle flux i.e. >70% on the low iota side and >40% for the high iota side is leaked back to the main divertor region, while higher incoming neutral fluxes facilitate the increase of the pumped flux as well as the decrease of the outflux. It has been estimated that a small fraction ∼3%–4% of the incoming neutral flux is being pumped via the turbo-molecular pumps. The closure of the toroidal leakages as well as the inclination of the pumping gap panel by 9 ^o facilitate the increase of the pumped flux, but considering the all the engineering constraints, the latter option seems to be more easy to be implemented. For low incoming neutral fluxes (∼10 ^20 H _2 s ^−1 ) and for the case of AEH section, free molecular flow conditions are estimated and therefore neutral-neutral collisions could be neglected. For higher incoming neutral fluxes and for both AEH and AEP sections neutral-neutral collisions play a significant role in the flow establishment. A comparison with available experimental measurements of the neutral pressure in the sub-divertor has been performed for Standard and High-Iota plasma discharges. The 3D DIVGAS simulations predict qualitatively the experimental data with relative deviation between 25 and 63%. All the above numerical findings will actively support the optimization of the W7-X particle exhaust, in view of the experimental campaign OP2.

Sawtooth crashes are observed during ECCD experiments at the superconducting optimized stellarator Wendelstein 7-X. The study and the characterization are necessary in order to understand under which condition ECCD can be driven without posing a risk to experimental operations. The development of automatic tools is crucial to speed up the analysis of extensive datasets. In this work, we report on the first attempt of using a data-driven approach to automatically characterize the sawtooth crashes. Cluster algorithms are applied to the dataset, confirming the existence of two distinct types of crashes. This approach allows to study the two groups separately and underlines the different plasma parameters that influence the sawtooth crash parameters, for instance crash amplitude and period.

The implementation of three-dimensional magnetic fields, such as the ones of stellarators, in the GBS code (Ricci et al 2012 Plasma Phys. Control. Fusion 54 124047; Giacomin et al 2022 J. Comput. Phys. 464 111294) is presented, and simulation results are discussed. The geometrical operators appearing in the drif-reduced Braginskii equations evolved by GBS are expanded considering the typical parameter ordering of stellarator configurations. It turns out that most of the operators have a similar structure as the one implemented in the tokamak axisymmetric version of the code. In particular, the perpendicular laplacian only acts on the poloidal plane, which avoids the need of a three-dimensional solver for the electrostatic potential. The simulation of an island divertor stellarator is then presented, showing the derivation of the magnetic equilibrium in detail and extending the results in (Coelho et al 2022 Nucl. Fusion 62 074004). Although the island magnetic field-lines divert the plasma towards the strike points of the walls, the islands do not seem to have a significant impact on the turbulence properties. The dominant mode, identified as interchange-driven, is field-aligned and breaks the stellarator toroidal symmetry. The radial and poloidal extensions of the mode are of the same order, in contrast to typical tokamak simulations. This has consequences on the poloidal dependence of turbulent transport.

A new self-sustained divertor oscillation is discovered in magnetic island induced detached plasmas in the Large Helical Device. The divertor oscillation is found to be a self-regulation of the width of an edge magnetic island accompanied by detachment-attachment transitions. The modified Rutherford equation combined with an ad-hoc bootstrap current equation is introduced to describe the divertor oscillation as a predator–prey model between the magnetic island width and a remnant X-point bootstrap current. The model successfully reproduces the experimental observations in terms of the oscillation frequency, the phase relation between variables, and the oscillation amplitude.

This contribution presents neutron transport studies for the 5-period helical-axis advanced stellarator stellarator using the Serpent2 code. These studies utilize a parametric geometry model, enabling scans in neutronics modeling by varying the thickness of the reactor layers. For example, the tritium breeding ratio (TBR) can be determined by exploring various blanket material options and thicknesses to identify the threshold configuration that meets the TBR design criterion of 1.15. We found out that with the helium-cooled pebble ped candidate option, the TBR criterion is met with a breeding zone thickness of 26 cm, while with the dual-coolant lithium lead the threshold is exceeded at a thickness of 46 cm. Furthermore, the geometry includes non-planar field coils, allowing to study the fast neutron flux in these superconducting coils with a technological limit of $1\times10^{9}\,1/\mathrm{cm}^{2}\,\mathrm{s}$ . It is shown that the neutron fast flux is not constant at the coils, necessitating a neutron transport simulation to determine the distribution of the fast-flux at the coils. We show that the peak fast flux can be more than a factor of 2 higher than the average flux, and that the peak flux location rotates helically.

Advanced stellarators are typically optimized in two stages. The plasma equilibrium is optimized first, followed by the design of coils/permanent magnets. However, the coils/permanent magnets in the second stage may become too complex to achieve the desired equilibrium. To address this problem, a quasi-single-stage optimization method has been proposed. In this paper, we introduce this method for designing permanent magnet (PM) stellarators. The new approach combines straightforward PM metrics to penalize the maximum required PM thickness and the mismatch between the fixed-boundary equilibrium and the free-boundary one, along with typical physical targets. Since the degrees of freedom of the PMs are not included and directly used to minimize the objective function in this method, so we call it ‘quasi-single-stage’ optimization. We apply this quasi-single-stage optimization method to find a new quasi-axisymmetric PM design. The new design starts from MUSE, which was initially designed using a two-stage optimization approach. The resulting design, MUSE++, exhibits an order of magnitude lower quasi-symmetric error and a one-order reduction in normal field error. We show that MUSE++ has approximately 30% fewer magnets compared to a proxy model ‘MUSE-0’ that uses the same FAMUS optimization without the benefit of a single-stage equilibrium optimization. These results demonstrate that the new single-stage optimization method can concurrently improve plasma properties and simplify permanent magnet complexity.

An important question for the outlook of stellarator reactors is their robustness against pressure driven modes, and the underlying mechanism behind experimentally observed soft β limits. Towards building a robust answer to these questions, simulation studies are presented using a recently derived reduced nonlinear MHD model. First, the initial model implementation is extended to capture fluid compression by including the influence of parallel flows. Linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and interchange modes in a finite β , net-zero current carrying stellarator with low magnetic shear are then used to demonstrate the modeling capabilities. Finally, a validation study is conducted on experimental reconstructions of finite β W7-AS discharges. In agreement with past experimental analysis, it is shown that (i) the MHD activity is resistive, (ii) a soft β limit is observed, when the plasma resistivity approaches the estimated experimental value, and (iii) low n MHD activity is observed at intermediate β values, particularly a nonlinearly dominant (2, 1) mode. The MHD activity is mild, explaining the soft β limit, because the plasma volume remains separated into distinct sub-volumes in which field lines are ergodically confined. For the assumed transport parameters, the enhanced perpendicular transport along stochastic magnetic field lines can be overcome with the experimental heating power. The limitations in the current modeling are described, alongside an outlook for characterizing the quasi-steady state operational limit in W7-AS and other devices in more detail in future work.

In the Wendelstein 7-X (W7-X) stellarator, turbulence is the dominant transport mechanism in most discharges. This leads to a ‘clamping’ of ion temperature over a wide range of heating power, predominantly flat density profiles where hollow profiles driven by neoclassical thermo-diffusion would be expected and by rapid impurity transport in injection experiments. Significantly reduced turbulent transport is observed in the presence of strong core density gradients found transiently after core pellet injection and irregularly after boronisation or boron pellet injection. Density peaking is also achieved in a controlled manner in purely neutral beam heated discharges where particle transport analysis reveals an abrupt reduction in the main-ion particle flux leading to significant density profile peaking not explained by the NBI particle source alone. The plasmas exhibit a heat diffusivity of around $\chi = 0.25 \pm 0.1\,\mathrm{m}^2\ \mathrm{s}^{-1}$ at mid radius, a factor of around 4 lower than ECRH dominated discharges. Despite the improved confinement, the achieved ion temperature is limited by broader heat deposition and the lower power-per-particle given the higher density. This is overcome with limited reintroduction of ECRH power, where the low heat diffusivity diffusivity is maintained, the density rise supressed and ion temperatures above the clamping limit are achieved. The applicability of these plasmas for a high performance scenario on transport relevant time scales is assessed, including initial predictions for planned heating upgrades of W7-X, based on a range of assumptions about particle transport.

We provide an overview of activities carried out at the TJ-II stellarator for improving our understanding of- and developing plasma physics models for particle density profiles in stellarators. Namely, we report on recent progress in turbulent particle transport simulation, validation of pellet deposition models, density profile shaping for performance control and new experimental techniques for edge turbulence and plasma-neutral interaction.

A spontaneous reduction in anomalous particle transport in the plasma core is seen experimentally in reproducible, purely neutral beam heated plasma phases at Wendelstein 7-X (W7-X). Heating and fueling the plasma exclusively with the neutral beam injection system for several seconds leads to continuously peaking plasma density profiles with strong gradients inside mid minor radius. A significant acceleration of the density peaking occurs after a certain onset time and is examined with a detailed particle transport analysis in several discharges. By invoking the particle continuity equation, the total experimental radial electron flux is deduced from the time evolution of the electron density profile and the radially resolved particle sources. Subtracting the modeled neoclassical particle flux contribution gives the anomalous particle flux. Exploiting the evolving plasma conditions, anomalous diffusion and convection coefficients are computed from the flux variation with density and density gradients. In several discharges a significant and consistent change of the anomalous transport coefficients is seen when crossing a specific normalized density gradient length.

The low magnetic shear in the Wendelstein 7-X (W7-X) stellarator makes it feasible to shape the separatrix by the large islands constituting an island-divertor, and this can be exploited to access various magnetic configurations, including samples of different internal island sizes and locations. To investigate the configuration effects on the plasma confinement, a configuration scan was performed by changing the coil currents to vary the rotational transform between values $5/4$ and $5/6$ at the plasma boundary with different power levels (2, 4, 6 MW) of electron cyclotron resonance heating (ECRH) at a maximum plasma density of $8 \times 10^{19}\,\textrm{m}^{-2}$ . neutral beam injection (NBI) heating was also applied during some configurations of the scan to create a density ramp and access high densities beyond the X2 ECRH cutoff. For the magnetic configurations, where the $5/5$ and $5/6$ island chains were moved closer to separatrix but remaining inside the last closed flux surface, the electron cyclotron emission shows that an electron temperature, $T_{\mathrm e}$ , pedestal develops already during ECRH heated plasma buildup phase indicating a transport barrier, and the barrier sustains irrespective of changed plasma heating conditions such as NBI in the later part of discharge. The transport barrier is broken by subsequent fast crashes, observed with multiple plasma diagnostics with characteristics such as tokamak edge localized modes, and the corresponding crash amplitude and frequency vary with plasma pressure. The impact of the transport barrier on plasma confinement can be seen through the increased core $T_{\mathrm e}$ profile, which could be responsible for the overall increase in the stored diamagnetic energy by approximately 10% for these configurations. After the plasma heating is terminated, a backwards transition to a degraded confinement state is also observed. These observations indicate a configuration triggered high confinement mode in low shear W7-X. This work focuses on the occurrence of this transport barrier for different magnetic configurations and its relation to internal magnetic islands.

We present the first validated synthetic diagnostic for fast ion loss detectors (FILDs) in the Wendelstein 7-X (W7-X) stellarator. This model has been developed on, and validated against experimental data from, a FILD provided by the National Institute for Fusion Science (NIFS-FILD), with potential future applicability to the existing Faraday Cup FILD (FC-FILD) on W7-X as well as the scintillating FILD (S-FILD) currently under development. A workflow combining Monte Carlo codes BEAMS3D and ASCOT5 is used to track fast ions produced by neutral beam injection from the moment of ionization until they are thermalized or lost from the last closed flux surface, and from there to a virtual plane which serves as a projection of the entrance aperture to the FILD. Simulations in ASCOT5 are analyzed via a geometric method to determine the probability of transmission through the FILD aperture and onto the detector as a function of normalized momentum, pitch angle, gyrophase, and position at the virtual plane. This probability is then applied to the simulated ions arriving from the plasma, producing a simulated signal from a computationally tractable number of simulated fast ions. Simulated signals are presented for two W7-X experiments with neutral beam injection and quantitatively compared with experimental measurements from the NIFS-FILD diagnostic. An estimate of the frequency of charge-exchange with neutral particles in the edge is performed, and it is found that this process may have a significant impact on the measured signals.

The results of the first experimental series to produce a plasma using the radio frequency discharge (RF) above the ion cyclotron frequency at relatively low magnetic fields (0.5–0.6 T) in the Large Helical Device (LHD) are presented 1.43 MW of RF power produced target plasma with density up to 6 × 10 ^18 m ^−3 to deuterium. Tangential NBI application into such a plasma increases plasma parameters. Electron temperatures up to ≈0.9 keV and densities up to ≈2.4 × 10 ^19 m ^−3 had been achieved, and the maximum value of < β _dia > was 2.6%. These experiments open possibilities for new regimes of LHD operation which are also interested to W7-X.

We directly optimize stellarator neoclassical ion transport while holding neoclassical electron transport at a moderate level, creating a scenario favorable for impurity expulsion and retaining good ion confinement. Traditional neoclassical stellarator optimization has focused on minimizing $\epsilon_\mathrm{eff}$ , the geometric factor that characterizes the amount of radial transport due to particles in the $1/\nu$ regime. Under expected reactor-relevant conditions, core electrons will be in the $1/\nu$ regime and core fuel ions will be in the $\sqrt{\nu}$ regime. Traditional optimizations thus minimize electron transport and rely on the radial electric field ( E _r ) that develops to confine the ions. This often results in an inward-pointing E _r that drives high- Z impurities into the core, which may be troublesome in future reactors. In this work, we increase the ratio of the thermal transport coefficients $L_{11}^{e} / L_{11}^{i}$ , which previous research has shown can create an outward-pointing E _r . This effect is very beneficial for impurity expulsion. We obtain self-consistent density, temperature, and E _r profiles at reactor-relevant conditions for an optimized equilibrium. This equilibrium is expected to enjoy significantly improved impurity transport properties.

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]

The initial operation of neutral beams in Wendelstein 7-X enabled the first measurements of carbon (C6+) temperature and rotation with a multi-chord charge exchange recombination spectroscopy system. In this article we analyse the velocity measurements obtained with this system to infer the profiles of radial electric field, E r, and net parallel velocity of fully stripped carbon ions, V ‖. We include a general treatment of the flow geometry and the velocity corrections due to the energy dependence of the charge exchange cross section. The inverted profiles are compared with neoclassical calculations for various plasma conditions and two magnetic configurations. It is found that both the E r and V ‖ experimental profiles agree in sign and order of magnitude with the neoclassical expectations and reproduce the expected dependencies on plasma parameters and magnetic configuration, within the reduced dataset presented. However, quantitative differences with respect to the neoclassical profiles are observed above the estimated errors in various conditions. [ABSTRACT FROM AUTHOR]

The structure was considered of the plasma column in the L-2M stellarator under different discharge conditions. The structure of perturbations was analyzed using a set of electrostatic (Langmuir) and magnetic probes spaced in the toroidal and poloidal directions. Time evolutions were analyzed of disturbances of the magnetic and electric fields in shots with short-duration transport transitions, and the data obtained before and after the transient processes was compared. Based on the spectral analysis of correlations between the signals, it was concluded that during the transient processes in plasma, the frequency and spatial structure of the modes changes. The high coherence between the fluctuations of the magnetic and electric fields observed before the transition suggests that, before the transition, the currents excited at the edge rational magnetic surfaces of the stellarator excite plasma fluctuations that results in the escape of electrons and occurrence of positive plasma potential. A decrease in turbulence occurring after the transition results in the reduction of electrons escape and drop of the positive potential. It was ascertained that during the discharge, plasma potential is positive, and during the transport transition, a decrease in the potential amplitude is observed. After the transition, two effects can arise: the improvement of electron confinement and a sharp increase in the ion loss at the plasma edge. The improvement of electron confinement can be associated with a decrease in fluctuations, while the rapid escape of ions can occur due to the effect of plasma–wall interaction. [ABSTRACT FROM AUTHOR]

The dynamics of the appearance of vortex low-frequency plasma turbulence structures was analyzed by processing the time samples of noisy broadband signals measured by small-angle scattering and collective backscattering of first-harmonic radiation (75 GHz) of a gyrotron under multipulse ERC heating in the L-2M stellarator with boronation of the inner wall of the chamber. The results from the high-frequency filtering of the time samples of diagnostic signals are presented alongside the correlation analysis, spectral Fourier analysis, and wavelet analysis of plasma turbulence signals. [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]