This study reports on a set of experiments designed to clarify the impact of the rotational transform on confinement quality at the TJ-II stellarator. For this purpose, the net plasma current is controlled using external coils, resulting in the modification of the rotational transform profile. Significant and systematic variations of the edge electron density gradients (up to $50\,\%{-}60\,\%$ ) and the plasma energy content ( $20\,\%{-}30\,\%$ ) are achieved. The explanation of this behaviour relies on the placement of low-order rational surfaces in relation to the edge gradient region, which affect local turbulence fluctuation levels, facilitating the formation of zonal flows and concomitant transport barriers. This hypothesis is confirmed experimentally on the basis of a broad array of diagnostic measurements. Calculations based on a resistive magnetohydrodynamic turbulence model provide qualitative support for this hypothesis, clarifying the impact on confinement of specific rational surfaces and highlighting the complex nature of magnetically confined fusion plasmas.

A synthetic Mirnov coil array diagnostic for non-axisymmetric magnetic configurations is presented and used to study the capabilities of the poloidal array of single-axis coils and the two helical arrays of tri-axial coils installed in the TJ-II stellarator. This tool integrates the plasma currents induced by Alfvén-like perturbations of the electric potential inside the plasma and provides the induced magnetic field oscillations anywhere outside of it. The simulated signals can then be analyzed in the same manner as the experimental ones, and a scan on the radial position and width of the potential perturbation is conducted to find the limiting values that produce identifiable signals. We find that core-localized (ρ ≲ 0.5) modes are indistinguishable from one another and that the identification of low-n, low-m modes is often subject to off-by-one errors. We also determine the optimal polarization basis in which to analyze the tri-axial coil signals and address the diagnostic performance when resolving components of gap modes. In addition, selected cases have been analyzed with a simplified plasma response model, showing that plasma shielding of the mode currents may further deteriorate the accuracy of the mode identification method. We conclude with the analysis of an experimental case taken from the TJ-II database to illustrate the usefulness of this synthetic diagnostic.

The generation of shear flows (SFs) by Alfven Eigenmodes (AEs) and energetic particle modes (EPMs) have important effects on the operation of future nuclear fusion reactors, because SFs regulate the saturation of the AEs/EPMs, the transport of EPs and thermal plasma, as well as the formation of transport barriers among other consequences. The aim of this study is the analysis of SFs generation during the saturation phase of AEs and EPMs in LHD plasma. Experiments performed in the 23rd and 24th LHD experimental campaigns are dedicated to explore the destabilization of AEs/EPMs in discharges with different heating patterns, thermal plasma and magnetic field configurations. In particular, the shots 176490 and 179697 show the destabilization of MHD bursts and energetic-ion-driven resistive interchange modes (EIC), respectively. Charge exchange spectroscopy measurements in both discharges indicate that the generation of SFs by AE/EPM is uncorrelated with the perturbation induced by the neutral beam injector (NBI). Nonlinear simulations performed using the gyro-fluid code FAR3d show the generation of zonal structures, especially SFs, induced during the saturation phase of Toroidal Alfven Eigenmodes (TAEs) triggered in the MHD burst as well as by the $1/1$ EIC in the bursting phase. The simulations indicate that SFs are caused by the radial electric fields powered by energy transfers from the unstable AE/EPM towards the thermal plasma. The strongest SFs are measured during the EIC bursting phase once the $1/1$ EPM overlaps with nearby resonances at the plasma periphery. Likewise, the largest SFs during the MHD burst are observed once TAEs radially overlap in the inner-middle plasma region.

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.

The development of reduced models provide efficient methods that can be used to perform short term experimental data analysis or narrow down the parametric range of more sophisticated numerical approaches. Reduced models are derived by simplifying the physics description with the goal of retaining only the essential ingredients required to reproduce the phenomena under study. This is the role of the gyro-fluid code FAR3d, dedicated to analyze the linear and nonlinear stability of Alfvén Eigenmodes (AE), Energetic Particle Modes (EPM) and magnetic-hydrodynamic modes as pressure gradient driven mode (PGDM) and current driven modes (CDM) in nuclear fusion devices. Such analysis is valuable for improving the plasma heating efficiency and confinement; this can enhance the overall device performance. The present review is dedicated to a description of the most important contributions of the FAR3d code in the field of energetic particles (EP) and AE/EPM stability. FAR3d is used to model and characterize the AE/EPM activity measured in fusion devices as LHD, JET, DIII-D, EAST, TJ-II and Heliotron J. In addition, the computational efficiency of FAR3d facilitates performing massive parametric studies leading to the identification of optimization trends with respect to the AE/EPM stability. This can aid in identifying operational regimes where AE/EPM activity is avoided or minimized. This technique is applied to the analysis of optimized configurations with respect to the thermal plasma parameters, magnetic field configuration, external actuators and the effect of multiple EP populations. In addition, the AE/EPM saturation phase is analyzed, taking into account both steady-state phases and bursting activity observed in LHD and DIII-D devices. The nonlinear calculations provide: the induced EP transport, the generation of zonal structures as well as the energy transfer towards the thermal plasma and between different toroidal/helical families. Finally, FAR3d is used to forecast the AE/EPM stability in operational scenarios of future devices as ITER, CFETR, JT60SA and CFQS as well as possible approaches to optimization with respect to variations in the most important plasma parameters.

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.

A novel sparse encoding algorithm is developed to detect and study plasma instabilities automatically. This algorithm, called Elastic Random Mode Decomposition, is applied to the Mirnov coil signals of a dataset of 1291 discharges of the TJ-II stellarator, enabling the identification of the Alfv & eacute;nic activity. In the presented approach, each signal is encoded as a collection of basic waveforms called atoms, drawn from a signal dictionary. Then the modes are identified using clustering and correlations with other plasma signals. The performance of the proposed algorithm is dramatically increased by using elastic net regularization and taking advantage of GPU architectures. Therefore the signal size and the number of dictionary elements are no longer limiting factors for encoding complex signals. Once the modes are retrieved from the shots, standard clustering and dimensionality reduction techniques are applied to obtain a 2D map featuring of the physical mode characteristics of this subset of TJ-II shots. The clustering features consider the relationship with the plasma current Ip, the diamagnetic energy W, and inverse square root of electron density 1/n, profiling different subtypes of Alfv & eacute;nic activity. The proposed algorithm can potentially create large databases of labeled modes with unprecedented detail.

Recently, experiments on basic plasma physics issues for solving future problems in fusion energy have been performed on a Large Helical Device. There are several problems to be solved in future devices for fusion energy. Emerging issues in burning plasma are: alpha-channeling (ion heating by alpha particles), turbulence and transport in electron dominant heating helium ash exhaust, reduction of the divertor heat load. To solve these problems, understanding the basic plasma physics of (1) wave–particle interaction through (inverse) Landau damping, (2) characteristics of electron-scale (high- k ) turbulence, (3) ion mixing and the isotope effect, and (4) turbulence spreading and detachment, is necessary. This overview discusses the experimental studies on these issues and turbulent transport in multi-ion plasma and other issues in the appendix.

The aim of the present study is to analyze the effect of the neutral beam current drive (NBCD), thermal plasma density, and NBI operational regime on the stability of pressure gradient-driven modes (PGDM) and Alfvén eigenmodes (AE) in LHD inward-shifted configurations. The stabilization of n/m=1/2 PGDM (n toroidal mode and m poloidal mode) is observed in the discharge 167 800 during the co-NBCD phase. The iota profile evolution measured by motional stark effect diagnostic may indicate the iota profile up-shift caused by the co-NBCD can induce a non-resonant transition of the rational surface 1/2 before the mode stabilization. The evolution of the iota profile and continuum gaps in the discharge 167 805 during the ctr-NBCD phase leads to the stabilization of the AE, caused by the narrowing of the continuum gap as the iota profile down-shift. Opposite stability trends are identified for PGDM and AE stability with respect to the thermal plasma density. A larger thermal plasma density (larger thermal β) further enhances PGDM although the continuum gaps are narrower leading to configurations with stable AEs. The linear stability of AEs is analyzed using the gyro-fluid FAR3d code to reproduce the AE stability trends observed in the experiments with respect to the NBCD and thermal plasma density. The analysis of hypothetical scenarios dedicated to study different NBI operational regimes with respect to EP energy, and β and radial density profiles indicate off-axis NBI operation shows a higher EP β threshold to destabilize AEs compared to on-axis configuration. This is explained by the presence of a TAE gap in the inner plasma region, easily destabilized by an on-axis NBI injection. The control of the NBCD and thermal plasma in the discharge 167 800 shows a transitory stabilization of PGDM and AEs, as well as an improved discharge performance identified by an increment of the neutron fluxes.

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.

In this paper, we analyze the results of neutral-beam current drive (NBCD) experiments performed in the TJ-II stellarator with the aim of validating the theoretical predictions. Both parallel and anti-parallel injection with respect to the magnetic field were explored using co (NBI1) and counter (NBI2) beams at different injected beam power and plasma densities. The fast-ion current driven by both beams was simulated with the Monte Carlo code ASCOT and the electron response to the fast-ion current was calculated analytically using a model valid for an arbitrary magnetic configuration and a low collisionality plasma. Despite the uncertainties associated to the determination of experimental inputs, the model reproduces with rather good agreement the toroidal current measured in NBI2 plasmas. However, the current driven by NBI1 is less than half the predicted one. Possible reasons for this discrepancy are discussed. Among the probable causes, yet to be studied, the most likely is the increased presence of lithium in the plasma when NBI1 is injected, this being the result of its irregular deposition during wall conditioning.

The formation of the radial electric field, E r in the scrape-off layer (SOL) has been experimentally studied for attached divertor conditions in stellarator W7-X. The main objective of this study is to test the validity in a complex three-dimensional (3D) island divertor of simple models, typically developed in tokamaks, relating E r in the SOL to the sheath potential drop gradient at the target. Additionally, we investigate the effect of the edge E r shear on the reduction of density fluctuation amplitude, a well-established phenomenon according to the existing bibliography. The main diagnostic for measurements in the SOL is a V-band Doppler reflectometer that can provide the measurement of the E r and density fluctuations with good spatial resolution. 3D measurements of divertor parameters have been carried out using infrared cameras, with the exponential decay length of the divertor heat flux ( λ q ) resulting in a suitable proxy for the model-relevant λ T , the exponential decay length of the temperature at the divertor. In the investigated attached regimes, it is shown for the first time that the formation of the E r in the SOL depends on parameters at the divertor, following a E r ∝ T e / λ q qualitatively similar to that found in a tokamak. Then, from the analyzed plasmas, the observed E r shear at the edge is linked to a moderate local reduction of the amplitude of density fluctuations.

This paper reports recent experiments in the TJ-II stellarator using a dual Heavy Ion Beam probe diagnostic. The studies were focused on characterizing plasma potential profiles, investigating self-organization mechanisms and Alfven Eigenmodes (AEs). Results showed plasma equipotential measurements consistent with vacuum magnetic surfaces and the presence of zonal flows in the plasma core region. The investigation of Alfven Eigen modes showed their radial localization and poloidal asymmetries in potential and density fluctuations driven by AEs.

The aim of the present study is to analyze the effect of the electron cyclotron heating (ECH) on the linear stability of Alfven Eigenmodes (AE) and energetic particle modes (EPM) triggered by energetic ions in Heliotron J plasma. The analysis is performed using the FAR3d code that solves a reduced MHD model to describe the thermal plasma coupled with a gyrofluid model for the energetic particles (EP) species. The simulations reproduce the AE/EPM stability trends observed in the experiments as the electron temperature (Te) increases, modifying the thermal plasma beta, EP beta and EP slowing down time. Particularly, the n/m=1/2 EPM and 2/4 Global AE (GAE) are stabilized in the low bumpiness (LB) configuration due to an enhancement of the continuum, Finite Larmor radius (FLR) and e-i Landau damping effects as the thermal beta increases. On the other hand, a larger ECH injection power cannot stabilize the AE/EPM in Medium (MB) and High bumpiness (HB) configurations because the damping effects are weaker compared to the LB case, unable to balance the further destabilization induced by an enhanced EP resonance as the EP slowing down time and EP beta increases with Te

2D plasma potential ϕ distribution was measured in the electron cyclotron resonance heating (ECRH) and neutral beam injection (NBI) plasmas of the TJ-II stellarator with the heavy ion beam probe for the whole radial range and wide area of the poloidal angle, and supported by Langmuir probe data at the edge. The whole operation domain for the on-axis ECRH was explored ( nˉe = 0.45–0.8 ×1019 m−3, P EC = 220–470 kW), in addition, NBI plasmas with nˉe = 0.9–1.3 × 1019 m−3 and P NBI = 510 kW were studied. In ECRH plasmas the density ramp-up is accompanied by the evolution of the potential from the bell-like to the Mexican hat profile, while the density profiles were flat or slightly hollow. The potential has the positive peak at the centre, and LFS-HFS (low field—high field sides) and up-down symmetry. Equipotential lines are consistent with vacuum magnetic flux surfaces. In the high-density NBI scenario, the ϕ profile was fully negative with a minimum up to −300 V at the centre, while at low-density ECRH plasma, ϕ has a maximum up to +0.9 kV at the centre. Fluctuations of potential and density are stronger in low-density scenarios and not poloidally symmetric. At the mid-radius (area of the maximum density), root mean square (RMS) of fluctuations were up to ϕ ∼ 15 V at LFS vs ∼20 V at HFS; RMS n e ∼ 2% at LFS vs ∼3% at HFS. In the NBI plasmas with the density rise, the asymmetry decreases and finally vanishing at nˉe = 1.2 × 1019 m−3. 2D distribution of the NBI-induced Alfvén eigenmodes (AEs) shows asymmetric ballooning structure: contrary to broadband turbulence, AE-associated potential perturbation dominates in the LFS with a factor up to 1.7 respect to the HFS. The electrostatic mode, excited in ECRH plasmas by suprathermal electrons also shows asymmetric structures: density perturbation dominates in the top-bottom direction compared to LFS-HFS direction.

The TJ-II stellarator neutral-beam injection (NBI) system, vacuum vessel and magnetic configuration have been included in the orbit-following Monte Carlo code ASCOT5 to simulate neutral-beam heating and current drive for high-density NBI plasmas. Co- and counter-injection beams are simulated separately. A scan in both electron density and temperature is carried out within the range of values corresponding to realistic high-density NBI plasmas, for which a low level of fast-ion losses due to charge-exchange reactions is expected, since the version of ASCOT5 used in the paper does not include such processes. The rest of the kinetic profiles (ion temperature, radial electric field and effective charge) are kept fixed. The initial distribution of markers shows that the amount of available power in the plasma carried by the beam ions depends slightly on the electron temperature and on the injection direction (co/counter). The steady-state fast-ion distribution function is obtained and used to calculate the three-dimensional fast-ion density, the neutral-beam driven current and the amount of power deposited to the plasma in the two injection scenarios. These three quantities are higher in the counter-injected case due to a lower amount of promptly lost particles. The neutral-beam current drive (NBCD) has been calculated using the fast-ion beam current given by ASCOT5 and the electron return current, which is computed with the analytic solution of the drift kinetic equation for electrons in the presence of fast ions in the low-collisionality regime. Neither the calculated fast-ion density nor the NBCD are flux functions, in consistency with the fact that fast-ion drift surfaces and flux surfaces are generally not aligned.

This paper describes two new helical arrays of magnetic coils recently installed inside the TJ-II vacuum vessel. Their main objective is the precise measurement of the spatial periodicity of the magnetohydrodynamic perturbations usually found in the TJ-II plasmas. Given the high probability of coil failures due to the harsh plasma environment and in view of the extremely difficult access to the TJ-II vessel interior for maintenance, the coil system has been divided in two quasi-identical helical arrays. Both arrays consist of 32 triaxial sensors measuring orthogonal components of the local magnetic field along an ideal helical path whose trajectory runs close to the plasma edge. A description of the main characteristics of coils and arrays as well as their nominal positioning along an ideal helical path, inside the vessel, is given. A precise experimental determination of the real spatial orientation of the coils is performed by comparing the signals measured in current ramp-up and ramp-down experiments with calculations based on a filamentary model for the TJ-II magnetic coils. After this fine calibration procedure, it is possible to analyze the dependence of the amplitude of the measured magnetic field and its fluctuations as a function of the coil distance to the last closed flux surface. The study of the phase evolution of the parallel and perpendicular oscillatory components is also enabled. Finally, two examples of mode number determination are shown. One corresponds to a low frequency mode appearing in pure electron cyclotron resonance heating plasma, and the other one shows several modes observed during combined injection of both co and counter neutral beams and identified as shear Alfvén waves.

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

TJ-II stellarator results on modelling and validation of plasma flow asymmetries due to on-surface potential variations, plasma fuelling physics, Alfvén eigenmodes (AEs) control and stability, the interplay between turbulence and neoclassical (NC) mechanisms and liquid metals are reported. Regarding the validation of the neoclassically predicted potential asymmetries, its impact on the radial electric field along the flux surface has been successfully validated against Doppler reflectometry measurements. Research on the physics and modelling of plasma core fuelling with pellets and tracer encapsulated solid pellet injection has shown that, although post-injection particle radial redistributions can be understood qualitatively from NC mechanisms, turbulence and fluctuations are strongly affected during the ablation process. Advanced analysis tools based on transfer entropy have shown that radial electric fields do not only affect the radial turbulence correlation length but are also capable of reducing the propagation of turbulence from the edge into the scrape-off layer. Direct experimental observation of long range correlated structures show that zonal flow structures are ubiquitous in the whole plasma cross-section in the TJ-II stellarator. Alfvénic activity control strategies using ECRH and ECCD as well as the relation between zonal structures and AEs are reported. Finally, the behaviour of liquid metals exposed to hot and cold plasmas in a capillary porous system container was investigated.

We study Alfvén eigenmodes (AEs) in the TJ-II heliac in hydrogen plasmas heated by hydrogen co-field neutral beam injector. Taking advantage of the unique TJ-II flexibility in a varying plasma current, we have observed strong variation of the AE frequency from fAE ∼ 30 to ∼220 kHz for selected modes. An advanced heavy-ion beam probe diagnostic determines the spatial location and internal amplitudes of the modes. The modes satisfy a local AE dispersion relation including the geodesic acoustic frequency that represents the lowest frequency of the mode. Linear MHD modeling with STELLGAP and FAR3D codes shows that the calculated temporal evolution of the mode frequency reproduces the observed maxima and minima at the same time intervals with a similar frequency range, and the radial profile peaks near the outer edge of the observed one.