We study the effect of turbulent transport in different magnetic configurations of the Weldenstein 7-X stellarator. In particular, we performed direct numerical simulations with the global gyrokinetic code GENE-3D, modeling the behavior of Ion Temperature Gradient turbulence in the Standard, High-Mirror, and Low-Mirror configurations of W7-X. We found that the Low-Mirror configuration produces more transport than both the High-Mirror and the Standard configurations. By comparison with radially local simulations, we have demonstrated the importance of performing global nonlinear simulations to predict the turbulent fluxes quantitatively.
We present a modified gyrokinetic theory to predict the critical gradient that determines the linear onset of the ion temperature gradient (ITG) mode in stellarator plasmas. A coarse-graining technique is applied to the drift curvature, entering the standard gyrokinetic equations, around local minima. Thanks to its simplicity, this novel formalism yields an estimate for the critical gradient with a computational cost low enough for application to stellarator optimization. On comparing against a gyrokinetic solver, our results show good agreement for an assortment of stellarator designs. Insigh…
We present a stellarator configuration optimized for a large threshold (``critical gradient'') for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with exce…
The global gyrokinetic toroidal code (GTC) has been recently upgraded to do simulations in non-axisymmetric equilibrium configuration, such as stellarators. Linear simulation of ion temperature gradient (ITG) driven instabilities has been done in Wendelstein7-X (W7-X) and Large Helical Device (LHD) stellarators using GTC. Several results are discussed to study characteristics of ITG in stellarators, including toroidal grids convergence, nmodes number convergence, poloidal and parallel spectrums, and electrostatic potential mode structure on flux surface.
A recent characterization of core turbulence carried out with a Doppler reflectometer in the optimized stellarator Wendelstein 7-X (W7-X) found that discharges achieving high ion temperatures at the core featured an ITG-like suppression of density fluctuations driven by a reduction of the gradient ratio $η_i = L_n/L_{T_i}$ [D. Carralero et al., Nucl. Fusion, 2021]. In order to confirm the role of ITG turbulence in this process, we set out to establish experimentally the relation between core density fluctuations, turbulent heat flux and global confinement. With this aim, we consider the scenar…
A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ITG, TEM and ETG modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the non…
We investigate the linear theory of the ion-temperature-gradient (ITG) mode, with the goal of developing a general understanding that may be applied to stellarators. We highlight the Wendelstein 7X (W7-X) device. Simple fluid and kinetic models that follow closely from existing literature are reviewed and two new first-principle models are presented and compared with results from direct numerical simulation. One model investigates the effect of regions of strong localized shear, which are generic to stellarator equilibria. These "shear spikes" are found to have a potentially significant stabil…
Reduction of particle and heat fluxes to plasma facing components is critical to achieve stable conditions for both the plasma and the plasma material interface in magnetic confinement fusion experiments. A stable and reproducible plasma state in which the heat flux is almost completely removed from the material surfaces was discovered recently in the Wendelstein 7-X stellarator experiment. At the same time also particle fluxes are reduced such that material erosion can be mitigated. Sufficient neutral pressure was reached to maintain stable particle exhaust for density control in this plasma …
Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-$J$ geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-iso…
The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, document…
A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized "spikes" in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that lo…
One metric for comparing confinement properties of different magnetic fusion energy configurations is the linear critical gradient of drift wave modes. The critical gradient scale length determines the ratio of the core to pedestal temperature when a plasma is limited to marginal stability in the plasma core. The gyrokinetic turbulence code GS2 was used to calculate critical temperature gradients for the linear, collisionless ion temperature gradient (ITG) mode in the National Compact Stellarator Experiment (NCSX) and a prototypical shaped tokamak, based on the profiles of a JET H-mode shot an…
Global gyrokinetic analysis of Wendelstein 7-X discharge: unveiling the importance of trapped-electron-mode and electron-temperature-gradient turbulence
本文首次对类 W7-X 仿星器放电进行含动理学电子、平衡径向电场及电磁碰撞效应的非线性径向全局回旋动理学模拟，揭示芯部湍流电子热通量主要由 TEM 和 ETG 驱动，并强调有限电子温度梯度的关键作用。
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 ITG 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 n…
Zonal flow suppression of turbulent transport in the optimized stellarators W7-X and QSTK
Indian Institute of Science（印度科学学院）；Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；University of California Irvine（加州大学尔湾分校）
In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the "trapped electron mode" (TEM) is stabilised if specific optimisation criteria are satisfied, as in the Wendelstein 7-X experiment (W7-X). Here we find, by numerical simulation, that W7-X indeed has low TEM-driven transport, and also benefits from stabilisation of the ion-temperature-gradient mode, giving theoretical support for the existence of enhanced confinement regimes at finite density gradients.
The first fast ion experiments in Wendelstein 7-X were performed in 2018. They are one of the first steps in demonstrating the optimised fast ion confinement of the stellarator. The fast ions were produced with a neutral beam injection (NBI) system and detected with infrared cameras (IR), a fast ion loss detector (FILD), fast ion charge exchange spectroscopy (FIDA), and post-mortem analysis of plasma facing components. The fast ion distribution function in the plasma and at the wall is being modelled with the ASCOT suite of codes. They calculate the ionisation of the injected neutrals and the …
In this work, a Serpent 2 neutronics model of the Wendelstein 7-X (W7-X) stellarator is prepared, and an response function for the Scintillating-Fibre neutron detector (SciFi) is calculated using the model. The neutronics model includes the simplified geometry for the key components of the stellarator itself as well as the torus hall. The objective of the model is to assess the 14.1 MeV neutron flux from deuteron-triton fusions in W7-X, where the neutrons are modelled only until they have slowed down to 1 MeV energy. The key messages of this article are: demonstration of unstructured mesh geom…
Turbulent transport is known to limit the plasma confinement of present-day optimized stellarators. To address this issue, a novel method to strongly suppress turbulence in such devices is proposed, namely the resonant wave-particle interaction of supra-thermal particles - e.g., from ion-cyclotron-resonance-frequency (ICRF) heating - with turbulence-driving microinstabilities like ion-temperature-gradient (ITG) modes. The effectiveness of this mechanism is demonstrated via analytic theory and large-scale gyrokinetic simulations, revealing an overall turbulence reduction by up to $80\%$. These …
XGC (X-point Gyrokinetic Code) is a whole-volume, total-f gyrokinetic particle-in-cell code developed for modelling tokamaks. In recent work, XGC has been extended to model more general 3D toroidal magnetic configurations, such as stellarators. These improvements have resulted in the XGC-S version. In this paper, XGC-S is benchmarked for linear electrostatic ion temperature gradient-driven microinstabilities, which can underlie turbulent transport in stellarators. An initial benchmark of XGC-S in tokamak geometry shows good agreement with the XGC1, ORB5, and global GENE codes. A benchmark betw…
In this work, a new version of KNOSOS is presented. KNOSOS is a low-collisionality radially-local, bounce-averaged neoclassical code that is extremely fast, and at the same time, includes physical effects often neglected by more standard codes: the component of the magnetic drift that is tangent to the flux-surface and the variation of the electrostatic potential on the flux-surface. An earlier version of the code could only describe configurations that were sufficiently optimized with respect to neoclassical transport. KNOSOS can now be applied to any large aspect ratio stellarator, and its p…
First results from the optimized helias Wendelstein 7-X stellarator (W7-X) have shown that core transport is no longer mostly neoclassical, as is the case in previous kinds of stellarators. Instead, turbulent transport poses a serious limitation to the global performance of the machine. Several studies have found this particularly relevant for ion transport, with core ion temperatures becoming clamped at relatively low values of $T_{i} \simeq 1.7$ keV, except in the few scenarios in which turbulence can be suppressed. In order to understand turbulent mechanisms at play, it is important to have…
In toroidal magnetic confinement devices, such as tokamaks and stellarators, neoclassical transport is usually an order of magnitude larger than its classical counterpart. However, when a high-collisionality species is present in a stellarator optimized for low Pfirsch-Schlüter current, its classical transport can be comparable to the neoclassical transport. In this letter, we compare neoclassical and classical fluxes and transport coefficients calculated for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we find that the classical transport of a collisional impurity is …
The gyrokinetic turbulence code GS2 was used to investigate the effects of plasma beta on linear, collisionless ion temperature gradient (ITG) modes and trapped electron modes (TEM) in National Compact Stellarator Experiment (NCSX) geometry. Plasma beta affects stability in two ways: through the equilibrium and through magnetic fluctuations. The first was studied here by comparing ITG and TEM stability in two NCSX equilibria of differing beta values, revealing that the high beta equilibrium was marginally more stable than the low beta equilibrium in the adiabatic-electron ITG mode case. Howeve…
With the advent of neoclassically optimised stellarators, optimising stellarators for turbulent transport is an important next step. The reduction of ion-temperature-gradient-driven turbulence has been achieved via shaping of the magnetic field, and the reduction of trapped-electron mode (TEM) turbulence is adressed in the present paper. Recent analytical and numerical findings suggest TEMs are stabilised when a large fraction of trapped particles experiences favourable bounce-averaged curvature. This is the case for example in Wendelstein 7-X [C.D. Beidler $\textit{et al}$ Fusion Technology $…
The stability of the ion-temperature gradient mode in quasisymmetric stellarators is assessed. This is performed using a set of analytical estimates together with linear gyrokinetic simulations. The peak growth rates, their corresponding real frequencies and wave-vectors are identified. A comparison is made between a first-order near-axis expansion model and eleven realistic designs obtained using numerical optimization methods. It is found that while the near-axis expansion is able to replicate the growth rates, real frequencies and perpendicular wave-vector at the inner core (both using simp…
In the present Letter, first-of-its-kind computer simulations predicting plasma profiles for modern optimized stellarators -- while self-consistently retaining neoclassical transport, turbulent transport with 3D effects, and external physical sources -- are presented. These simulations exploit a newly developed coupling framework involving the global gyrokinetic turbulence code GENE-3D, the neoclassical transport code KNOSOS, and the 1D transport solver TANGO. This framework is used to analyze the recently observed degradation of energy confinement in electron-heated plasmas in the Wendelstein…
Avoiding impurity accumulation is a requirement for steady-state stellarator operation. The accumulation of impurities can be heavily affected by variations in their density on the flux-surface. Using recently derived semi-analytic expressions for the transport of a collisional impurity species with high-$Z$ and flux-surface density-variation in the presence of a low-collisionality bulk ion species, we numerically optimize the impurity density-variation on the flux-surface to minimize the radial peaking factor of the impurities. These optimized density-variations can reduce the core impurity d…
High-Z impurities in magnetic confinement devices are prone to develop density variations on the flux-surface, which can significantly affect their transport. In this paper, we generalize earlier analytic stellarator calculations of the neoclassical radial impurity flux in the mixed-collisionality regime (collisional impurity and low-collisionality bulk ions) to include the effect of such flux-surface variations. We find that only in the homogeneous density case is the transport of highly collisional impurities (in the Pfirsch-Schlüter regime) independent of the radial electric field. We study…
The core collapse events observed in a stellarator experiment are studied by a three-dimensional nonlinear MHD simulations. In the low magnetic shear configuration like the Wendelstein 7-X, the rotational transform profile is very sensitive to the toroidal current density. The 3D equilibrium with localized toroidal current density is studied. If the toroidal current density follows locally in the middle of the plasma minor radius, the rotational transform is also changed locally. Sometimes, the magnetic topology changes due to appearing the magnetic island. The nonlinear behaviors of the MHD i…
Modelling the scrape-off layer of a stellarator is challenging due to the complex magnetic 3D geometry. The here presented study analyses simulations of the scrape-off layer (SOL) of the stellarator Wendelstein 7-X (W7-X) using the EMC3-EIRENE code for the magnetic standard configuration. Comparing with experimental observations, the transport model is validated. Based on the experimentally observed strike line width, the anomalous transport coefficients, used as input to the code are determined to around $0.2\,$m$^2/$s. This is however in disagreement with upstream measurements, where such sm…
Asymptotic scaling theory of electrostatic turbulent transport in magnetised fusion plasmas
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；University of Maryland（马里兰大学）；University of Oxford（牛津大学）；Princeton University（普林斯顿大学）；Institute for Research in Electronics and Applied Physics（电子与应用物理研究所）；United Kingdom Atomic Energy Authority（英国原子能管理局）；University of New Hampshire（新罕布什尔大学）；University of Otago（奥塔哥大学）
A large diffusive turbulent contribution to the radial impurity transport in Wendelstein 7-X (W7-X) plasmas has been experimentally inferred during the first campaigns and numerically confirmed by means of gyrokinetic simulations with the code stella. In general, the absence of strong impurity accumulation during the initial W7-X campaigns is attributed to this diffusive term. In the present work the diffusive contribution is also calculated in other stellarator plasmas. In particular, the diffusion (D) and convection (V) coefficients of carbon and iron impurities produced by ion-temperature-g…
The formation of the radial electric field, $E_{\rm r}$ in the 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 3D island divertor of simple models, typically developed in tokamaks, relating $E_{\rm r}$ to the sheath potential drop gradient at the target. Additionally, we investigate the effect of the edge $E_{\rm r}$ shear on the reduction of density fluctuation amplitude, a well-established phenomenon according to the existing bibliography. The main diagnostic for measurements in th…
Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014) 042503] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations …
Electromagnetic turbulence is addressed in tokamak and stellarator plasmas with the global gyrokinetic particle-in-cell codes ORB5 [E. Lanti et al, Comp. Phys. Comm, vol. 251, 107072 (2020)] and EUTERPE [V. Kornilov et al, Phys. Plasmas, vol. 11, 3196 (2004)]. The large-aspect-ratio tokamak, down-scaled ITER, and Wendelstein 7-X geometries are considered. The main goal is to increase the plasma beta, the machine size, the ion-to-electron mass ratio, as well as to include realistic-geometry features in such simulations. The associated numerical requirements and the computational cost for the ca…
