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DOE OSTI2023

First feedback-controlled divertor detachment in W7-X: Experience from TDU operation and prospects for operation with actively cooled divertor

In the last experimental campaign (OP1.2b) of the stellarator Wendelstein 7-X (W7-X), boronisation as a mean for first wall conditioning was applied for the first time which led to strongly reduced impurity fluxes from plasma-facing components. Thermal detachment at the uncooled target plates of the test divertor unit (TDU) was reached at higher plasma densities and was accompanied by high recycling of neutrals at the target plate. A feedback control system was established in W7-X to actively control the gas injection (actuator) for plasma fuelling and impurity seeding [3] through the divertors. It allowed very successful stabilisation of the detached plasma condition state as well as mitigation of thermal overloads to some baffle tiles. Different routinely available diagnostic signals were used as input parameters (sensors). We describe the setup of the feedback control system, its performance and provide some example results with the main focus on the development of the control scheme which led to the detachment stabilisation over the entire longest (30 s) high-power discharge at W7-X so far. In view of the achieved very successful detachment stabilisation and the necessity to include simultaneous optimisation of the core performance in the future, the feedback control system is being upgraded for the upcoming campaign (OP2.1) in which the water cooled and hereby inherently steady-state capable divertor has been currently installed. The prospects and some experiment ideas for active detachment control are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

Physics↗

DOE OSTI2021

Improvement in the spatial resolution of heavy ion beam probe measurements through application of ion optics

A technique for more accurately modeling and improving the spatial resolution of heavy ion beam probe measurements is described. We use a set of particle trajectories to numerically determine the focusing properties of a complicated three-dimensional magnetic field and characterize those properties with a transfer matrix. We then modify the transfer matrix approach of traditional ion optics to include a parameter that describes the ionization location of the detected ions. The ion optics model calculated using this technique enables a more accurate description of the particle trajectories than previously feasible. The model also allows one to easily determine an initial beam focus that could be used during experimental operation to optimize the spatial resolution of measurements. The technique has been applied to the design of a heavy ion beam probe diagnostic for the Wendelstein 7-X stellarator and improvements in the modeled spatial resolution by a factor of about 2 over previous estimates are possible. As a result, the improved spatial resolution will enable measurements of plasma fluctuations with smaller wavelengths than would otherwise be possible.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. Here, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 –9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

EMC3-EIRENE simulation of first wall recycling fluxes in W7-X with relation to H-alpha measurements

In the Wendelstein 7-X stellarator, the main locations of particle sources are expected to be the carbon divertors, baffles and graphite heat shield first wall. In this paper, the heat shield is implemented in EMC3-EIRENE to understand the expected areas and magnitudes of the recycling flux to this component. It is found that in the simulation the heat shield is not a significant source of recycling neutrals. The areas of simulated recycling flux are shown to correlate well with footprints of plasma-wetting seen in post-experimental campaign in-vessel inspection photos. EMC3-EIRENE reconstruction of line-integrated H-alpha measurements at the heat shield indicate that the majority of emission does not come from local recycling neutrals. Rather, the H-alpha signals at the heat shield are dominated by ionization of neutrals which have leaked from the divertor/baffle region into the midplane. The magnitude of the H-alpha line emission from the synthetic reconstruction is consistent with the experiment, indicating that a large overestimation of heat shield recycling would occur if these measurements were assumed to be from local recycling sources. In the future, it may be possible to obtain some information of local recycling from the heat shield since it was found that the majority of the recycling flux occurs on two well-localized areas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Simulating fusion alpha heating in a stellarator reactor

Gyrocenter following simulations of fusion born alpha particles in a stellarator reactor are preformed using the BEAMS3D code. The Wendelstein 7-X high mirror configuration is scaled in geometry and magnetic field to reactor relevant parameters. A $2\,\times\,10^{20}m^{-3}$ density plasma with 20 keV core temperatures is assumed and fusion birth rates calculated for various fusion products assuming a 50/50 deuterium-tritium mixture. It is found that energetic He 4 ions comprise the vast majority of the energetic particle inventory. Slowing down simulations of the He4 population suggest plasma heating consistent with scaled energy confinement times for a stellarator reactor. Losses for this configuration appear large suggesting optimization beyond the scope of the W7-X device is key to a future fusion reactor. These first simulations are designed to demonstrate the capability of the BEAMS3D code to provide fusion alpha birth and heating profiles for stellarator reactor designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Radial coordinate maps, radial vectors, and binormal vectors for 5/6, 5/5 and 5/4 edge island domains in W7-X

Abstract The edge island domain in Wendelstein 7-X consists of divertor islands whose position coincide with the location of rational values of the rotational transform - ι ≈ ( 5 / 6 , 5 / 5 , 5 / 4 ) and surround the main confinement volume (the ‘main plasma’), providing the magnetic topology for an island divertor. The 5/5 edge consists of five individual islands that are unconnected. In contrast, a single island connects onto itself after 6 or 4 toroidal transits in the 5/6 or 5/4 edge, respectively. Many interesting phenomena are related to these islands and diagnostic analyses require a mapping from ‘laboratory’ or real space coordinates to the island coordinate system (ICS). A procedure is described here to calculate several scalar and vector quantities for closed island structures which can be utilized in fast interpolation schemes for inverse maps. For the 5/5 edge, a fixed-boundary vacuum (zero beta) magneto-hydrodynamic solution of the 5/5 island is found with the Variational Moments Equilibrium Code, VMEC. The solution is compatible with already existing routines which determine the radial and binormal vectors of VMEC solutions at arbitrary laboratory coordinates. VMEC does not support solutions for the 5/4 and 5/6 islands, but the radial and binormal vectors are available in a local 2D Fourier ICS.

Physics↗

DOE OSTI2021

Optimized finite-build stellarator coils using automatic differentiation

A new stellarator coil design code is introduced that optimizes the position and winding pack orientation of finite-build coils. The new code, called flexible optimized curves in space using automatic differentiation (AD) and finite build (FOCUSADD), performs gradient-based optimization in a high-dimensional, non-convex space. The derivatives with respect to parameters of finite-build coils are easily and efficiently computed using AD. FOCUSADD parametrizes coil positions in free space using a Fourier series and uses a multi-filament approximation to the coil winding pack. The orientation of the winding pack is parametrized with a Fourier series and can be optimized as well. Optimized finite-build coils for a Wendelstein 7-X (W7-X)-like stellarator are found, and compared with filamentary coil results. The final positions of optimized finite-build W7-X-like coils are shifted, on average, by approximately 2.5 mm relative to optimized filamentary coils. These results suggest that finite-build effects should be accounted for in the optimization of stellarators with low coil tolerances.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

2D measurements of parallel counter-streaming flows in the W7-X scrape-off layer for attached and detached plasmas

Abstract Investigations of particle parallel flow velocities have been carried out for the scrape-off layer (SOL) of the Wendelstein 7-X (W7-X) stellarator, in order to gain insights on the SOL transport properties during attached and detached plasma scenarios. The experimental evidence is based on the coherence imaging spectroscopy (CIS) diagnostic, able to measure 2D impurity emission intensity and flow velocity. The impurity monitored by CIS is C 2+ , characterized by a line-emission intensity observed to be linearly proportional to the total plasma radiated power in both attached and detached plasmas. The related C 2+ velocity shows a strong dependence on the line-averaged electron density while remaining insensitive to the input power. During attached plasmas, the velocity increases with increasing line-averaged density. The tendency reverses in the transition to and during detachment, in which the velocity decreases by at least a factor of 2. The sharp drop in velocity, together with a rise in line-emission intensity, is reliably correlated to the detachment transition and can therefore be used as one of its signatures. The impurity flow velocity appears to be well coupled with the main ions’ one, thus implying the dominant role of impurity-main ion friction in the parallelimpurity transport dynamics. In view of this SOL impurity transport regime, the CIS measurement results are here interpreted with the help of EMC3-Eirene simulations, and their major trends are already explainable with a simple 1D fluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Model for current drive induced crash cycles in W7-X

In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι–profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

First-principles based plasma profile predictions for optimized stellarators

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 7-X stellarator, where the central ion temperature was 'clamped' to $T_\textrm i \approx 1.5$ keV regardless of the external heating power. By performing first-principles based simulations, we provide key evidence to understand this effect, namely the inefficient thermal coupling between electrons and ions in a turbulence-dominated regime, which is exacerbated by the large $T_\textrm e/T_\textrm i$ ratios, and show that a more efficient ion heat source, such as direct ion heating, will increase the on-axis ion temperature. This work paves the way towards the use of high-fidelity models for the development of the next generation of stellarators, in which neoclassical and turbulent transport are optimized simultaneously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Modeling of plasma beta effects on the island divertor transport in the standard configuration of W7-X

The influence of plasma beta effects on the edge plasma transport in the Wendelstein 7-X standard configuration is studied systematically by using EMC3-EIRENE combined with a 3D equilibrium code named HINT. The magnetic topology changes induced by plasma beta effects are significantly reflected in plasma transport behaviors and heat flux patterns on divertor targets. After validating the modeling strategy by comparisons with experimental data, the extended simulations for high performance plasmas show that the threshold separatrix density for accessing the power detachment is reduced in higher beta plasmas. Compared with the vacuum field case, the impurity radiation distributions with finite beta effects are modified in the magnetic island region. The divertor heat flux is distributed more evenly along the toroidal direction on the strike line at the vertical target. The strike line on the horizontal target moves towards the pumping gap with an increase in the plasma beta. In addition, the different pressure profiles with the same central beta also result in a modified heat flux pattern on the divertor targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Long plasma duration operation analyses with an international multi-machine (tokamaks and stellarators) database

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

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Validation of the ERO2.0 code using W7-X and JET experiments and predictions for ITER operation

Abstract The paper provides an overview of recent modelling of global material erosion and deposition in the fusion devices Wendelstein 7-X (W7-X), JET and ITER using the Monte-Carlo code ERO2.0. For validating the modelling tool in a three-dimensional environment, W7-X simulations are performed to describe carbon erosion from the graphite test divertor units, which were equipped in operational phase OP 1.2 and analysed post-mortem. Synthetic spectroscopy of carbon line emission is compared with experimental results from the divertor spectrometer measurement system, showing a good agreement in the e-folding lengths in the radial intensity profiles of carbon. In the case of metallic wall materials, earlier modelling of the Be/W environment in JET and ITER is revisited and extended with an updated set of sputtering and reflection data, as well as including the mixing model for describing the Be/W dynamics in the divertor. Motivated by recent H/D/T isotope experiments in JET, limited and diverted configuration pulses are modelled, showing the expected trend of both Be and W erosion increasing with isotope mass. For the JET diverted configuration pulses, it is shown that Be migrates predominantly to the upper part of the inner divertor where it initially leads to strong W erosion. With longer exposure time, the growth of a Be deposited layer leads to a reduction of W erosion in that region. A similar trend is observed in simulations of the ITER baseline Q = 10 scenario, however with a more symmetric Be migration pattern leading to deposition also on the outer divertor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Electron transport barrier and high confinement in configurations with internal islands close to the plasma edge of W7-X

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 × 10 19 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 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 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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

First experimental confirmation of island SOL geometry effects in a high radiation regime on W7-X

Abstract This work characterizes the detachment behavior and radiation characteristics of the lowiota configuration in the Wendelstein 7-X (W7-X) stellarator. The island scrape-off layer (SOL) of thelow iota has a poloidal mode number of 6 islands surrounding the last closed flux surface (LCFS).The island geometry of the low iota configuration is significantly different to that of the standardmagnetic field configuration, whose detachment characteristics have already been described in previouswork[2, 3, 4]. Experimental results show that the radiation pattern in the low iota configurationis starkly different to that of the standard magnetic field configuration, with radiation concentratedat the island SOL O-points, rather than the X-points. Additionally, this O-point localized radiationpattern is associated with unstable detachment, with both radiation oscillations in experiments and thelack of a self-consistent plasma solution at high radiated power fraction in EMC3-Eirene simulations.EMC3-Eirene simulations are used to understand the radiation distribution. It was found that the O-point localized radiation arises first from local impurity accumulation near the parallel flow stagnation,which is located close to the geometrical center of the island (”O-point”). The local cooling in thisregion leads to plasma condensation in the islands in closest magnetic connection to the divertor targetplates. The heat source to this region of the island, which is thermally isolated from the upstream heatsource in terms of parallel transport, must arise via perpendicular heat transport. This heat source isexpected to be large for the low iota configuration due to its very small internal island field line pitch.This work highlights the importance (complementary to previous work, e. g. [5, 6]) of the internalisland field line pitch not only on the radiation pattern, but also the detachment performance of theisland divertor.

Winters, Victoria (ORCID:0000000181087774)↗

DOE OSTI2024

Reduction or Enhancement of Stellarator Turbulence by Impurities

A systematic study of the impact of impurities on the turbulent heat fluxes is presented for the stellarator Wendelstein 7-X (W7-X) and, for comparison, the Large Helical Device and ITER. By means of nonlinear multispecies gyrokinetic simulations, it is shown that impurities, depending on the sign of their density gradient, can significantly enhance or reduce turbulent ion heat losses. For the relevant scenario of turbulence reduction, an optimal impurity concentration that minimizes the ion heat diffusivity emerges as a universal feature. This result demonstrates the potential of impurities for controlling turbulence and accessing enhanced confinement regimes in fusion plasmas and, in particular, in W7-X. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.

Ren, Congrong [The Ohio State Univ., Columbus, OH ↗