Helically Symmetric Experiment Research Articles

On the effect of flux-surface shaping on trapped-electron modes in quasi-helically symmetric stellarators

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

Including the parallel mass flow in calculating the steady-state solutions and stability of the momentum balance equations for a quasisymmetric stellarator

The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices.

The universal instability in optimised stellarators

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

Optimizing the HSX stellarator for microinstability by coil-current adjustments

The optimization of helically symmetric experiment (HSX) for reduced microinstability has been achieved by examining a large set of configurations within a neighborhood of the standard operating configuration. This entailed generating a database of more than 106 magnetic-field configurations for HSX by varying the currents in external coils. Using a set of volume-averaged metrics and gyrokinetic simulations, this database has helped to identify a set of configurations that can be used to regulate trapped-electron-mode stability in HSX. This set of configurations is also found to correlate flux-surface elongation and triangularity with an increase in magnetic-well depth, an increase in rotational transform, and low neoclassical heat-flux relative to the standard quasi-helically-symmetric configuration. These results demonstrate sensitivity of plasma behavior in response to changes in a 3D magnetic field to both neoclassical and gyrokinetic models, and the experimental potential in HSX to explore turbulence optimization. This perturbative optimization approach is not unique to HSX, and can readily be deployed on existing fusion devices to identify novel magnetic-fields to be used in turbulence-optimization experiments.

Upgrade of the helically symmetric experiment Thomson scattering diagnostic suite.

The Helically Symmetric eXperiment (HSX) Thomson Scattering (TS) diagnostic is being upgraded to decrease uncertainty in electron temperature and density measurements. Upgrades to the HSX TS diagnostic will consist of a novel redesign of polychromator electronics and digitization of the TS output signal. Here, we also present a study of the benefits of an additional spectral channel that will sample the red-shifted band of the scattered spectrum. To maximize system bandwidth (BW) and gain, while minimizing noise, the existing low-BW polychromator electronics on HSX will be replaced by high-BW, high gain circuitry designed in-house.

Kinetic-ballooning-mode turbulence in low-average-magnetic-shear equilibria

Kinetic-ballooning-mode (KBM) turbulence is studied via gyrokinetic flux-tube simulations in three magnetic equilibria that exhibit small average magnetic shear: the Helically Symmetric eXperiment (HSX), the helical-axis Heliotron-J and a circular tokamak geometry. For HSX, the onset of KBM being the dominant instability at low wavenumber occurs at a critical value of normalized plasma pressure $\beta ^{\rm KBM}_{\rm crit}$ that is an order of magnitude smaller than the magnetohydrodynamic (MHD) ballooning limit $\beta ^{\rm MHD}_{\rm crit}$ when a strong ion temperature gradient (ITG) is present. However, $\beta ^{\rm KBM}_{\rm crit}$ increases and approaches the MHD ballooning limit as the ITG tends to zero. For these configurations, $\beta ^{\rm KBM}_{\rm crit}$ also increases as the magnitude of the average magnetic shear increases, regardless of the sign of the normalized magnetic shear. Simulations of Heliotron-J and a circular axisymmetric geometry display behaviour similar to HSX with respect to $\beta ^{\rm KBM}_{\rm crit}$ . Despite large KBM growth rates at long wavelengths in HSX, saturation of KBM turbulence with $\beta > \beta _{\rm crit}^{\rm KBM}$ is achievable in HSX and results in lower heat transport relative to the electrostatic limit by a factor of roughly five. Nonlinear simulations also show that KBM transport dominates the dynamics when KBMs are destabilized linearly, even if KBM growth rates are subdominant to ITG growth rates.

Development of beam emission spectroscopy in the helically symmetric experiment stellarator

This study shows the feasibility of a beam emission spectroscopy (BES) diagnostic in the Helically Symmetric eXperiment (HSX) stellarator for obtaining the spatiotemporal structure of density fluctuation. A beam emission simulation was applied to HSX plasmas to design and optimize viewing chords and to estimate the beam emission spectrum. A Doppler-shifted beam emission spectrum was measured from a 30 kV, 4A diagnostic neutral beam injected into HSX plasmas. The beam emission was measured with a high-time-resolution avalanche photodiode (APD) assembly to determine the feasibility of BES in HSX. For HSX plasmas heated by 28GHz electron cyclotron heating, a mode around f = 15 kHz was observed in the BES signal. The coherence between the BES signal and the density fluctuation measured by an interferometer system was significant. A plan for improving the BES system to enable the measurement of higher frequency related to turbulent transport is presented. The array of sightlines proposed in this study can be used to measure beam emission with a Doppler shift larger than 3nm (blue shift), which enables the use of a wide passband interference filter to obtain higher throughput. The adoption of a large objective optics and a chilled APD assembly will improve the signal-to-noise ratio.

Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators

The linear collisionless damping of zonal flows is calculated for quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and full-volume geometry. Equilibria are studied from the quasi-helical symmetry configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry configuration of HSX, and the quasi-axial symmetry geometry of the National Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time damping affect the zonal flow evolution, and the zonal flow residual goes to zero for small radial wavenumber. The oscillation frequency and damping rate depend on the bounce-averaged radial particle drift in accordance with theory. While each flux tube on a flux surface is unique, several different flux tubes in HSX or NCSX can reproduce the zonal flow damping from a flux-surface calculation given an adequate parallel extent. The flux-surface or flux-tube calculations can accurately reproduce the full-volume long-time residual for moderate kx, but the oscillation and damping time scales are longer in local representations, particularly for small kx approaching the system size.

Stellarator microinstabilities and turbulence at low magnetic shear

Gyrokinetic simulations of drift waves in low-magnetic-shear stellarators reveal that simulation domains comprised of multiple turns can be required to properly resolve critical mode structures important in saturation dynamics. Marginally stable eigenmodes important in saturation of ion temperature gradient modes and trapped electron modes in the Helically Symmetric Experiment (HSX) stellarator are observed to have two scales, with the envelope scale determined by the properties of the local magnetic shear and an inner scale determined by the interplay between the local shear and magnetic field-line curvature. Properly resolving these modes removes spurious growth rates that arise for extended modes in zero-magnetic-shear approximations, enabling use of a zero-magnetic-shear technique with smaller simulation domains and attendant cost savings. Analysis of subdominant modes in trapped electron mode (TEM)-driven turbulence reveals that the extended marginally stable modes play an important role in the nonlinear dynamics, and suggests that the properties induced by low magnetic shear may be exploited to provide another route for turbulence saturation.

Impact of magnetic islands in the plasma edge on particle fueling and exhaust in the HSX and W7-X stellarators

The edge magnetic structure in the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X) stellarators has been shown to have a significant impact on the particle fueling and exhaust of the plasma main species (hydrogen) as well as impurity helium. For HSX, the plasma sourcing to exhaust ratio, quantified by the effective and global particle confinement times τp* and τp,H, respectively, increases when a magnetic island chain is located in the plasma edge. The fueling efficiency is reduced by 25% when the plasma boundary is deformed by the magnetic islands. The X-point geometry also yields higher plasma temperatures in front of the main recycling region. When the island is moved radially inward, both τp* and τp decrease by 10%–25% depending on plasma density. The τp,H results rely heavily on EMC3-EIRENE modeling which confirms reduced fueling efficiency due to more rapid ionization in the outward shifted island position. These findings suggest that for a helically optimized system like HSX, the plasma fueling from the recycling source, as well as from active gas injection, can be controlled by the magnetic island chain in the plasma edge—which is a basic requirement for a divertor system. This process is also effective for the control of effective helium exhaust times, as τp,He* measured by perturbative gas puff experiments is reduced by up to 40% when the islands are shifted inwards. For Wendelstein 7-X, a similar reduction of τp,He* was inferred when magnetic islands were moved from the far plasma edge into the confined plasma region. However, the effective confinement features of H as the main plasma species were not affected due to the non-optimal position of the magnetic islands with respect to the highly localized ionization domain during the limiter startup campaign.

Development of a 3-D visible limiter imaging system for the HSX stellarator.

A visible camera diagnostic has been developed to study the Helically Symmetric eXperiment (HSX) limiter plasma interaction. A straight line view from the camera location to the limiter was not possible due to the complex 3D stellarator geometry of HSX, so it was necessary to insert a mirror/lens system into the plasma edge. A custom support structure for this optical system tailored to the HSX geometry was designed and installed. This system holds the optics tube assembly at the required angle for the desired view to both minimize system stress and facilitate robust and repeatable camera positioning. The camera system has been absolutely calibrated and using Hα and C-III filters can provide hydrogen and carbon photon fluxes, which through an S/XB coefficient can be converted into particle fluxes. The resulting measurements have been used to obtain the characteristic penetration length of hydrogen and C-III species. The hydrogen λiz value shows reasonable agreement with the value predicted by a 1D penetration length calculation.

HSX as an example of a resilient non-resonant divertor

This paper describes an initial description of the resilient divertor properties of quasi-symmetric (QS) stellarators using the HSX (Helically Symmetric eXperiment) configuration as a test-case. Divertors in high-performance QS stellarators will need to be resilient to changes in plasma configuration that arise due to evolution of plasma pressure profiles and bootstrap currents for divertor design. Resiliency is tested by examining the changes in strike point patterns from the field line following, which arise due to configurational changes. A low strike point variation with high configuration changes corresponds to high resiliency. The HSX edge displays resilient properties with configuration changes arising from the (1) wall position, (2) plasma current, and (3) external coils. The resilient behavior is lost if large edge islands intersect the wall structure. The resilient edge properties are corroborated by heat flux calculations from the fully 3-D plasma simulations using EMC3-EIRENE. Additionally, the strike point patterns are found to correspond to high curvature regions of magnetic flux surfaces.

A synthetic diagnostic for beam emission spectroscopy in the helically symmetric experiment stellarator.

The Helically Symmetric Experiment (HSX) has a number of active spectroscopy diagnostics. Due to the relatively large beam width compared to the plasma minor radius, it is difficult to achieve good spatial resolution at the core of the HSX plasma. This is due to the fact that the optical sightline cuts through many flux surfaces with varying field vectors within the beam. In order to compare the experimental results with theoretical models it is important to accurately model the beam width effects. A synthetic diagnostic has been developed for this purpose. This synthetic diagnostic calculates the effect of spot size and beam width on the measurements of quantities of interest, including radial electric field, flow velocity, and Stark polarization.

Three-dimensional scrape off layer transport in the helically symmetric experiment HSX

The edge topology of helically symmetric experiment (HSX) in the quasi-helically symmetric configuration is characterized by an 8/7 magnetic island remnant embedded in a short connection length scrape-off layer (SOL) domain. A 2D mapping of edge plasma profiles within this heterogeneous SOL has been constructed using a movable, multi-pin Langmuir probe. Comparisons of these measurements to edge simulations using the EMC3-EIRENE 3D plasma fluid and kinetic neutral gas transport model have been performed. The measurements provide strong evidence that particle transport is diffusive within the island region and dominantly convective in the SOL region. Measurements indicate that phenomenological cross-field diffusion coefficients are low in the SOL region between the last closed flux surface and edge island (i.e. m2 s−1). This level of transport was found to increase by a factor of two when a limiter is inserted almost completely into the magnetic island. A reduction in gradients of the edge electrostatic plasma potential was also measured in this configuration, suggesting that the reduced electric field may be linked to the increased cross-field transport observed.

Ray tracing and ECRH absorption modeling in the HSX stellarator

To increase flexibility in ECRH experiments on the helically symmetric experiment (HSX), a second gyrotron and transmission line have been installed. The second antenna includes a steerable mirror for off-axis heating, and the launched power may be modulated for use in heat pulse propagation experiments. The extraordinary wave at the second harmonic of the electron gyrofrequency or the ordinary wave at the fundamental resonance are used for plasma start-up and heating on HSX. The tracing visualized ray tracing code (Marushchenko et al 2007 Plasma Fusion Res. 2 S1129) is used to estimate single-pass absorption and to model multi-pass wave damping in the three-dimensional HSX geometry. The single-pass absorption of the ordinary wave at the fundamental resonance is calculated to be as high as 30%, while measurements of the total absorption indicate that 45% of the launched power is absorbed. A multi-pass ray tracing model correctly predicts the experimental absorption and indicates that the launched power is absorbed within the plasma core ().

Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator

Gyrokinetic simulations of plasma microturbulence in the Helically Symmetric eXperiment are presented. Using plasma profiles relevant to experimental operation, four dominant drift wave regimes are observed in the ion wavenumber range, which are identified as different flavors of density-gradient-driven trapped electron modes. For the most part, the heat transport exhibits properties associated with turbulence driven by these types of modes. Additionally, long-wavelength, radially localized, nonlinearly excited coherent structures near the resonant central flux surface, not predicted by linear simulations, can further enhance flux levels. Integrated heat fluxes are compatible with experimental observations in the corresponding density gradient range. Despite low shearing rates, zonal flows are observed to regulate turbulence but can be overwhelmed at higher density gradients by the long-wavelength coherent structures.

Profile stiffness measurements in the Helically Symmetric experiment and comparison to nonlinear gyrokinetic calculationsa)

Stiffness measurements are presented in the quasi-helically symmetric experiment (HSX), in which the neoclassical transport is comparable to that in a tokamak and turbulent transport dominates throughout the plasma. Electron cyclotron emission is used to measure the local electron temperature response to modulated electron cyclotron resonant heating. The amplitude and phase of the heat wave through the steep electron temperature gradient (ETG) region of the plasma are used to determine a transient electron thermal diffusivity that is close to the steady-state diffusivity. The low stiffness in the region between 0.2 ≤ r/a ≤ 0.4 agrees with the scaling of the steady-state heat flux with temperature gradient in this region. These experimental results are compared to gyrokinetic calculations in a flux-tube geometry using the gyrokinetic electromagnetic numerical experiment code with two kinetic species. Linear simulations show that the ETG mode may be experimentally relevant within r/a ≤ 0.2, while the Trapped Electron Mode (TEM) is the dominant long-wavelength microturbulence instability across most of the plasma. The TEM is primarily driven by the density gradient. Non-linear calculations of the saturated heat flux driven by the TEM and ETG bracket the experimental heat flux.

Modeling, measurement, and 3-D equilibrium reconstruction of the bootstrap current in the Helically Symmetric Experiment

The bootstrap current for three electron cyclotron resonance heated plasma scenarios in a quasihelically symmetric stellarator (the Helically Symmetric Experiment) are analyzed and compared to a neoclassical transport code PENTA. The three conditions correspond to 50 kW input power with a resonance that is off-axis, 50 kW on-axis heating and 100 kW on-axis heating. When the heating location was moved from off-axis to on-axis with 50 kW heating power, the stored energy and the extrapolated steady-state current were both observed to increase. When the on-axis heating power was increased from 50 kW to 100 kW, the stored energy continued to increase while the bootstrap current slightly decreased. This trend is qualitatively in agreement with the calculations which indicate that a large positive electric field for the 100 kW case was driving the current negative in a small region close to the magnetic axis and accounting for the decrease in the total integrated current. This trend in the calculations is only observed to occur when momentum conservation between particle species is included. Without momentum conservation, the calculated bootstrap current increases monotonically. We show that the magnitude of the bootstrap current as calculated by PENTA agrees better with the experiment when momentum conservation between plasma species is included in the calculation. The total current was observed in all cases to flow in a direction to unwind the transform, unlike in a tokamak in which the bootstrap current adds to the transform. The 3-D inductive response of the plasma is simulated to predict the evolution of the current profile during the discharge. The 3-D equilibrium reconstruction code V3FIT is used to reconstruct profiles of the plasma pressure and current constrained by measurements with a set of magnetic diagnostics. The reconstructed profiles are consistent with the measured plasma pressure profile and the simulated current profile when the reconstruction is constrained by the measured data from a diagnostic array that is internal to the vacuum chamber.

Simulations of edge configurations in quasi-helically symmetric geometry using EMC3–EIRENE

Simulations of the edge of a quasi-helically symmetric (QHS) stellarator with geometry based on the Helically Symmetric eXperiment (HSX) are performed using the coupled codes EMC3–EIRENE. The standard configuration of HSX has an island structure outside the separatrix, corresponding to the 8/7 resonance. In addition to the standard configuration, two other configurations are examined: one with small islands outside the separatrix corresponding to the 16/15 resonance, and one with large islands corresponding to the 4/4 resonance. Using EMC3–EIRENE, density scans are employed, while scaling input power linearly with density, in order to determine the transition point from a low- to a high-recycling regime. The small island and the standard cases show markedly similar behaviour, but the large island configuration transitions to high-recycling and detached regimes at significantly lower plasma densities. Reducing the perpendicular diffusion coefficients creates behaviour more consistent with two-point model predictions by reducing the role of perpendicular transport through edge islands and reducing friction loss from counter-streaming parallel flows. When carbon impurities are added, the large island configuration exhibits a large increase in radiated power, while the two configurations with smaller islands do not.

Core density gradient fluctuation measurement by differential interferometry in the helically symmetric experiment stellarator

The interferometer system on the Helically Symmetric eXperiment (HSX) stellarator uses an expanded beam and linear detector array to realize a multichord measurement. Unlike conventional interferometry which determines the plasma phase shift with respect to a reference, directly evaluating the phase between two adjacent chords can be employed to measure the change in plasma phase with impact parameter. This approach provides a measure of the equilibrium density gradient or the density gradient fluctuations and is referred to as differential interferometry. For central chords, measurements are spatially localized due to a geometrical weighting factor and can provide information on core density gradient fluctuations. The measurement requires finite coherence between fluctuations in the two spatially offset chords. This technique is applied on the HSX stellarator to measure both broadband turbulence and coherent modes. Spatial localization is exploited to isolate core turbulence changes associated with change in magnetic configuration or heating location.