Stellarator Configurations Research Articles

Reduced electrostatic turbulence in the quasi-isodynamic stellarator configuration CIEMAT-QI4

Abstract CIEMAT-QI4 is a quasi-isodynamic stellarator configuration that simultaneously features very good fast-ion confinement in a broad range of β values, low neoclassical transport and bootstrap current, and ideal magnetohydrodynamic stability up to β=5%. In this paper it is shown that CIEMAT-QI4 also exhibits reduced turbulent transport. This is demonstrated through nonlinear electrostatic simulations with the gyrokinetic code stella, including kinetic ions and electrons. The relation between reduced turbulent transport and the fact that CIEMAT-QI4 very approximately satisfies the so-called maximum-J property is discussed.

Modelling of ICRH slow wave propagation and absorption in Wendelstein 7-X stellarator

Abstract The propagation and absorption of the slow waves in the three-ion plasma of the Wendelstein 7-X stellarator have been investigated by ray tracing. The aim of the study is to obtain a qualitative notion of the penetration into the plasma and absorption of the wave excited by the potential difference between the antenna conductors and the antenna box. It has been discovered that the rays propagate along the magnetic field lines over a significant distance, up to 6 m, from the antenna. They weakly, to a depth of 0.1 m, penetrate into the plasma. Absorption of the slow waves by electrons does not lead to the generation of the currents capable of affecting the plasma equilibrium. Most of the slow waves are absorbed beyond the region of ion-ion hybrid resonance in the zone of cyclotron resonance of He3 ions at the periphery of the plasma. The ICRH of the three-ion W 7-X plasma will be used to heat He3 ions to high energies and simulate the confinement of alpha particles in an optimized stellarator configuration. The presence of a source of hot He3 ions, which are poorly confined, at the periphery of the plasma can affect the experimental results.

Global fluid simulation of plasma turbulence in stellarators with the GBS code

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

Assessing core ion thermal confinement in critical-gradient-optimized stellarators

We investigate the core confinement properties of two recently devised quasi-helically symmetric stellarator configurations, HSK and QSTK. Both have been optimized for large critical gradients of the ion temperature gradient mode, which is an important driver of turbulent transport in magnetic confinement fusion devices. To predict the resulting core plasma profiles, assuming a fixed edge temperature, we utilize an advanced theoretical framework based on the gyrokinetic codes GENE and GENE-3D, coupled to the transport code TANGO. Compared to the HSX stellarator, both HSK and QSTK achieve significantly higher core-to-edge temperature ratios, partly thanks to their smaller aspect ratios, with the other part due to more detailed shaping of the magnetic geometry achieved during optimization. The computed core confinement time, however, is less sensitive to core temperature than the fixed edge temperature, simply due to the disproportionate influence, the edge has on stored plasma energy. We, therefore, emphasize the possible benefits of further optimizing turbulence in the outer core region, and the need to include accurate modeling of confinement in the edge region in order to assess overall plasma performance of turbulence optimized stellarators.

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul (Phys. Rev. Lett., vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. (Phys. Plasma, vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

Reduction of electrostatic turbulence in a quasi-helically symmetric stellarator via critical gradient optimization

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 excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill.

ParaStell: parametric modeling and neutronics support for stellarator fusion power plants

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

Global fluid turbulence simulations in the scrape-off layer of a stellarator island divertor

Isothermal fluid turbulence simulations have been performed in the edge and scrape-off layer (SOL) of an analytic stellarator configuration with an island divertor, thereby providing numerical insight into edge turbulence in regions around islands in a stellarator. The steady-state transport follows the a curvature drive that is inverse to the major radius ( $1/R$ ) toward the outboard side, but large fluctuations are present throughout the island divertor region, with the average wavelength of similar size to the island width. The system exhibits a prominent $m=2$ , $n=5$ mode, where m is the poloidal mode number and n is the toroidal mode number, although other modes are present. The amplitude and radial extent of the density fluctuations are similar throughout the edge and SOL, but can decrease near island O-points. The fluctuations exhibit a predominantly positive skewness on the outboard midplane, indicating blob-like perturbations for the transport into the outer SOL. It is determined that a point on the separatrix is generally more correlated with regions outside of the SOL than a nearby reference point which does not lie on the separatrix.

Energetic particle tracing in optimized quasi-symmetric stellarator equilibria

Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has been proven to enable the construction of magnetic configurations with good confinement properties while taking only a fraction of the usual computation time to generate optimized magnetic equilibria. However, not much is known about the overall features of fast-particle orbits computed in such analytical, yet simplified, equilibria when compared with those originating from accurate equilibrium solutions. This work aims to assess and demonstrate the potential of the near-axis expansion to provide accurate information on particle orbits and to compute loss fractions in moderate to high aspect ratios. The configurations used here are all scaled to fusion-relevant parameters and approximate quasi-symmetry to various degrees. This allows us to understand how deviations from quasi-symmetry affect particle orbits and what are their effects on the estimation of the loss fraction. Guiding-centre trajectories of fusion-born alpha particles are traced using gyronimo and SIMPLE codes under the NEAT framework, showing good numerical agreement. Discrepancies between near-axis and magnetohydrodynamic fields have minor effects on passing particles but significant effects on trapped particles, especially in quasi-helically symmetric magnetic fields. Effective expressions were found for estimating orbit widths and passing–trapped separatrix in quasi-symmetric near-axis fields. Loss fractions agree in the prompt losses regime but diverge afterwards.

The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

The separation between the last closed flux surface of a plasma and the external coils that magnetically confine it is a limiting factor in the construction of fusion-capable plasma devices. This plasma-coil separation must be large enough so that components such as a breeding blanket and neutron shielding can fit between the plasma and the coils. Plasma-coil separation affects reactor size, engineering complexity, and particle loss due to field ripple. For some plasmas it can be difficult to produce the desired flux surface shaping with distant coils, and for other plasmas it is infeasible altogether. Here, we seek to understand the underlying physics that limits plasma-coil separation and explain why some configurations require close external coils. In this paper, we explore the hypothesis that the limiting plasma-coil separation is set by the shortest scale length of the magnetic field as expressed by the ∇B tensor. We tested this hypothesis on a database of > 40 stellarator and tokamak configurations. Within this database, the coil-to-plasma distance compared to the minor radius varies by over an order of magnitude. The magnetic scale length is well correlated to the coil-to-plasma distance of actual coil designs generated using the REGCOIL method (Landreman 2017 Nucl. Fusion 57 046003). Additionally, this correlation reveals a general trend that larger plasma-coil separation is possible with a small number of field periods.

Economically optimized design point of high-field stellarator power-plant

High temperature superconductors (HTSs) expand the design space of stellarator power-plants (PPs) toward high magnetic fields B, enabling compact major radii R. The present paper scans the space of B, R and other design parameters, finding solutions that are promising from a physics and engineering standpoint, while minimizing the capital cost of the PP and the levelized cost of fusion electricity. Similarly, it identifies minimum-cost design points for next-step burning plasma stellarator experiments of fusion gain 1<Q<10 . The study assumes advanced stellarator configurations of reduced aspect ratio, heated by neutral beam injection. Plasma-facing, flowing liquid metal (LM) walls protect it from high heat and neutron fluxes. The study relies on analytical first-principle calculations, and established zero-dimensional (0D) empirical scaling laws. Power flows are illustrated by Sankey diagrams. Plasma operating contours are used to determine the reactor’s start-up path. Sensitivity analyses are conducted to identify the most critical reactor parameters within physics, engineering and costing, quantifying their influence on the economics of the PPs. Such 0D study suggests that the assumed next generation HTS, flowing LM walls, and advances in compact plasma configurations could lead to an ignited stellarator PP of aspect ratio A∼4 , R⩽4 m, B > 9 T, and normalized plasma pressure β∼5% which would minimize both the cost of electricity and capital cost while achieving a net electric power of about 1 GW.

Coherence of turbulent structures with varying drive in stellarator edge plasmas

This work investigates the parallel coherence of plasma filaments through numerical simulations using the hot-ion two-fluid hermes-2 model within the BOUT++ framework. Realistic field lines in the scrape-off layer (SOL) of magnetic fusion devices, especially in stellarator configurations possess a highly varying curvature along the magnetic field line. A varying curvature creates a parallel velocity gradient which might tear the filament apart. The main parameters controlling this process are the collisionality and the electron plasma beta. Simulations of realistic curvature variations along field lines in a circular ASDEX Upgrade-like tokamak and Wendelstein 7-X stellarator (W7-X) show the parallel displacement between different filament sections to correlate with the curvature. The rapidly varying W7-X curvature and the low average curvature drive reduce the propagation of the filament to only a few hundred meters per second. The effect of a finite ion temperature on filament propagation in a W7-X field line geometry is found to be a higher diamagnetic current resulting in stronger charge separation. This work supports simulations and experimental findings that filaments in W7-X are comparably slow due to the large major radius of the device. They do not perform ballistic motion and hence do not drive significant turbulence spreading in the SOL.

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.

A quasi-isodynamic configuration with good confinement of fast ions at low plasma β

A new quasi-isodynamic (QI) stellarator configuration optimized for the confinement of energetic ions at low plasma β is obtained. The numerical optimization is carried out using the STELLOPT suite of codes. New proxies to measure closeness to quasi-isodynamicity and quality of fast ion confinement have been included. The new configuration has poloidally closed contours of magnetic field strength, low magnetic shear and a rotational transform profile allowing an island divertor. It shows ideal and ballooning magnetohydrodynamic stability up to , reduced effective ripple, with in the plasma core. Even at low β, the configuration approximately satisfies the maximum-J property, and the confinement of fast ions is good at and becomes excellent at reactor values, . An evaluation of the D 31 neoclassical mono-energetic coefficient supports the expectation of a reduced bootstrap current for plasmas confined in QI configurations. A set of filamentary coils that preserve the good confinement of fast ions in the core is presented.

Instabilities and turbulence in stellarators from the perspective of global codes

In this work, a comparison of the global gyrokinetic codes EUTERPE and GENE-3D in stellarator configurations of the Large Helical Device (LHD) and the Wendelstein 7-X (W7-X) is carried out. In linear simulations with adiabatic electrons, excellent agreement is found in the mode numbers, growth rate, frequency, mode structure, and spatial localization of the most unstable mode in LHD. In W7-X, the dependence of the growth rate and frequency with the mode number is well reproduced by both codes. The codes are also compared in linear simulations with kinetic ions and electrons in W7-X using model profiles, and reasonable agreement is found in the wavenumber of the most unstable modes. A stabilization of small-scale modes in kinetic-electron simulations with respect to the adiabatic-electron case is consistently found in both codes. Nonlinear simulations using adiabatic electrons and model profiles are also studied and the heat fluxes are compared. Very good agreement is found in the turbulent ion heat fluxes in both LHD and W7-X. Two problems that cannot be properly accounted for in local flux tube codes are studied: the localization of instabilities and turbulence over the flux surface and the influence of a background long-wavelength electric field. Good agreement between codes is found with respect to the spatial localization of instabilities and turbulence over the flux surface. The localization of saturated turbulence is found in both codes to be much smaller than that of the linear instabilities and smaller than previously reported in full-surface radially-local simulations. The influence of the electric field on the localization is also found to be smaller in the developed turbulent sate that in the linear phase, and smaller than in previous works. A stabilizing effect of a constant electric field on the linearly unstable modes is found in both codes. A moderate reduction of turbulent transport by the radial electric field, with small dependence with the sign of the electric field, is also found.

Merging of the superbanana plateau and transport regimes in nearly quasisymmetric stellarators

Alpha particle confinement is one of the most demanding issues for stellarators. It now seems clear that it is possible to design optimized stellarators that confine the background plasma at near tokamak radial transport levels. Moreover, adequate collisionless alpha particle confinement is possible in the core of a highly optimized stellarator. Here, the collisional confinement of barely trapped alphas in an optimized stellarator is considered by accounting for the resonance due to the reversal in direction of the drift within a flux surface and investigating the sensitive role of magnetic shear in keeping this resonance close to the passing boundary in some nearly quasisymmetric stellarator configurations. The treatment relies on a narrow collisional boundary layer formulation that combines the responses of both these resonant pitch angle alphas and the remaining barely trapped alphas. A novel merged regime treatment leads to explicit expressions for the energy diffusivity for both superbanana plateau (or resonant plateau) and $\sqrt \nu$ transport in the large aspect ratio limit for a slowing down tail alpha distribution function, where $\nu$ is the effective pitch angle scattering collision frequency of the trapped alphas off the background ions. Depending on the details of the optimization scheme and the sign of the magnetic shear, modest magnetic shear can be used to reduce superbanana (or resonant) plateau transport to below the $\sqrt \nu$ transport level. In addition, a quasilinear equation retaining spatial diffusion is derived for a general alpha distribution function that allows the radial alpha transport to modify the distribution so it is no longer isotropic in velocity space.

Resonant transport of fusion alpha particles in quasisymmetric stellarators

In modern, highly optimized stellarator configurations where prompt fusion alpha particle losses from the plasma core are absent, alpha particles can still be lost due to stochastic orbits which result in delayed losses. One mechanism leading to stochastic orbits are changes in the particle trapping class during drift motion along the contours of the parallel adiabatic invariant J ∥ leading to jumps in J ∥ when crossing class boundaries. Another mechanism, which is of main interest here, is the resonance between particle drift and bounce motion (drift-orbit resonance). The first mechanism affects mainly trapped particles near the trapped-passing boundary in the phase space of quasi-symmetric and quasi-isodynamic devices, and can be minimized there by aligning local magnetic field maxima on a given flux surface. The second mechanism may affect a broader range in the trapped particle domain where contours of J ∥ still remain closed. Drift-orbit resonances modify the topology of orbits leading to island-like structures on Poincaré plots where these islands may overlap thus leading to the stochastic transport. In this report, we study this stochastization mechanism in quasi-symmetric stellarator configurations with help of the Hamiltonian drift-kinetic code NEO-RT as well as orbit classification and direct computation of fusion alpha losses within the symplectic orbit following code SIMPLE. The width and overlap of resonances in phase-space is studied using Hamiltonian perturbation theory. Based on optimized reactor configurations we assess if this approach can be used as a fast metric for fusion alpha losses in stellarator optimization.

Identification of fast ion wall loads in Wendelstein 7-X from thermographic measurements

Fast ion wall loads can result in excessively high heat fluxes to the plasma-facing components (PFCs). To allow for the development of mitigation strategies, and thereby protect the PFCs, the fast ion losses have to be predicted by faithful models. To ensure that fast ion models are an accurate representation of the real world, they need to be verified. The neutral-beam experiments performed in Wendelstein 7-X (W7-X) allow to investigate and verify models of the fast ion losses in the stellarator configuration. Infrared thermographic measurements were used to obtain the heat flux to both the baffle plates and the divertor. We found evidence of fast ion wall loads on the baffle plates, with loads between 100 kW m−2 and 1 MW m−2. The loads are attributed to fast ions which escape the main plasma via magnetic ripples. The fast ion wall loads on the baffle plates show up-down and toroidal asymmetry. The experimental results were compared to numerical simulations performed by the BEAMS3D and ASCOT codes. Qualitative agreement in up-down asymmetry is found, but the magnitude and toroidal asymmetry are not yet well predicted by the simulations. The asymmetries of the strike lines on the divertor suggest that fast ions also play a role here. Specifically, a second strike line emerged consistently in the high-iota configuration on the horizontal divertor. The shape and magnitude of the strike lines changed considerably during the neutral-beam injection (NBI) operation phase. Although no damage to steel components of W7-X was found, fast ion loads to the baffle plates could possibly limit the NBI operation in the upcoming campaigns of W7-X.

Energetic particle loss mechanisms in reactor-scale equilibria close to quasisymmetry

Collisionless physics primarily determines the transport of fusion-born alpha particles in 3D equilibria. Several transport mechanisms have been implicated in stellarator configurations, including stochastic diffusion due to class transitions, ripple trapping, and banana drift-convective orbits. Given the guiding center dynamics in a set of six quasihelical and quasiaxisymmetric equilibria, we perform a classification of trapping states and transport mechanisms. In addition to banana drift convection and ripple transport, we observe substantial non-conservation of the parallel adiabatic invariant which can cause losses through diffusive banana tip motion. Furthermore, many lost trajectories undergo transitions between trapping classes on longer time scales, either with periodic or irregular behavior. We discuss possible optimization strategies for each of the relevant transport mechanisms. We perform a comparison between fast ion losses and metrics for the prevalence of mechanisms such as banana-drift convection (Velasco et al 2021 Nucl. Fusion 61 116059), transitioning orbits, and wide orbit widths. Quasihelical configurations are found to have natural protection against ripple-trapping and diffusive banana tip motion leading to a reduction in prompt losses.

A single-field-period quasi-isodynamic stellarator

A single-field-period quasi-isodynamic stellarator configuration is presented. This configuration, which resembles a twisted strip, is obtained by the method of direct construction, that is, it is found via an expansion in the distance from the magnetic axis. Its discovery, however, relied on an additional step involving numerical optimization, performed within the space of near-axis configurations defined by a set of adjustable magnetic field parameters. This optimization, completed in 30 s on a single CPU core using the SIMSOPT code, yields a solution with excellent confinement, as measured by the conventional figure of merit for neoclassical transport, effective ripple, at a modest aspect ratio of eight. The optimization parameters that led to this configuration are described, its confinement properties are assessed and a set of magnetic field coils is found. The resulting transport at low collisionality is much smaller than that of W7-X, and the device needs significantly fewer coils because of the reduced number of field periods.