Stellarator Configurations Research Articles

Near-magnetic-axis geometry of a closely quasi-isodynamic stellarator

It is shown that the condition of stationary second adiabatic invariant at the magnetic axis of a stellarator configuration can be satisfied to good accuracy for all reflected particles.

Self-consistent simulations of nonlinear magnetohydrodynamics and profile evolution in stellarator configurations

Self-consistent extended MHD framework is used to investigate nonlinear macroscopic dynamics of stellarator configurations. In these calculations, initial conditions are given by analytical 3-D vacuum solutions. Finite beta discharges in a straight stellarator are simulated. Vacuum magnetic fields are applied to produce stellarator-like rotational transform profiles with iota(0) ≤ 0.5 and iota(0) ≥ 0.5. The vacuum magnetic fields are either helically symmetric or spoiled by the presence of magnetic harmonics of incommensurate helicity. As heat is added to the system, pressure-driven instabilities are excited when a critical β is exceeded. These instabilities may grow to large amplitude and effectively terminate the discharge, or they may saturate nonlinearly as the configuration evolves. In all of these studies, anisotropic heat conduction is allowed with κ∥/κ⊥=104−107.

Comparing linear ion-temperature-gradient-driven mode stability of the National Compact Stellarator Experiment and a shaped tokamak

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 and the stronger shaping of ARIES-AT. While a concern was that the narrow cross section of NCSX at some toroidal locations would result in steep gradients that drive instabilities more easily, it is found that other stabilizing effects of the stellarator configuration offset this so that the normalized critical gradients for NCSX are competitive with or even better than for the tokamak. For the adiabatic ITG mode, NCSX and the tokamak had similar adiabatic ITG mode critical gradients, although beyond marginal stability, NCSX had larger growth rates. However, for the kinetic ITG mode, NCSX had a higher critical gradient and lower growth rates until a/LT≈1.5 a/LT,crit, when it surpassed the tokamak's. A discussion of the results presented with respect to a/LT vs. R/LT is included.

Gyrokinetic TEM stability calculations for quasi-isodynamic stellarators

Recent theoretical findings suggest that in perfectly quasi-isodynamic stellarators, the trapped-particle instability as well as the ordinary electron-density-gradient-driven trapped-electron mode are stable in the electrostatic and collisionless approximation. In these configurations contours of constant magnetic field strength B are poloidally closed, the second adiabatic invariant J is constant on flux surfaces and peaks in the centre. It follows that the diamagnetic drift frequency ω*α and the bounce-averaged magnetic drift frequency are in opposite directions, 0, everywhere on the flux surface. This is the signature of average "good curvature" for trapped particles and, thanks to this property, particles that bounce faster than the frequency of any unstable mode must draw energy from it near marginal stability. Consequently, the point of marginal stability cannot exist for the collisionless trapped-particle mode, and hence this mode will be absent. By a similar argument, the ordinary trapped-electron mode is also stable. Because perfect quasi-isodynamicity can never be reached, it is necessary to test configurations approaching quasi-isodynamicity numerically in order to probe their resilience against trapped-particle modes. Progress has been made to extend gyrokinetic simulations to stellarator geometries, enabling us to perform the first linear gyrokinetic simulations of density-gradient-driven modes in stellarator configurations approaching quasi-isodynamicity, such as Wendelstein 7-X and more recently found configurations. These simulations appear to confirm the analytical predictions.

Stellarator Configuration Improvement Using High Temperature Superconducting Monoliths

Substantial advances have been made in the design of stellarator configurations to satisfy physics properties and fabrication feasibility requirements for experimental devices. However, reactors will require further advances in configuration design, in particular with regard to maintenance and operational characteristics, in order to have high availability. The diamagnetic properties of bulk high temperature superconductor (HTS) material can be used to provide simple mechanisms for magnetic field-shaping by arranging them appropriately in an ambient field produced by relatively simple coils.A stellarator configuration has been developed based on this concept. A small number of toroidal field coils carrying appropriate current would be sufficient to create a background toroidal field. Discrete HTS monoliths (“pucks” or “tiles”) are placed on a shaped structure that can be split in the poloidal direction at arbitrary locations. This allows modular stellarators to be designed with large openings that provide access to remove interior plasma facing components, no longer restricted by highly shaped back legs of the modular coil winding. Unlike a coil, the structure can be assembled and disassembled in pieces of convenient size, facilitating maintenance.Calculations of the effect of the use of monoliths for field modification in stellarators and tokamaks will be described.

Experimental Investigation of the Magnetic Configuration Dependence of Turbulent Transport

The dependence of turbulent transport on magnetic field properties is measured in detail on a plasma in a stellarator configuration. Pronounced poloidal asymmetries of fluctuation amplitudes and turbulent transport are observed. The transport maximum is located in regions where normal curvature of the magnetic field is negative and simultaneously the geodesic curvature has positive values. A major role of the local magnetic shear cannot be confirmed. The results can have important implications for the optimization of stellarators and the power influx into the scrape-off layer.

Destruction of hyperbolic magnetic axes in steady three-dimensional toroidal magnetic structures

A study is made of the boundary regions of magnetic structures formed either near the last closed flux surface of the main magnetic configuration in a stellarator or near magnetic islands in more general toroidal confinement systems with topologically equivalent sheared magnetic configurations. With a relatively simple approximate analytic model based on the perturbation method, it was possible not only to reproduce earlier results on the destruction of hyperbolic magnetic axes in the three-dimensional toroidal magnetic configurations under consideration but also to obtain some new results, in particular, to analytically estimate the sizes of the separatrix regions of stochastic magnetic fields that arise in the main stellarator configuration and also near the inner chains of magnetic islands in any magnetic configuration under consideration. It is notable that the boundary region of the main stellarator magnetic configuration is a multiply connected structure, the outer part of which is largely governed by the current distribution in the magnetic system creating this configuration.

Three-dimensional effects on energetic particle confinement and stability

Energetic particle populations in magnetic confinement systems are sensitive to symmetry-breaking effects due to their low collisionality and long confined path lengths. Broken symmetry is present to some extent in all toroidal devices. As such effects preclude the existence of an ignorable coordinate, a fully three-dimensional analysis is necessary, beginning with the lowest order (equilibrium) magnetic fields. Three-dimensional techniques that have been extensively developed for stellarator configurations are readily adapted to other devices such as rippled tokamaks and helical states in reversed field pinches. This paper will describe the methods and present an overview of recent examples that use these techniques for the modeling of energetic particle confinement, Alfvén mode structure and fast ion instabilities.

Effects of Three-Dimensional Magnetic Field Structure on MHD Equilibrium and Stability

The stellarator and heliotron are alternate candidates for magnetically confined fusion devices. A major difference is the source of the rotational transform ι = 1/q. In tokamaks, the rotational transform ι is produced by coupling the symmetric toroidal field and the poloidal field produced by the plasma current along the toroidal direction. Strictly speaking, the tokamak configuration can be assumed to be a two-dimensional (2-D) system. Note that the rotational transform does not exist for the vacuum. For stellarator and heliotron configurations, the rotational transform is produced by the shaping of flux surfaces. To shape flux surfaces, the vacuum magnetic field is produced by external coils with helical-winding laws. This means the vacuum magnetic field produced for the vacuum is intrinsically three dimensional (3-D). Thus, the plasma current is not required to make flux surfaces. This characteristic is an advantage. Since the plasma current is not necessary, disruptions do not appear and steady-state operation is possible. However, because of the 3-D plasma responses, experimental and theoretical studies become more complex.

Simulation of Residual Zonal Flow Levels in Stellarators Including a Radial Electric Field

AbstractResults from simulations of the Rosenbluth‐Hinton initial value problem for different stellarator configurations using the global gyrokinetic code EUTERPE are shown. Especially the influence of an external radial electric field on the residual flow level is investigated. It is found that generally an external field can lead to an increase in the flow levels for small to moderate Mach numbers (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Clustered frequency analysis of shear Alfvén modes in stellarators

The shear Alfvén spectrum in three-dimensional configurations, such as stellarators and rippled tokamaks, is more densely populated due to the larger number of mode couplings caused by the variation in the magnetic field in the toroidal dimension. This implies more significant computational requirements that can rapidly become prohibitive as more resolution is requested. Alfvén eigenfrequencies and mode structures are a primary point of contact between theory and experiment. A new algorithm based on the Jacobi–Davidson method is developed here and applied for a reduced magnetohydrodynamics model to several stellarator configurations. This technique focuses on finding a subset of eigenmodes clustered about a specified input frequency. This approach can be especially useful in modeling experimental observations, where the mode frequency can generally be measured with good accuracy and several different simultaneous frequency lines may be of interest. For cases considered in this paper, it can be a factor of 102–103 times faster than more conventional methods.

A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations

The GENE/GIST code package is developed for the investigation of plasma microturbulence, suitable for both stellarator and tokamak configurations. The geometry module is able to process typical equilibrium files and create the interface for the gyrokinetic solver. The analytical description of the method for constructing the geometric elements is documented, together with several numerical evaluation tests. As a concrete application of this product, a cross-machine comparison of the anomalous ion heat diffusivity is presented.

Engineering Accomplishments in the Construction of NCSX

The National Compact Stellarator Experiment (NCSX) was designed to test a compact, quasi-axisymmetric stellarator configuration. Flexibility and accurate realization of its complex 3D geometry were key requirements affecting the design and construction. While the project was terminated before completing construction, there were significant engineering accomplishments in design, fabrication, and assembly. The design of the stellarator core device was completed. All of the modular coils, toroidal field coils, and vacuum vessel sectors were fabricated. Critical assembly steps were demonstrated. Engineering advances were made in the application of CAD modeling, structural analysis, and accurate fabrication of complex-shaped components and sub-assemblies. The engineering accomplishments of the project are summarized.

Momentum correction techniques for neoclassical transport in stellarators

In the traditional neoclassical ordering for stellarators, monoenergetic transport coefficients are evaluated using the simplified Lorentz form of the pitch-angle collision operator which violates momentum conservation. In this paper, the parallel momentum balance with radial parallel momentum transport and viscosity terms is analyzed, in particular, with respect to the radial electric field. Next, the impact of momentum conservation in the stellarator long-mean-free-path regime is estimated for the radial transport and the parallel electric conductivity. Two different momentum correction techniques are described based on monoenergetic transport coefficients calculated by the DKES code [W. I. van Rij and S. P. Hirshman, Phys. Fluids B 1, 563 (1989)]. The benchmarking of the parallel electric conductivity and of the bootstrap current is presented for a tokamak as well as for two W7-X stellarator configurations [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)]. Finally, the impact of the momentum correction on the expected total bootstrap current is briefly analyzed for two W7-X scenarios.

Fast recovery of the magnetic vacuum configurations of the WEGA stellarator with error field effects

With a background of having obtained positive results with function parametrization (FP) applied to stellarator configurations, the technique was used once again for recovering the vacuum magnetic field configurations of the WEGA stellarator including the main symmetry-breaking magnetic islands. A classical stellarator of type l = 2, WEGA has an inherent n = 1 (leading order) field perturbation responsible for these islands. The perturbation is assumed to be generated by a misalignment between the centres of the toroidal and helical field generating coil systems. These n = 1-periodic WEGA configurations, displaying no stellarator symmetry, were numerically generated around the experimental boundaries and analysed with FP. For the first time FP models with 4th order polynomials and non-linear regressions with rational functions were needed to parametrize the physical state of the configurations. Modelling of the widths of the magnetic islands was challenging, however. The FP-functions are in the process of being implemented to run with the WEGA control system.

Physics Design for ARIES-CS

Novel stellarator configurations have been developed for ARIES-CS. These configurations are optimized to provide good plasma confinement and flux surface integrity at high beta. Modular coils have been designed for them in which the space needed for the breeding blanket and radiation shielding was specifically targeted such that reactors generating GW electrical powers would require only moderate major radii (<10 m). These configurations are quasi-axially symmetric in the magnetic field topology and have small numbers of field periods (≤3) and low aspect ratios (≤6). The baseline design chosen for detailed systems and power plant studies has three field periods, aspect ratio 4.5, and major radius 7.5 m operating at β ~ 6.5% to yield 1 GW of electric power. The shaping of the plasma accounts for ≥75% of the rotational transform. The effective helical ripples are very small (<0.6% everywhere), and the energy loss of alpha particles is calculated to be ≤5% when operating in high-density regimes. An interesting feature in this configuration is that instead of minimizing all residues in the magnetic spectrum, we preferentially retained a small amount of the nonaxisymmetric mirror field. The presence of this mirror and its associated helical field alters the ripple distribution, resulting in the reduced ripple-trapped loss of alpha particles despite the long connection length in a tokamak-like field structure. Additionally, we discuss two other potentially attractive classes of configurations, both quasi-axisymmetric: one with only two field periods, very low aspect ratios (~2.5), and less complex coils, and the other with the plasma shaping designed to produce low-shear rotational transform so as to ensure the robustness and integrity of flux surfaces when operating at high β.

The ARIES-CS Compact Stellarator Fusion Power Plant

An integrated study of compact stellarator power plants, ARIES-CS, has been conducted to explore attractive compact stellarator configurations and to define key research and development (R&D) areas. The large size and mass predicted by earlier stellarator power plant studies had led to cost projections much higher than those of the advanced tokamak power plant. As such, the first major goal of the ARIES-CS research was to investigate if stellarator power plants can be made to be comparable in size to advanced tokamak variants while maintaining desirable stellarator properties. As stellarator fusion core components would have complex shapes and geometry, the second major goal of the ARIES-CS study was to understand and quantify, as much as possible, the impact of the complex shape and geometry of fusion core components. This paper focuses on the directions we pursued to optimize the compact stellarator as a fusion power plant, summarizes the major findings from the study, highlights the key design aspects and constraints associated with a compact stellarator, and identifies the major issues to help guide future R&D.

Systems Studies and Optimization of the ARIES-CS Power Plant

A stellarator systems/optimization code is used to optimize the ARIES-CS fusion power plant parameters for minimum cost of electricity subject to a large number of physics, engineering, and in-vessel component constraints for a compact stellarator configuration. Different physics models, reactor component models, and costing algorithms are used to test sensitivities to models and assumptions. The most important factors determining the size of the fusion power core are the allowable neutron and radiative power fluxes to the wall, the distance needed between the edge of the plasma and the nonplanar magnetic field coils for the intervening components, and an adequate tritium breeding ratio. The magnetic field and coil parameters are determined from both plasma performance and constraints on the Nb3Sn superconductor. The same costing approach and algorithms used in previous ARIES studies are used with updated material costs. The result is a compact stellarator reactor with a major radius close to that of tokamaks. A one-dimensional power balance code is used to study the path to ignition and the effect of different plasma and confinement assumptions on plasma performance for the reference plasma and coil configuration. A number of variations are studied that affect the size and cost of the fusion power core: maximum field at the coils, component cost penalties, a different blanket and shield approach, alternative plasma and coil configurations, etc. Comparisons are made with some earlier ARIES power plant studies. A number of issues for the development of compact quasi-axisymmetric stellarators are identified.

Design and performance study of the helium-cooled T-tube divertor concept

The ARIES-CS study has been launched with the goal of developing through physics and engineering optimization an attractive power plant concept based on a compact stellarator configuration. The study included an effort to characterize the divertor location and corresponding heat load distribution, and to develop a He-cooled divertor concept that could accommodate a heat flux of at least 10 MW/m 2, and that would integrate well with the other power core components. This paper describes the design study of this divertor concept, which, although developed for a compact stellarator, is well suited for a tokamak configuration also.

Recent progress in the ARIES compact stellarator study

An integrated study of compact stellarator power plants, ARIES-CS, was initiated recently to explore attractive compact stellarator configurations and to define key R&D areas. Optimization of any stellarator configuration represents a large number of trade-offs among physics parameters and engineering constraints. As such, the ARIES-CS study was divided into three phases. The first phase was devoted to initial exploration of physics and engineering options, requirements, and constraints. In the second phase, we explored the configuration space for compact stellarators, aiming at configurations that satisfy physics/engineering constraints. This paper summarizes our work to date. We have identified several promising quasi-axisymmetric configurations, all aimed at low plasma aspect ratios and compact size. In each case, trade-offs among plasma parameters (e.g., α-particle loss versus β) were explored. Modular coils were designed to examine the geometric complexity and the constraints of the maximum field, desirable coil-plasma and coil-coil spacing, etc. Our examination of engineering options is reported here. In particular, we find that by employing “shield-only” zones in strategic areas, the minimum plasma-coil distance can be reduced by ∼40%. This approach, together with the relatively low aspect ratio of quasi-axisymmetric stellarators leads to devices which are similar in size to advanced tokamak power plants.