Quasi-axisymmetric Stellarator Research Articles

Linear stability studies for a quasi-axisymmetric stellarator configuration including effects of parallel viscosity, plasma flow, and resistive walls

We present linear stability studies performed with the newly developed CASTOR3D code. This code is a very flexible and versatilely applicable numerical tool to study the stability properties of 3D equilibria. Ideal external kink modes of a quasi-axisymmetric (QA) equilibrium are investigated taking into account effects of parallel viscosity, plasma flow, and resistive walls. The results are compared with those obtained for an axisymmetric approximation of this equilibrium. Two major differences in the stability properties are found: (i) the QA equilibrium is vertically stable, while the axisymmetric equilibrium is vertically unstable; (ii) a mode of the QA equilibrium only oscillates when the plasma rotates with a minimum rotation frequency, or faster. This mininum rotation frequency depends on the n*-type of mode (with n* being the dominant toroidal Fourier harmonic contributing to the mode). Resistive wall structures in combination with plasma flow, however, lead to resistive wall modes and/or plasma modes for both types of equilibria.

Engineering Design of the Chinese First Quasi-Axisymmetric Stellarator (CFQS)

The Chinese First Quasi-Axisymmetric Stellarator (CFQS) is being constructed as an international joint project between the National Institute for Fusion Science in Japan and Southwest Jiaotong University in China. It is being designed as a low-aspect-ratio quasi-axisymmetric stellarator with a modular coil system in a CHS-qa configuration. The physics design is almost finished, and we are now proceeding with the engineering design. Its physical properties are as follows: toroidal periodic number m = 2, aspect ratio Ap = 4, magnetic field strength Bt = 1 T, major radius R0 = 1 m, and typical rotational transform iota-bar = 0.4 in the all-radial region. We are currently evaluating the design's technical feasibility and manufacturability using a 3D CAD system, together with structural and electromagnetic analysis software. This paper reports on the CFQS's feasibility from an engineering design viewpoint. We are currently targeting 16 normal conducting modular coils, divided into four types, and a total current of 5MAT. Each coil has a rectangular cross section of 132×69 mm2, and is composed of 72 hollow copper conductors with water-cooling holes. These conductors carry currents of 4.3 kA, with a current density of 74 A/mm2.

Current Status of NIFS-SWJTU Joint Project for Quasi-Axisymmetric Stellarator CFQS

Current Status of NIFS-SWJTU Joint Project for Quasi-Axisymmetric Stellarator CFQS

Feasibility Study of Neutral Beam Injection on Chinese First Quasi-Axisymmetric Stellarator (CFQS)

Feasibility Study of Neutral Beam Injection on Chinese First Quasi-Axisymmetric Stellarator (CFQS)

Configuration Property of the Chinese First Quasi-Axisymmetric Stellarator

Configuration Property of the Chinese First Quasi-Axisymmetric Stellarator

Magnetic Configuration and Modular Coil Design for the Chinese First Quasi-Axisymmetric Stellarator

Magnetic Configuration and Modular Coil Design for the Chinese First Quasi-Axisymmetric Stellarator

Three Confinement Systems—Spherical Tokamak, Standard Tokamak, and Stellarator: A Comparison of Key Component Cost Elements

Since the 1950s “next-step” fusion devices and power plant studies have been developed for a number of magnetic confinement systems but an open question remains: can a magnetic fusion device be simplified to the point where it will be cost competitive and operate with high availability? Concept designs based on the ARIES advanced tokamak, spherical tokamak (ST), and the quasi-axisymmetric (QAS) stellarator option have progressed in recent years through a series of Princeton Plasma Physics Laboratory (PPPL) studies with an underlying intent to improve the engineering feasibility of each, giving special attention to concepts that simplify the device configuration and improve maintenance features. For the ST option, design details centered on a 3-m Fusion Nuclear Science Facility that evolved to incorporate vertical maintenance, high temperature superconductor magnets, a small inboard duel coolant lead lithium blanket, and a liquid metal divertor. In collaboration with the Korean fusion demonstration reactor (K-DEMO) and CFETR concept study teams the tokamak design has evolved to increase plasma component access within a vertical maintenance approach using enlarged toroidal field coils incorporating a low- and high-field Nb3Sn winding pack that provide a peak field of 16 T. A recent PPPL stellarator study focused on simplifying the stellarator winding topology to improve access to in-vessel components; combining coil optimization with winding surfaces that incorporated geometry constraints specified by engineering. This paper centered on a 1000-MW power plant design with a tokamak like vertical maintenance scheme that allows access to remove large internal blanket sectors. Results of three confinement studies (PPPL developed ST, K-DEMO, and QAS stellarator) will be presented to highlight concepts that simplify each device configuration and improved their maintenance features. Scaling each option to a common 1000-MW net electric power plant mission allows comparisons to be made of key cost elements such as the size of major core components, sizing of the reactor hall, or external facilities needed to handle and store activated in-vessel components.

Recent advances in stellarator optimization

Computational optimization has revolutionized the field of stellarator design. To date, optimizations have focused primarily on optimization of neoclassical confinement and ideal MHD stability, although limited optimization of other parameters has also been performed. The purpose of this paper is to outline a select set of new concepts for stellarator optimization that, when taken as a group, present a significant step forward in the stellarator concept. One of the criticisms that has been leveled at existing methods of design is the complexity of the resultant field coils. Recently, a new coil optimization code—COILOPT++, which uses a spline instead of a Fourier representation of the coils,—was written and included in the STELLOPT suite of codes. The advantage of this method is that it allows the addition of real space constraints on the locations of the coils. The code has been tested by generating coil designs for optimized quasi-axisymmetric stellarator plasma configurations of different aspect ratios. As an initial exercise, a constraint that the windings be vertical was placed on large major radius half of the non-planar coils. Further constraints were also imposed that guaranteed that sector blanket modules could be removed from between the coils, enabling a sector maintenance scheme. Results of this exercise will be presented. New ideas on methods for the optimization of turbulent transport have garnered much attention since these methods have led to design concepts that are calculated to have reduced turbulent heat loss. We have explored possibilities for generating an experimental database to test whether the reduction in transport that is predicted is consistent with experimental observations. To this end, a series of equilibria that can be made in the now latent QUASAR experiment have been identified that will test the predicted transport scalings. Fast particle confinement studies aimed at developing a generalized optimization algorithm are also discussed. A new algorithm developed for the design of the scraper element on W7-X is presented along with ideas for automating the optimization approach.

A Systematic study of modular coil characteristics for 2-field periods quasi-axisymmetric stellarator QAS-LA

Modular coil characteristics of a 2-field periods quasi-axisymmetric stellarator QAS-LA configuration with an aspect ratio Ap=3, magnetic pressure ∼4% and rotational transform ι∼0.15 per field period supplied by its own shaping have been detailed studied. In addition, the characteristics of modular coils for QAS-LA were compared with those of an intermediate QA configuration QAS-LAx and a tokamak based on the same center magnet field B0, aspect ratio and number of coils. As expected, the Bmax/B0, force F and overturning moment M, increase with the increased complexity of the coil shape. The relationships between the modular coils’ parameters (such as radius curvature ρ, distance from coil to coil Δc–c and the cross-section of coils) and the electromagnetic characteristics have been systematically summarized. The approximate formula for the maximum magnetic field in the coil body as functions of modular coil parameters (Δc–c, ρ) was derived for a simple two wire system which will be useful when optimizations of coil properties are called for.

Next Steps in Quasi-Axisymmetric Stellarator Research

The quasi-axisymmetric (QA) stellarator, a 3-D magnetic configuration with close connections to tokamaks, offers solutions for a steady state, disruption-free fusion system. A new experimental facility, QUASAR, provides a rapid approach to the next step in QA development, an integrated experimental test of its physics properties, taking advantage of the designs, fabricated components, and detailed assembly plans developed for the NCSX project. A scenario is presented for constructing the QUASAR facility for physics research operations starting in 2019. Operating in deuterium, such a facility would investigate the scale-up in size and pulse length from QUASAR, while a suitably equipped version operating in deuterium-tritium (DT) could address fusion nuclear missions. New QA optimization strategies, aimed at improved engineering attractiveness, would also be tested.

Integrated modelling of ICRH in a quasi-axisymmetric stellarator

We apply the code package SCENIC to a two field-period quasi-axisymmetric stellarator. Ion cyclotron resonance heating (ICRH) is applied both on the high- and low-field side to a 1% 3He minority in a deuterium plasma. It is shown that due to toroidal variations, the results are considerably different from similar tokamak studies. In particular, toroidal variations in power deposition and pressure are created and accentuated during radio frequency heating, such that modifications to the magnetic equilibrium depend on toroidal angle. We demonstrate that due to enhanced particle loss, low-field side heating is significantly less efficient than high-field side heating, and that toroidally trapped particles impose upper power limits for efficient radio frequency injection.

Reducing turbulent transport in toroidal configurations via shaping

Recent progress in reducing turbulent transport in stellarators and tokamaks by 3D shaping using a stellarator optimization code in conjunction with a gyrokinetic code is presented. The original applications of the method focused on ion temperature gradient transport in a quasi-axisymmetric stellarator design. Here, an examination both of other turbulence channels and other starting configurations is initiated. It is found that the designs evolved for transport from ion temperature gradient turbulence also display reduced transport from other transport channels whose modes are also stabilized by improved curvature, such as electron temperature gradient and ballooning modes. The optimizer is also applied to evolving from a tokamak, finding appreciable turbulence reduction for these devices as well. From these studies, improved understanding is obtained of why the deformations found by the optimizer are beneficial, and these deformations are related to earlier theoretical work in both stellarators and tokamaks.

Integrated modeling for ion cyclotron resonant heating in toroidal systems

An integrated model capable of self-consistent Ion Cyclotron Resonant Heating (ICRH) simulations has been developed. This model includes both full shaping and pressure effects, warm contributions to the dielectric tensor, pressure anisotropy and finite orbit width. It evolves the equilibrium, wave field and full hot particle distribution function until a self-consistent solution is found. This article describes the workings of the three codes VMEC, LEMan and VENUS and how they are linked for iterated computations in a code package we have named SCENIC. The package is thoroughly tested and it is demonstrated that a number of iterations have to be performed in order to find a consistent solution. Since the formulation of the problem can treat general 3D systems, we show a quasi-axisymmetric stellarator low power test case, and then concentrate on experimentally relevant Joint European Torus (JET) 2D configurations.

Modular coils and plasma configurations for quasi-axisymmetric stellarators

Characteristics of modular coils for quasi-axisymmetric stellarators that are related to the plasma aspect ratio, number of field periods and rotational transform have been examined systematically. It is observed that, for a given plasma aspect ratio, the coil complexity tends to increase with the increased number of field periods. For a given number of field periods, the toroidal excursion of coil winding is reduced as the plasma aspect ratio is increased. It is also clear that the larger the coil–plasma separation is, the more complex the coils become. It is further demonstrated that it is possible to use other types of coils to complement modular coils to improve both the physics and the modular coil characteristics.

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.

Three-dimensional anisotropic pressure free boundary equilibria

Free boundary three-dimensional anisotropic pressure magnetohydrodynamic equilibria with nested magnetic flux surfaces are computed through the minimisation of the plasma energy functional W = ∫ V d 3 x [ B 2 / ( 2 μ 0 ) + p ∥ / ( Γ − 1 ) ] . The plasma–vacuum interface is varied to guarantee the continuity of the total pressure [ p ⊥ + B 2 / ( 2 μ 0 ) ] across it and the vacuum magnetic field must satisfy the Neumann boundary condition that its component normal to this interface surface vanishes. The vacuum magnetic field corresponds to that driven by the plasma current and external coils plus the gradient of a potential function whose solution is obtained using a Green's function method. The energetic particle contributions to the pressure are evaluated analytically from the moments of the variant of a bi-Maxwellian distribution function that satisfies the constraint B ⋅ ∇ F h = 0 . Applications to demonstrate the versatility and reliability of the numerical method employed have concentrated on high- β off-axis energetic particle deposition with large parallel and perpendicular pressure anisotropies in a 2-field period quasiaxisymmetric stellarator reactor system. For large perpendicular pressure anisotropy, the hot particle component of the p ⊥ distribution localises in the regions where the energetic particles are deposited. For large parallel pressure anisotropy, the pressures are more uniform around the flux surfaces.

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.

Novel design methods for magnetic flux loops in the National Compact Stellarator Experiment

Magnetic pickup loops on the vacuum vessel (VV) can provide an abundance of equilibrium information for stellarators. A substantial effort has gone into designing flux loops for the National Compact Stellarator Experiment (NCSX) [Zarnstorff et al., Plasma Phys. Controlled Fusion 43, A237 (2001)], a three-field period quasi-axisymmetric stellarator under construction at the Princeton Plasma Physics Laboratory. The design philosophy, to measure all of the magnetic field distributions normal to the VV that can be measured, has necessitated the development of singular value decomposition algorithms for identifying efficient loop locations. Fields are expected to be predominantly stellarator symmetric (SS)—the symmetry of the machine design—with toroidal mode numbers per torus (n) equal to a multiple of 3 and possessing reflection symmetry in a period. However, plasma instabilities and coil imperfections will generate non-SS fields that must also be diagnosed. The measured symmetric fields will yield important information on the plasma current and pressure profile as well as on the plasma shape. All fields that obey the design symmetries could be measured by placing flux loops in a single half-period of the VV, but accurate resolution of nonsymmetric modes, quantified by the condition number of a matrix, requires repositioning loops to equivalent locations on the full torus. A subarray of loops located along the inside wall of the vertically elongated cross section was designed to detect n=3, m=5 or 6 resonant field perturbations that can cause important islands. Additional subarrays included are continuous in the toroidal and poloidal directions. Loops are also placed at symmetry points of the VV to obtain maximal sensitivity to asymmetric perturbations. Combining results from various calculations which have made extensive use of a database of 2500 free-boundary VMEC equilibria, has led to the choice of 225 flux loops for NCSX, of which 151 have distinct shapes.

NCSX Magnetic Configuration Flexibility and Robustness

The National Compact Stellarator Experiment (NCSX) will study the physics of low-aspect ratio, high-β, quasi-axisymmetric stellarators. To achieve the scientific goals of the NCSX mission, the device must be capable of supporting a wide range of variations in plasma configuration about a reference baseline equilibrium. We demonstrate the flexibility of NCSX coils to support such configuration variations and demonstrate the robustness of performance of NCSX plasmas about reference design values of the plasma current Ip, β, and profile shapes. The robustness and flexibility calculations make use of free-boundary plasma equilibrium constructions using a combination of nonaxisymmetric modular coils and axisymmetric toroidal and poloidal field coils. The primary computational tool for the studies is STELLOPT, a free-boundary optimization code that varies coil currents to target configurations with specific physics properties.

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.