Quasi-axisymmetric Research Articles

Effect of discreteness and misalignment on magnetic field and charged particle confinement in CFQS quasi-axisymmetric stellarator

The Chinese first quasi-axisymmetric stellarator (CFQS), which will be the first quasi-axisymmetric (QA) stellarator in the world, is now under construction. The primary task of the CFQS project is to realize a QA configuration and to examine its physical properties. Based on this task, two important issues were investigated in this work in order to estimate the robustness of the CFQS design from a physical perspective. One was the toroidal field (TF) ripple due to the discreteness of modular coils (MCs) which could potentially degrade the charged particle confinement in the CFQS configuration. The other was a possible MC misalignment in the assembly that would affect the magnetic field and charged particle confinement in the CFQS. Moreover, since the stellarator symmetry might be broken by the MC misalignment, such a case was also investigated in this work. By performing a magnetic field line tracing and charged particle orbit tracing calculation, it was found that the TF ripple does not affect the confinement property significantly and the magnetohydrodynamics equilibrium was robust against possible MC misalignments. These results are helpful in defining the reasonable tolerance of assembly accuracy.

Effects of bootstrap current on magnetic configuration in Chinese first quasi-axisymmetric stellarator

Neoclassical properties in quasi-axisymmetric (QA) stellarators are analogous to these in tokamaks. Consequently, a substantial bootstrap current could significantly modify the MHD equilibrium properties of a QA stellarator, which is an important characteristic in this type of stellarator. This paper is dedicated to systemically investigate the effects of bootstrap current on the magnetic configuration in Chinese first quasi-axisymmetric stellarator (CFQS). For the first time, self-consistent bootstrap currents in free-boundary equilibria are calculated with an accurate Fokker–Planck neoclassical numerical mode in CFQS. Several important results are achieved: (a) as the bootstrap current grows with increasing volume-averaged normalized pressure , magnetic shear develops in the bulk plasma and meanwhile, a deep magnetic well is robustly sustained, which leads to improved stabilization of interchange modes up to . (b) In the analysis of global ideal MHD instability, as the bootstrap current rises to 39 kA (), external kink modes become destabilized and the unstable mode with m/n = 2/1 is dominant. (c) From to 1.5%, the bootstrap current hardly changes the QA property and a low neoclassical transport is maintained. However, as is enhanced beyond 2.0%, the substantial bootstrap current gives rise to an increase of non-QA magnetic field components, which weakens the neoclassical transport properties. (d) An increase of the negative magnetic shear at the core region by the bootstrap currents has a favorable effect on the properties of J (second adiabatic invariant). The maximum-J region can be extended by raising bootstrap currents.

Identification of electrostatic microinstability maps in quasi-axisymmetric stellarator

Microinstabilities such as ion temperature gradient (ITG) mode and trapped electron mode (TEM) in quasi-axisymmetric (QA) stellarator are investigated by using gyrokinetic Vlasov simulations, where the QA configuration of Chinese first quasi-axisymmetric stellarator is utilized. Extensive parameter scans with respect to the density and temperature gradients for the zero beta cases identify the microinstability maps that indicate the transition boundary among ITG and TEM. It is found that, in particular for the modes with the ion-gyroradius scale, a relatively more stabilized regime appears along the transition boundary of ITG–TEM. Such a valley-like stability structure is not observed in the other cases with the sub-ion-gyroradius-scale. A stabilization effect attributed to the hollow density profile is also demonstrated.

Nonlinear MHD simulations of external kinks in quasi-axisymmetric stellarators using an axisymmetric external rotational transform approximation

Reduced magnetohydrodynamic (MHD) equations are used to study the nonlinear dynamics of external kinks in a quasi-axisymmetric (QA) stellarator with varying fractions of external rotational transform. The large bootstrap currents associated with high beta plasmas may make QA configurations susceptible to low n external modes, limiting their operational space. The violence of the nonlinear dynamics, and, in particular, when these modes lead to a disruption, is not yet understood. In this paper, the nonlinear phase of external kinks in an unstable QA configuration with an edge safety factor below two is simulated. An axisymmetric approximation of this stellarator is constructed in the nonlinear MHD code, JOREK, capturing the influence of the external rotational transform. The use of this approximation for the considered stellarator is validated by comparing the linear dynamics against the linear viscoresistive MHD code, CASTOR3D. The nonlinear dynamics of this stellarator approximation are compared with an equivalent tokamak to understand the influence of a relatively small external rotational transform. While the external rotational transform does have a stabilizing influence on the MHD activity, it remains violent. To explore the first order influence of a larger external rotational transform, this equilibrium parameter is artificially increased for the considered stellarator, reducing the effective plasma current. The violence of the kink instability is quantified, and shown to reduce with the increasing external rotational transform. At the same time, the external kink triggers internal modes that exacerbate the loss in confinement during the nonlinear phase, such that it remains large over much of the parameter space. It is only with a significant fraction of external rotational transform that these subsequent modes are stabilized.

Ion-temperature-gradient stability near the magnetic axis of quasisymmetric stellarators

The stability of the ion-temperature gradient mode in quasisymmetric stellarators is assessed. This is performed using a set of analytical estimates together with linear gyrokinetic simulations. The peak growth rates, their corresponding real frequencies and wave-vectors are identified. A comparison is made between a first-order near-axis expansion model and eleven realistic designs obtained using numerical optimization methods. It is found that while the near-axis expansion is able to replicate the growth rates, real frequencies and perpendicular wave-vector at the inner core (both using simplified dispersion relations and first-principle gyrokinetic simulations), it leads to an overestimation of the growth rate at larger radii. An approximate analytic solution of the ITG dispersion relation for the non-resonant limit suggests growth rates could be systematically higher in quasi-axisymmetric (QA) configurations compared to quasi-helically (QH) symmetric ones. However except for very close to the axis, linear gyrokinetic simulations do not show systematic differences between QA and QH configurations.

Preliminary design and analysis of the CFQS supporting structure

The Chinese First Quasi-axisymmetric Stellarator (CFQS) is now under design and construction. It will be the first quasi-axisymmetric (QA) configuration device to be operated in the world. The main parameters of the CFQS are as follows: the toroidal periodic number Np = 2, major radius R = 1.0 m, aspect ratio Ap = 4.0 and magnetic field strength Bt = 1.0 T. The low Ap makes it quite challenging to design a supporting structure because of the limited space and strong electromagnetic (EM) force. In this paper, a cage-like supporting structure is proposed for the CFQS modular coil (MC) system to sustain the EM force and the weight of entire device. A finite element analysis is carried out for ensuring the reliability of the supporting structure. The analysis results of the CFQS global model indicate that the cage-like supporting structure can basically satisfy the requirement.

Optimization of quasi-axisymmetric stellarators with varied elongation

An optimization study of Quasi-Axisymmetric (QA) stellarators with varied elongation has been carried out using the optimization code STELLOPT. The starting point of our optimization is a previously obtained QA stellarator with three field periods and an aspect ratio of 6. A series of QA stellarators are obtained at zero plasma beta with the varied elongation value ranging from 2.5 to 3.7. A good quasi-symmetry is kept when the elongation value is reduced from the original value of 3.7. The rotational transform profile and aspect ratio are kept fixed. The plasma volume is ether kept fixed or varied linearly with elongation. Furthermore, finite beta QA stellarators are considered. The corresponding bootstrap currents are calculated using the kinetic code SFINCS. A series of kink-stable QA stellarators are obtained via optimization with varied plasma beta up to 5% and self-consistent bootstrap current. This work demonstrates that good QA stellarators with finite beta and varied elongation exist that are stable to external kink modes.

Local axisymmetry-breaking–induced transition of trapped-particle orbit and loss channels in quasi-axisymmetric stellarators

The transition of trapped-particle orbit topologies has been investigated in quasi-axisymmetric (QA) configurations, such as the Chinese First Quasi-axisymmetric Stellarator (CFQS). It is found that the axisymmetry-breaking phenomenon in QA configurations is of great significance at some specific locations, which could easily induce blocked particles to transit into localized particles. A novel aspect is presented to interpret the transition mechanism of trapped-particle orbit topologies in this paper, i.e., as the amplitudes of non-axisymmetric field increase along the radius direction, the region of large toroidal inhomogeneity is gradually generated, which makes the length of the trapped-particle trajectory substantially short, and hence, may restrict particles to a single helical field period. Meanwhile, at such locations the “pseudo-axisymmetric” field results in coupling of the maximum radial drift and the minimum poloidal drift, which enables the transition of trapped-particle orbit topologies considerably and forms specific loss channels, degrading plasma confinement. These results may shed light on the optimization of QA configurations via avoidance of such coupling with respect to energetic particle confinement. Moreover, this work is also relevant to the generation of inhomogeneity of particle flux deposition on the devertor plates.

A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator

Ion-temperature-gradient-driven (ITG) turbulence is compared for two quasi-symmetric (QS) stellarator configurations to determine the relationship between linear growth rates and nonlinear heat fluxes. We focus on the quasi-helically symmetric (QHS) stellarator HSX and the quasi-axisymmetric (QAS) stellarator NCSX. In normalized units, HSX exhibits higher growth rates than NCSX, while heat fluxes in gyro-Bohm units are lower in HSX. These results hold for simulations made with both adiabatic and kinetic electrons. The results show that HSX has a larger number of subdominant modes than NCSX and that eigenmodes are more spatially extended in HSX. We conclude that the consideration of nonlinear physics is necessary to accurately assess the heat flux due to ITG turbulence when comparing QS stellarator equilibria.

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.

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.

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.

The drift reversal capability in quasi-axisymmetric stellarators

The drift reversal capability of trapped particles has beeninvestigated in quasi-axisymmetric (QA) configurations for theconfinement improvement as has been experimentally demonstrated inother axisymmetric configurations. The properties of J (secondadiabatic invariance), its profile and maximum-J capability are examinedfor this purpose. Due to the non-axisymmetric nature of themagnetic field strength, a region of local maximum of J is created tocause the drift reversal. This region can be controlled radially andalso toroidally with the introduction of symmetric breaking componentsof B, externally. The increase of magnetic shear in finite betaequilibria also has a favourable effect on the drift reversal. Thus,maximum-J capability and its external controllability are demonstratedfor QA stellarators, by which the impact of magnetic configuration onturbulent transport can be studied.

Maximum-Jcapability in a quasiaxisymmetric stellarator

Maximum-J (J is the second adiabatic invariant) capability, i.e., the radial derivative of J has the same sign as that of pressure, is investigated in a quasiaxisymmetric (QA) stellarator to investigate improved confinement. Due to the existence of nonaxisymmetry of the magnetic field strength, a local maximum of J is created to cause the drift reversal. External controllability of the maximum-J condition is also demonstrated, by which the impact of magnetic configuration on turbulent transport can be studied.

Control-matrix approach to stellarator design and control

The full space Z≡{Zj=1,…,Nz} of independent variables defining a stellarator configuration is large. To find attractive design points in this space, or to understand operational flexibility about a given design point, one needs insight into the topography in Z-space of the physics figures of merit Pi which characterize the machine performance, and means of determining those directions in Z-space which give one independent control over the Pi, as well as those which affect none of them, and so are available for design flexibility. The control matrix (CM) approach described here provides a mathematical means of obtaining these. In this work, the CM approach is described and used in studying some candidate Quasi-Axisymmetric (QA) stellarator configurations the National Compact Stellarator Experiment design group has been considering. In the process of the analysis, a first exploration of the topography of the configuration space in the vicinity of these candidate systems has been performed, whose character is discussed.

Realization and classification of symmetric stellarator configurations through plasma boundary modulations

The basic roles of several of the principal modulations of plasma boundary shape on MHD equilibria are investigated. The appropriate combination of the principal helical modulations for elimination of the bumpy field component in the realization of the quasi-axisymmetric (QAS) and quasi-helically symmetric (QHS) configurations is explained by considering the variation of the areas of the magnetic surface cross-sections. A triangular modulation is utilized effectively to form a magnetic well by shifting the magnetic axis outward compared with the centre of mass of the magnetic surface cross-section. The spatialization of the magnetic axis or the bumpy modulations of the plasma boundary are rather important for reducing the toroidicity in the magnetic field, which can lead to QHS configurations. Some stellarator magnetic configurations at present in the design stage or in existing experimental devices are discussed from the point of view of plasma boundary modulations. On the basis of these main findings about plasma boundary modulations, examples of the essential approach to QAS and QHS configurations are demonstrated step by step. The possibility of a quasi-bumpy (or poloidally) symmetric (QBS) configuration is also mentioned.