The new class of compact quasi-axisymmetric stellarators with a wide range of field periods offers the unique potential to combine the advantages of the two leading magnetic confinement fusion devices, tokamaks and stellarators. Here we present the first numerical optimization of this class which has so far only been obtained analytically. Our approach finds significantly improved quasi-axisymmetric equilibria at aspect ratio $< 2.5$, resulting in no losses of alpha particles at reactor volume while also satisfying improved magnetohydrodynamic stability and a self-consistent plasma current.
It is demonstrated that finite-pressure, approximately quasi-axisymmetric stellarator equilibria can be directly constructed (without numerical optimization) via perturbations of given axisymmetric equilibria. The size of such perturbations is measured in two ways, via the fractional external rotation and, alternatively, via the relative magnetic field strength, i.e. the average size of the perturbed magnetic field, divided by the unperturbed field strength. It is found that significant fractional external rotational transform can be generated by quasi-axisymmetric perturbations, with a simila…
Analytic non-axisymmetric 3D MHD equilibria without stellarator symmetry
Google DeepMind（谷歌DeepMind）；Department of Mechanical and Aerospace Engineering, University of California San Diego（加州大学圣地亚哥分校机械与航空航天工程系）；University of Maryland, College Park（马里兰大学帕克学院）
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 belo…
The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-$C^1$ code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-$C^1$. A $C^1$ coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-$C^1$ extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approac…
The nonlinear gyrokinetic code GS2 has been extended to treat non-axisymmetric stellarator geometry. Electromagnetic perturbations and multiple trapped particle regions are allowed. Here, linear, collisionless, electrostatic simulations of the quasi-axisymmetric, three-field period National Compact Stellarator Experiment (NCSX) design QAS3-C82 have been successfully benchmarked against the eigenvalue code FULL. Quantitatively, the linear stability calculations of GS2 and FULL agree to within ~10%.
The usage of permanent magnets to shape the confining magnetic field of a stellarator has the potential to reduce or eliminate the need for non-planar coils. As a proof-of-concept for this idea, we have developed a procedure for designing an array of cubic permanent magnets that works in tandem with a set of toroidal-field coils to confine a stellarator plasma. All of the magnets in the design are constrained to have identical geometry and one of three polarization types in order to simplify fabrication while still producing sufficient field accuracy. We present some of the key steps leading t…
In stellarators, zonal flow activity depends sensitively on geometry of the three dimensional magnetic field, via an interplay of mechanisms that is not fully understood. In this work, we investigate this by studying three magnetic configurations of the Wendelstein 7-X stellarator. We find that variation in linear zonal flow damping is accompanied by variation in nonlinear drive, and identify key geometric features that control these effects. Understanding the resulting balance is important for the development of reduced models of turbulent transport.
Compact quasiaxisymmetric stellarators, a near axisymmetric theory
Princeton University（普林斯顿大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Max Plank Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford, OX1 3PU, UK（牛津大学鲁道夫·皮尔斯理论物理中心）
Here we present first results simulating plasma filaments in non-axisymmetric geometries, using a fluid turbulence extension of the \boutxx~framework. This is made possible by the implementation of the Flux Coordinate Independent scheme for parallel derivatives, an extension of the metric tensor components which allows them to vary in three dimensions, and development of grid generation. Tests have been performed to confirm that the extension to three dimensional metric tensors does not compromise the accuracy and stability of the associated numerical operators. Recent changes to the FCI grid …
In recent years many efforts have been undertaken to simplify coil designs for stellarators due to the difficulties in fabricating non-planar coils. The FOCUS code removes the need for a winding surface and represents the coils as arbitrary curves in 3D. In the following work, the implementation of a spline representation for the coils in FOCUS is described, along with the implementation of a new engineering constraint to design coils with a straighter outer section. The new capabilities of the code are shown as an example on HSX, NCSX, and a prototype quasi-axisymmetric reactor-sized stellara…
Characterizing Flux-Surface Shapes in Tokamaks and Quasi-Symmetric Stellarators
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Max Planck Institute for Plasma Physics（马普等离子体物理研究所）；Dutch Institute for Fundamental Research（荷兰基础研究所）；Eindhoven University of Technology（埃因霍温理工大学）；Ruhr-Universität Bochum（波鸿鲁尔大学）
Flux tube simulations of plasma turbulence in stellarators and tokamaks typically employ coordinates which are aligned with the magnetic field lines. Anisotropic turbulent fluctuations can be represented in such field-aligned coordinates very efficiently, but the resulting non-trivial boundary conditions involve all three spatial directions, and must be handled with care. The standard "twist-and-shift" formulation of the boundary conditions [Beer, Cowley, Hammett \textit{Phys. Plasmas} \textbf{2}, 2687 (1995)] was derived assuming axisymmetry and is widely used because it is efficient, as long…
Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014) 042503] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations …
A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and quasisymmetry, expanded in the small distance from the magnetic axis, as formulated by Garren and Boozer [Phys. Fluids B, 3, 2805 (1991)]. Due to the reduction of the equations by the expansion, the computational cost is significantly reduced, to times on the order of 1 cpu-second, enabling wide and high-resolution scans over parameter space. In contrast to trad…
