The optimized stellarator is an attractive concept for which the averaged particle radial drift is zero, and the single particle loss can be significantly reduced. But for the reactor design, global physics such as turbulent transport also need to be optimized besides the confined single particle orbit, or properties estimated using local estimations and heuristic formulations. The first-principle global transport code is too computationally expensive to integrate into the optimization process. The fast surrogate global transport model based on machine learning is a good alternative choice, but the amount of data required to train the surrogate model is numerous due to the high degree-of-freedom of the stellarator design. The work shows that the stellarator design with quasi-helically(QH) symmetric geometry is approximately distributed in a low dimensional latent space, which can be explicitly found by deep learning. This discovery makes it possible to generate global gyrokinetic simulation data for training surrogate models to directly optimize the stellarator geometry for turbulent transport, energetic particle instability, and MHD modes. Using the low dimensional latent space and data analysis methods, the relation between linear zonal residues and axis-excursion is found, providing a simple guide to optimize low turbulent transport QH stellarators.
In the complex 3D magnetic fields of stellarators, ion-temperature-gradient turbulence is shown to have two distinct saturation regimes, as revealed by petascale numerical simulations, and explained by a simple turbulence theory. The first regime is marked by strong zonal flows, and matches previous observations in tokamaks. The newly observed second regime, in contrast, exhibits small- scale quasi-two-dimensional turbulence, negligible zonal flows, and, surprisingly, a weaker heat flux scaling. Our findings suggest that key details of the magnetic geometry control turbulence in stellarators.
The design of turbulence optimized stellarators has so far relied on three-dimensional equilibrium codes such as VMEC in order to find the minimum of a given objective function. In this work, we propose a complimentary approach based on the near-axis expansion to compute the geometry parameters of neoclassicaly optimized stellarators used in turbulence studies. As shown here, the near-axis expansion can be a reasonable approximation of the geometric parameters relevant for turbulence and stability simulations of the core of existing optimized stellarator designs. In particular, we examine the …
Turbulent transport is known to limit the plasma confinement of present-day optimized stellarators. To address this issue, a novel method to strongly suppress turbulence in such devices is proposed, namely the resonant wave-particle interaction of supra-thermal particles - e.g., from ion-cyclotron-resonance-frequency (ICRF) heating - with turbulence-driving microinstabilities like ion-temperature-gradient (ITG) modes. The effectiveness of this mechanism is demonstrated via analytic theory and large-scale gyrokinetic simulations, revealing an overall turbulence reduction by up to $80\%$. These …
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 exce…
An optimized compact stellarator with four simple coils is obtained from direct optimization via coil shape. The new stellarator consists of two interlocking coils and two vertical field coils similar to those of the Columbia Non-neutral Torus (CNT)[Pedersen et al. Phys. Rev. Lett. 88, 205002 (2002)]. The optimized configuration has global magnetic well and a low helical ripple level comparable to that of Wendelstein 7-X (W7-X)[Wolf et al. Nucl. Fusion 57, 102020 (2017)]. The two interlocking coils have a smooth three-dimensional shape much simpler than those of advanced stellarators such as W…
With the advent of neoclassically optimised stellarators, optimising stellarators for turbulent transport is an important next step. The reduction of ion-temperature-gradient-driven turbulence has been achieved via shaping of the magnetic field, and the reduction of trapped-electron mode (TEM) turbulence is adressed in the present paper. Recent analytical and numerical findings suggest TEMs are stabilised when a large fraction of trapped particles experiences favourable bounce-averaged curvature. This is the case for example in Wendelstein 7-X [C.D. Beidler $\textit{et al}$ Fusion Technology $…
In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the "trapped electron mode" (TEM) is stabilised if specific optimisation criteria are satisfied, as in the Wendelstein 7-X experiment (W7-X). Here we find, by numerical simulation, that W7-X indeed has low TEM-driven transport, and also benefits from stabilisation of the ion-temperature-gradient mode, giving theoretical support for the existence of enhanced confinement regimes at finite density gradients.
Most quasisymmetric stellarators to date have been designed by numerically optimizing the plasma boundary shape to minimize symmetry-breaking Fourier modes of the magnetic field strength $B$. At high aspect ratio, a faster approach is to directly construct the plasma shape from the equations of quasisymmetry near the magnetic axis derived by Garren and Boozer [Phys Fluids B 3, 2805 (1991)]. Here we show that the core shape and rotational transform of many optimization-based configurations can be accurately described by this direct-construction approach. This consistency supports use of the nea…
Designing A Buildable Optimized Stellarator to Confine Electron-Positron Plasmas
Max-Planck-Institut für Plasmaphysik（德国马普等离子体物理研究所）；Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）；Department of Physics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校物理系）；SchulerTEC；Department of Mechanical Engineering, McGill University（麦吉尔大学机械工程系）
Results of a three-dimensional, flux-driven, electrostatic, global, two-fluid turbulence simulation for a 5-field period stellarator with an island divertor are presented. The numerical simulation is carried out with the GBS code, recently extended to simulate plasma turbulence in non-axisymmetric magnetic equilibria. The vacuum magnetic field used in the simulation is generated with the theory of Dommaschk potentials, and describes a configuration with a central region of nested flux surfaces, surrounded by a chain of magnetic islands, similarly to the diverted configurations of W7-X. The hea…
Nine stellarator configurations, three quasiaxisymmetric, three quasihelically symmetric and three non-quasisymmetric are scaled to ARIES-CS size and analyzed for energetic particle content. The best performing configurations with regard to energetic particle confinement also perform the best on the neoclassical Γc metric, which attempts to align contours of the second adiabatic invariant with flux surfaces. Quasisymmetric configurations that simultaneously perform well on Γc and quasisymmetry have the best overall confinement, with collisional losses under 3%, approaching the performance of I…
In toroidal magnetic confinement devices, such as tokamaks and stellarators, neoclassical transport is usually an order of magnitude larger than its classical counterpart. However, when a high-collisionality species is present in a stellarator optimized for low Pfirsch-Schlüter current, its classical transport can be comparable to the neoclassical transport. In this letter, we compare neoclassical and classical fluxes and transport coefficients calculated for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we find that the classical transport of a collisional impurity is …
In the present Letter, first-of-its-kind computer simulations predicting plasma profiles for modern optimized stellarators -- while self-consistently retaining neoclassical transport, turbulent transport with 3D effects, and external physical sources -- are presented. These simulations exploit a newly developed coupling framework involving the global gyrokinetic turbulence code GENE-3D, the neoclassical transport code KNOSOS, and the 1D transport solver TANGO. This framework is used to analyze the recently observed degradation of energy confinement in electron-heated plasmas in the Wendelstein…
The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren and Boozer (1991a). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman and Sengupta (2018); Landreman et al. (2019), enables their efficient numerica…
The confinement of guiding center trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r, θ, φ)$, but $B(r,θ,φ)$ depends on the flux surface shape in a complicated way. Here we derive equations relating $B(r,θ,φ)$ in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer [Phys. Fluids B 3, 2805 (1991)] based on the Frenet-Serret frame, which can be discontinuous anywhere the…
Long range correlations were measured using two remote reciprocating Langmuir probe systems at TJ-II. The influence of the rotational transform on the correlation was studied by scanning the magnetic configuration. A simple drift wave correlation model, assuming an exponential decay of the correlation with different correlation lengths in the directions parallel and perpendicular to the field lines, was found to describe the observations well at low densities. The experiment was repeated at gradually higher densities, and an additional correlation was detected at a critical value of the densit…
Zonal flow suppression of turbulent transport in the optimized stellarators W7-X and QSTK
Indian Institute of Science（印度科学学院）；Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；University of California Irvine（加州大学尔湾分校）
A new stellarator coil design code is introduced that optimizes the position and winding pack orientation of finite-build coils. The new code, called FOCUSADD, performs gradient-based optimization in a high-dimensional, non-convex space. The derivatives with respect to parameters of finite-build coils are easily and efficiently computed using automatic differentiation. FOCUSADD parametrizes coil positions in free space using a Fourier series and uses a multi-filament approximation to the coil winding pack. The orientation of the winding pack is parametrized with a Fourier series and can be opt…
Quasisymmetric stellarators are appealing intellectually and as fusion reactor candidates since the guiding center particle trajectories and neoclassical transport are isomorphic to those in a tokamak, implying good confinement. Previously, quasisymmetric magnetic fields have been identified by applying black-box optimization algorithms to minimize symmetry-breaking Fourier modes of the field strength $B$. Here instead we directly construct magnetic fields in cylindrical coordinates that are quasisymmetric to leading order in distance from the magnetic axis, without using optimization. The met…
On shear Alfvén wave-induced energetic ion transport in optimized stellarators
Columbia University（哥伦比亚大学）；Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Cornell University（康奈尔大学）；Oak Ridge National Laboratory（橡树岭国家实验室）
Fluid simulation of stellarator edge transport is difficult due to the complexities of mesh generation; the stochastic edge and strong nonaxisymmetry inhibit the use of field aligned coordinate systems. The recent implementation of the Flux Coordinate Independent method for calculating parallel derivatives in BOUT++ has allowed for more complex geometries. Here we present initial results of nonaxisymmetric diffusion modelling as a step towards stellarator turbulence modelling. We then present initial (non-turbulent) transport modelling using the FCI method and compare the results with analytic…
Plasma turbulence is studied using Doppler reflectometry at the TJ-II stellarator. By scanning the tilt angle of the probing beam, different values of the perpendicular wave numbers are probed at the reflection layer. In this way, the interaction between zonal flows and turbulence is reported with (a) spatial, (b) temporal, and (c) wavenumber resolution for the first time in any magnetic confinement fusion device. We report measurements of the bicoherence across the Low to High (L--H) confinement transition at TJ-II. We examine both fast transitions and slow transitions characterized by an int…
AI-Accelerated Gyrokinetic Predictions of Turbulent Transport for Stellarator Design Optimization and Experimental Planning
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；University of Maryland, College Park（马里兰大学帕克分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；Type One Energy；California Institute of Technology（加州理工学院）；Argonne National Laboratory（阿贡国家实验室）；Princeton University（普林斯顿大学）；University of Wisconsin, Madison（威斯康星大学麦迪逊分校）
We have developed a fast method to design perpendicular permanent magnets for simplifying stellarator coils based on existing codes. Coil complexity is one of the main challenges for stellarators. To date, only electromagnetic coils have been used to generate 3D fields for stellarators. Permanent magnets provide an alternative way to produce the desired magnetic field for optimized stellarators. In this paper, we revisit the concept of representing surface current using magnetic dipoles and carry out numerical validations. A surface magnetization is proven to be equivalent to the surface curre…
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…
A stellarator is said to be omnigeneous if all particles have vanishing average radial drifts. In omnigeneous stellarators, particles are perfectly confined in the absence of turbulence and collisions, whereas in non-omnigeneous configurations, particle can drift large radial distances. One of the consequences of omnigeneity is that the unfavorable inverse scaling with collisionality of the stellarator neoclassical fluxes disappears. In the pioneering and influential article [Cary~J~R and Shasharina~S~G 1997 {\it Phys. Plasmas} {\bf 4} 3323], the conditions that the magnetic field of a stellar…
This paper describes a new and efficient method of defining an annular region of a curl-free magnetic field with specific physics and coil properties that can be used in stellarator design. Three statements define the importance: (1) Codes can follow an optimized curl-free initial state to a final full-pressure equilibrium. The large size of the optimization space of stellarators, approximately fifty externally-produced distributions of magnetic field, makes success in finding a global optimum largely determined by the starting point. (2) The design of a stellarator is actually improved when t…
