Experimental and numerical study of error fields in the CNT stellarator

Hammond, K. C.; Anichowski, Alek; Brenner, P. W.; Pedersen, T. S.; Raftopoulos, S.; Traverso, P.; Volpe, F.

doi:10.1088/0741-3335/58/7/074002

Cited by 15 publications

(21 citation statements)

References 27 publications

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“…On the Columbia Non-neutral Torus (CNT), Kremer [7] analyzed the volume of magnetic surfaces under hundreds of random coil displacements, including shifts and rotations of coils and he suggested the PF coils could be misplaced by a maximum distance of 1 cm while inter-linked (IL) coils could only be perturbed up to 2 mm. This was also observed later by Hammond et al [8] when the gradient of the rotational transform on the magnetic axis with respect to several defined rigid More recently, there are several new approaches proposed to address the challenge of tight coil tolerance for stellarators. A shape gradient method was developed by Landreman & Paul [15] to compute local coil tolerance after calculating all the derivatives of a figure of merit with respect to coil parameters.…”

Section: Introductionsupporting

confidence: 55%

Identification of important error fields in stellarators using the Hessian matrix method

et al. 2019

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Error fields are predominantly attributed to inevitable coil imperfections. Controlling error fields during coil fabrication and assembly is crucial for stellarators. Excessively tight coil tolerance increases time and cost, and, in part, led to the cancellation of NCSX and delay of W7-X. In this paper, we improve the recently proposed Hessian matrix method to rapidly identify important coil deviations. Two of the most common figures of merit, magnetic island size and quasi-symmetry, are analytically differentiated over coil parameters. By extracting the eigenvectors of the Hessian matrix, we can directly identify sensitive coil deviations in the order of the eigenvalues. The new method is applied to the upcoming CFQS configuration. Important perturbations that enlarge n/m=4/11 islands and deteriorate quasi-axisymmetry of the magnetic field are successfully determined. The results suggest each modular coil should have separate tolerance and some certain perturbation combinations will produce significant error fields. By relaxing unnecessary coil tolerance, this method will hopefully lead to substantial a reduction in time and cost.Keywords Stellarator coils · error field · Hessian matrix · sensitivity analysis arXiv:1904.04147v2 [physics.plasm-ph] 4 Sep 2019 IDENTIFICATION OF IMPORTANT ERROR FIELDS IN STELLARATORS USING HESSIAN MATRIX METHOD displacements were calculated by the finite difference. NCSX investigated the impacts of systematic coil geometric perturbations and tolerance schemes on magnetic island size [9]. Local errors including coil-plasma spacing, short wavelet orthogonal displacements, and broad coil deformations causing coil length errors were also examined [10]. The results from NCSX suggested that modular coils required more tight tolerance (about 1.5 mm) than PF & TF coils, and particularly the inboard regions of modular coils had more significant effects on flux quality, while errors in other regions might approach 3 mm or even larger coil tolerance. As the largest stellarator, the Wendelstein 7-X (W7-X) performed extensive studies on coil tolerance [11]. The primary criteria were the resonant magnetic perturbations, B 11 , B 22 , B 33 & B 44 since W7-X has a m/n = 5/5 island chain outside the last closed flux surface (LCFS). Numerical investigations [12,13] showed that the resonant magnetic field perturbations were the most sensitive to rotations of coils and modules, after the effects of manufacturing errors, shifts and rotations of individual coils and modules were compared. With numerous efforts and advanced manufacturing techniques, W7-X superconducting coil system was built and assembled with impressively high accuracy. The maximum deviation for non-planar coils from the average shape is of the order of 2 mm [14] and the average alignment deviation for all 70 main field coils after the assembly is 1.2 mm [5].

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Section: Introductionsupporting

confidence: 55%

Identification of important error fields in stellarators using the Hessian matrix method

et al. 2019

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“…However, it is known that CNT's coils have significant misalignments and exhibit field errors that break the two-field-period stellarator symmetry. 16 The principal effect of these errors was shown to be an offset of the rotational transform profiles associated with each setting of I IL /I P F . Hence, incorporating CNT's field errors is expected to result in an offset of the plots shown in Fig.…”

Section: Free-boundary and Stability Resultsmentioning

confidence: 95%

High-β equilibrium and ballooning stability of the low aspect ratio CNT stellarator

2017

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The existence and ballooning-stability of low aspect ratio stellarator equilibria is predicted for the Columbia Neutral Torus (CNT) with the aid of 3D numerical tools. In addition to having a low aspect ratio, CNT is characterized by a low magnetic field and small plasma volume. Also, highly overdense plasmas were recently heated in CNT by means of microwaves. These characteristics suggest that CNT might attain relatively high values of plasma beta and thus be of use in the experimental study of stellarator stability to high-beta instabilities such as ballooning modes. As a first step in that direction, here the ballooning stability limit is found numerically. Depending on the particular magnetic configuration we expect volume-averaged β limits in the range 0.9-3.0%, and possibly higher, and observe indications of a second region of ballooning stability. As the aspect ratio is reduced, stability is found to increase in some configurations and decrease in others. Energy-balance estimates using stellarator scaling laws indicate that the lower β limit may be attainable with overdense heating at powers of of 40 to 100 kW. The present study serves the additional purpose of testing VMEC and other stellarator codes at high values of β and at low aspect ratios. For this reason, the study was carried out both for free boundary, for maximum fidelity to experiment, as well as with a fixed boundary, as a numerical test.

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“…The relative importance of the IL coils in this configuration is similar to previous observations for CNT configurations. In the paper of Hammond et al [13], it was concluded that the separation and tilt angle between circular, planar IL coils had the most dominant influence on ι -axis of the actual CNT stellarator. Kremer also suggested that the IL coils were less tolerable to displacements than the PF coils by comparing the Poincaré plots produced by misaligned coils [12].…”

Section: Eigenvalues Of the Hessian Matrix Used To Determine The Erromentioning

confidence: 99%

Hessian matrix approach for determining error field sensitivity to coil deviations

Zhu

Hudson

Lazerson

et al. 2018

Plasma Phys. Control. Fusion

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Abstract. The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code [Zhu et al., Nucl. Fusion 58(1):016008 (2018)] is utilized to provide fast and accurate calculations of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.

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Experimental and numerical study of error fields in the CNT stellarator

Cited by 15 publications

References 27 publications

Identification of important error fields in stellarators using the Hessian matrix method

Identification of important error fields in stellarators using the Hessian matrix method

High-β equilibrium and ballooning stability of the low aspect ratio CNT stellarator

Hessian matrix approach for determining error field sensitivity to coil deviations

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