Identification of important error fields in stellarators using Hessian matrix method

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 a substantial reduction in time and cost.Comment: Accepted by Nuclear Fusio

Quasi-Splines and their moduli

We study what we call quasi-spline sheaves over locally Noetherian schemes. This is done with the intention of considering splines from the point of view of moduli theory. In other words, we study the way in which certain objects that arise in the theory of splines can be made to depend on parameters. In addition to quasi-spline sheaves, we treat ideal difference-conditions, and individual quasi- splines. Under certain hypotheses each of these types of objects admits a fine moduli scheme. The moduli of quasi-spline sheaves is proper, and there is a natural compactification of the moduli of ideal difference-conditions. We include some speculation on the uses of these moduli in the theory of splines and topology, and an appendix with a treatment of the Billera-Rose homogenization in scheme theoretic language

Wilson line correlator in the MV model: relating the glasma to deep inelastic scattering

In the color glass condensate framework the saturation scale measured in deep inelastic scattering of high energy hadrons and nuclei can be determined from the correlator of Wilson lines in the hadron wavefunction. These same Wilson lines give the initial condition of the classical field computation of the initial gluon multiplicity and energy density in a heavy ion collision. In this paper the Wilson line correlator in both adjoint and fundamental representations is computed using exactly the same numerical procedure that has been used to calculate gluon production in a heavy ion collision. In particular the discretization of the longitudinal coordinate has a large numerical effect on the relation between the color charge density parameter g^2 mu and the saturation scale Qs. Our result for this relation is Qs = 0.6 g^2 mu, which results in the classical Yang-Mills value for the "gluon liberation coefficient" c = 1.1.Comment: 8 pages, 10 figures, RevTEX4, V2: typo corrections, V3: small clarifications, to be published in EPJ

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

0000-0002-5601-7106The 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.journal articl

Engineering design and manufacturing of the modular coil system for the quasi-axisymmetric stellarator CFQS-T

The Quasi-axisymmetric Stellarator CFQS has been constructed as an international joint project between the National Institute for Fusion Science in Japan and Southwest Jiaotong University in China. Its physical properties are as follows: toroidal periodic number m = 2, aspect ratio Ap = 4, maximum magnetic field strength Bt= 1 T, and major radius of magnetic axis in vacuum R0 = 1 m. The CFQS employs four different types of 16 modular coils to realize a quasi-axisymmetric magnetic field configuration. The CFQS plasma experiment is planned to have two stages. The first is a 0.09 T long-pulse operation with a simplified modular coil support structure referred to as “CFQS-T”. The second is a 1 T short pulse rated operation known as “CFQS” after reinforcing the modular coil system's support structure against a large electromagnetic force. This paper reports on the finalized engineering design of the modular coil system with simplified coil support structures for CFQS-T, including a validity evaluation result with finite element analysis method software ANSYS. Furthermore, the established manufacturing method of the modular coil system for CFQS-T is described. All modular coils for CFQS-T have been manufactured and its main body assembly, with modular coils and a vacuum vessel, has been completed. Currently the commissioning, including a coil energization test and magnetic field line mapping, is ongoing.journal articl

Investigation of modular coil misalignment on magnetic flux surface in the CFQS quasi-axisymmetric stellarator

The CFQS is a quasi-axisymmetric stellarator of which the concept combines the advantage of good confinement of a tokamak and the steady-state operation capability of a stellarator. The CFQS has 16 modular coils (MCs), which consist of four independent shapes. Accurate positioning of MCs is one of the most important requirements, in particular, in stellarator since coil misalignment may have a significant effect on the quality of magnetic flux surfaces. Assuming some cases of displacement of MCs, we have investigated the effect on rotational transform profile and magnetic flux surfaces in the vacuum field. According to the results, it was found that MC misalignment has no significant effect on the CFQS plasma if the displacement is within a range expected in the actual MC installation.journal articl