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

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