与非绝缘高温超导磁体兼容的非平面线圈绕线角度优化
Non-Planar Coil Winding Angle Optimization for Compatibility with Non-Insulated High-Temperature Superconducting Magnets
摘要：
高温超导体（HTS）技术的迅速发展为非平面非绝缘HTS磁体的发展提供了新的机遇。这种类型的HTS磁体通过其简单性、鲁棒性提供了有吸引力的特性，并且非常适合中等尺寸的稳态应用，例如中等规模的仿星器。在非平面线圈应用中，HTS带可能经受严重的短轴弯曲应变（$ε_{bend}$）、扭转应变（$ε_{tor}$）和横向磁场分量（$B_\perp$），所有这些都会限制磁体操作空间。本文提出了一种新的缠绕角度优化方法来克服这些限制。本质上，这种方法：1）计算沿着输入线圈轨迹的任意缠绕角的峰值ε弯曲和B \perp，2）定义包括两者的成本函数，并且然后3）使用张紧样条来定义减小$ε$ tor并优化ε弯曲和$B_\perp$成本函数的缠绕角。由于即使没有$B_\perp$也存在应变极限，因此这种优化能够提供对任意非平面非绝缘HTS线圈的最小可构建尺寸的评估。该优化发现，对于标准的4 mm宽的HTS带，现有的HSX、NCSX和W7-X仿星器几何形状的最小尺寸线圈的半径约为0.3 - 0.5 m。对于大于该尺寸的弹簧圈，允许有限（但可耐受）应变可减少$B_\perp$。这使得能够减少实现给定设计磁场所需的HTS带长度，或者等效地增加固定HTS带长度的可实现磁场。还讨论了优化仿星器线圈组以进一步简化与非绝缘HTS磁体的兼容性的独特考虑。
英文摘要：
The rapidly emerging technology of high-temperature superconductors (HTS) opens new opportunities for the development of non-planar non-insulated HTS magnets. This type of HTS magnet offers attractive features via its simplicity, robustness, and is well-suited for modest size steady-state applications such as a mid-scale stellarator. In non-planar coil applications the HTS tape may be subject to severe minor-axis bending strain ($ε_{bend}$), torsional strains ($ε_{tor}$) and transverse magnetic field components ($B_\perp$), all of which can limit the magnet operating space. A novel method of winding angle optimization is here presented to overcome these limitations. Essentially, this method: 1) calculates the peak εbend and B\perp for arbitary winding angle along an input coil filamentary trajectory, 2) defines a cost function including both, and then 3) uses tensioned splines to define a winding angle that reduces $ε$tor and optimizes the εbend and $B_\perp$ cost function. As strain limits are present even without $B_\perp$, this optimization is able to provide an assessment of the minimimum buildable size of an arbitrary non-planar non-insulating HTS coil. This optimization finds that for standard 4 mm wide HTS tapes the minimum size coils of the existing HSX, NCSX, and W7-X stellarator geometries are around 0.3 - 0.5 m in radius. For coils larger than this size, permitting a finite (yet tolerable) strain allows reduction of $B_\perp$. This enables a reduction of the HTS tape length required to achieve a given design magnetic field or equivalently an increase in the achievable magnetic field for fixed HTS tape length. The distinct considerations for optimizing a stellarator coilset to further ease compatibility with non-insulated HTS magnets are also discussed.
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