非轴对称等离子体几何的快速真空响应计算

中文摘要 AI 辅助

我们提出了一种快速、开源的真空响应矩阵和非轴对称几何中表面电感的计算方法，该方法能够在笔记本电脑上以多达10^5个边界点在数十秒内运行。自由边界模式的理想磁流体动力学（MHD）稳定性建模需要扰动的真空能量。我们将VACUUM代码扩展到非轴对称几何，在新的广义扰动平衡代码的Julia实现中，结合了边界积分方程的配置方法与高阶奇异性修正方案。该修正被重铸为作用于配置值的显式求积权重，使得修正后的算子能够显式组装，而不是应用于给定的表面场，并且利用该矩阵在场周期和仿星器对称性下的结构来减少存储和求解成本。我们发现真空响应矩阵在网格间距上以四阶或更高阶收敛，在较粗的网格上达到给定精度，优于没有高阶方法的先前实现。非轴对称计算收敛于托卡马克的轴对称VACUUM结果和W7-X仿星器平衡的CAS3D结果。这项工作使得仿星器中快速自由边界理想MHD稳定性和扰动平衡计算成为可能。

英文摘要

We present a fast, open-source calculation of the vacuum response matrix and surface inductance in non-axisymmetric geometries capable of running with up to 10^5 boundary points in tens of seconds on a laptop. Ideal magneto-hydrodynamic (MHD) stability modeling for free boundary modes requires the perturbed vacuum energy. We extend the VACUUM code to non-axisymmetric geometries in the new Julia implementation of the Generalized Perturbed Equilibrium Code, combining a collocation approach to the boundary integral equations with a high-order singularity correction scheme. The correction is recast into explicit quadrature weights acting on the collocation values, which allows the corrected operator to be assembled explicitly rather than applied to a given surface field, and the structure of that matrix under field-period and stellarator symmetry is then exploited to reduce storage and solve cost. We find that the vacuum response matrix converges at fourth order or greater in the grid spacing, reaching a given accuracy on a coarser grid than previous implementations without the high-order method. The non-axisymmetric calculation converges to the axisymmetric VACUUM result for a tokamak and the CAS3D result for a W7-X stellarator equilibrium. This work enables fast free boundary ideal MHD stability and perturbed equilibrium calculations in stellarators.

发表机构

• Columbia University（哥伦比亚大学）
• Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）

机构由 AI 辅助整理，请以论文原文为准。

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13 pages, 4 figures