论文标题
准对称配置空间中的阶段和相变
Phases and phase-transitions in quasisymmetric configuration space
论文作者
论文摘要
我们探索了准对称构型空间的结构，该构型通过其磁轴（称为3D封闭曲线）识别它们的结构。我们证明，这种拓扑视角将所有构型的空间划分为分离良好的准对称相。每个阶段的特征是自链数（拓扑不变），定义了不同的对称配置（准轴对称或准螺旋对称性）。相变歧管对应于准静脉构型。通过考虑一些封闭曲线的模型（最著名的是圆环未开关），可以探索与这些相关的一般特征。还建立和利用了一些一般标准，以提供一种简单的方法来描述现有的准对称设计。这构成了程序中的第一步，该步骤识别具有降低的功能和参数集的准对称配置，以加深对配置空间的理解，并为替代方法提供替代方法，以从磁性轴开始并向外构建恒星优化。
We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into well-separated quasisymmetric phases. Each phase is characterized by the self-linking number (a topological invariant), defining different symmetry configurations (quasi-axisymmetry or quasi-helical symmetry). The phase-transition manifolds correspond to quasi-isodynamic configurations. By considering some models for closed curves (most notably torus unknots), general features associated with these phases are explored. Some general criteria are also built and leveraged to provide a simple way to describe existing quasisymmetric designs. This constitutes the first step in a program to identify quasisymmetric configurations with a reduced set of functions and parameters, to deepen understanding of configuration space, and offer an alternative approach to stellarator optimization that begins with the magnetic axis and builds outward.
