For the representation of axi-symmetric plasma configurations (tokamaks), it is natural to use cylindrical coordinates $(R,Z,\phi)$, where $\phi$ is an independent coordinate. The same cylindrical coordinates have also been widely used for representing 3D MHD equilibria of non-axisymmetric configurations (stellarators), with cross-sections, defined in $(R,Z)$-planes, that vary over $\phi$. Stellarator equilibria have been found, however, for which cylindrical coordinates are not at all a natural choice, for instance certain stellarators obtained using the near-axis expansion (NAE), defined by a magnetic axis curve and its Frenet frame. In this contribution we demonstrate how to use an \emph{axis-following frame} that we call a 'generalized Frenet frame', as an alternative to using cylindrical coordinates in a 3D MHD equilibrium solver. We see two advantages: 1) the capability to easily represent configurations where the magnetic axis is highly non-planar or even knotted. 2) a reduction in the degrees of freedom needed for the geometry, enabling progress in optimization of these configurations. We discuss the definition of the generalized Frenet frame, and details of the implementation of the new frame in the 3D MHD equilibrium solver GVEC. Furthermore, we demonstrate for a highly shaped QI-optimized stellarator that far fewer degrees of freedom are necessary to find a high quality equilibrium solution, compared to the solution computed in cylindrical coordinates.

翻译：对于轴对称等离子体构型（托卡马克）的表示，自然采用柱坐标$(R,Z,\phi)$，其中$\phi$为独立坐标。同样的柱坐标也已被广泛用于表示非轴对称构型（仿星器）的三维磁流体力学平衡，其截面定义于$(R,Z)$平面并随$\phi$变化。然而，已发现某些仿星器平衡并不适合采用柱坐标，例如通过近轴展开方法获得的某些仿星器构型，该方法由磁轴曲线及其Frenet标架定义。本文提出采用一种我们称为“广义Frenet标架”的沿轴跟随标架，作为三维磁流体力学平衡求解器中柱坐标的替代方案。我们认为该方法具有两大优势：1) 能够轻松表示磁轴高度非平面甚至打结的构型；2) 减少几何描述所需的自由度，从而推动此类构型的优化进程。我们将讨论广义Frenet标架的定义，以及其在三维磁流体力学平衡求解器GVEC中的具体实现细节。此外，通过对一个高度变形的准等旋优化仿星器的计算演示，我们发现与柱坐标下的解相比，采用新标架仅需极少自由度即可获得高质量的平衡解。