发表机构
Princeton University; Max Planck Institute for Plasma Physics; Thea Energy（普林斯顿大学; 马克斯·普朗克等离子体物理研究所; Thea能源公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出在单个环向平面预设庞加莱截面作为新的边界条件，在DESC中实现，相比固定LCFS更灵活且计算成本不变，能提高收敛性并降低力误差，且可直接作为优化变量用于准螺旋配置设计。
AI 中文摘要
仿星器理想磁流体动力学（MHD）代码，如 \ exttt{VMEC} 和 \ exttt{DESC}，通过预设总环向磁通、等离子体剖面和最后一个闭合磁面（LCFS）来求解平衡问题，这在解析上确定了真空中的唯一场，而在有限 $\eta$ 下，文献中已报道了共享同一边界的分叉和不同平衡。在本文中，我们提出在单个环向平面上预设场的庞加莱截面，并在 \ exttt{DESC} 中实现，其中新条件仅通过线性约束进入，因此成本不超过固定 LCFS 求解。将几何固定在一个平面上而非整个环向表面，通常会使更多的谱系数保持自由，而释放的系数正是携带边界磁面环向变化的那些，而预设的 LCFS 在每个环向角上固定这些系数；这些共同允许更好的收敛数值解。我们从固定截面开始求解平衡，要么从该截面环向旋转得到的轴对称形状开始，要么从现有的固定 LCFS 解开始。在后一种情况下，体积平均归一化力误差下降一个数量级，而配置保持接近原始配置，并且用传统的固定 LCFS 求解器重新求解所得边界可恢复相同的平衡。我们进一步表明，庞加莱系数可以直接用作设计变量，通过优化一个准螺旋配置，在整个过程中保持高保真力平衡。
英文摘要
Stellarator ideal magnetohydrodynamic (MHD) codes that assume nested flux surfaces such as \texttt{VMEC} and \texttt{DESC} solve the equilibrium problem by prescribing the total toroidal magnetic flux, plasma profiles and the last closed flux surface (LCFS), which analytically determines the unique field in vacuum, whereas at finite $β$ bifurcations and distinct equilibria sharing the same boundary have been reported in the literature. In this paper, we propose prescribing the Poincaré cross-section of the field at a single toroidal plane, and implement it in \texttt{DESC}, where the new condition enters only through the linear constraints and therefore costs no more than a fixed-LCFS solve. Fixing the geometry on one plane rather than on a full toroidal surface generally leaves more of the spectral coefficients free, and the ones it frees are those carrying the toroidal variation of the boundary flux surface, which a prescribed LCFS holds fixed at every toroidal angle; together these allow better-converged numerical solutions. We solve equilibria with the cross-section held fixed, starting either from the axisymmetric shape obtained by revolving that cross-section toroidally, or from an existing fixed-LCFS solution. In the latter case, the volume-averaged normalized force error falls by an order of magnitude while the configuration stays close to the original one, and re-solving the resulting boundary with the conventional fixed-LCFS solver recovers the same equilibrium. We further show that the Poincaré coefficients can be used directly as design variables by optimizing a quasi-helical configuration that maintains high-fidelity force balance throughout the process.
