A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.

中文翻译：

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靠近磁轴的仿星器的品质因数

最近已经展示了一种用于快速仿星器配置设计的新范例，其中准对称或全能通量表面的形状是直接使用距磁轴小距离的扩展来计算的。为了进一步发展这种方法，我们在这里推导出其他几个可以从这种近轴扩展中快速计算出来的感兴趣的量。首先， $\boldsymbol {\nabla }\boldsymbol {B}$ 和 $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ 计算张量，可用于基于直接导数的电磁线圈形状优化，以实现所需的磁性配置。此外，如果这些张量的范数与给定磁场的场强相比较大，则该场必须具有较短的长度尺度，这表明使用适当远离的线圈可能难以产生。其次，我们评估了通量表面形状变得奇异的小半径，提供了可实现纵横比的下限。这个界限也被证明与平衡β极限有关。最后，对于构造为在展开中实现所需磁场强度到一阶的配置，我们计算由于二阶项而产生的误差场。