论文标题
磁轴附近恒星的功绩图
Figures of merit for stellarators near the magnetic axis
论文作者
论文摘要
最近已经证明了一种新的用于快速恒星构型构型设计的范式，其中直接使用距磁轴较小距离的膨胀来直接计算出准对称或异常通量表面的形状。为了进一步开发这种方法，我们在这里得出了其他数量的兴趣，可以从这种近轴扩展中快速计算出来。首先，计算$ \ nabla \ vec {b} $和$ \ nabla \ nabla \ nabla \ vec {b} $张量，可用于基于直接衍生的基于基于电磁线圈形状的优化，以实现所需的磁性配置。此外，如果与给定磁场的磁场强度相比，这些张量的标准很大，则该场必须具有短长度的比例，这表明可能很难用适合远距离的线圈产生。其次，我们评估了通量表面形状将变得奇异的小半径，从而在可实现的纵横比上提供了下限。该结合也证明与平衡β极限有关。最后，对于构造的配置以达到所需的磁场强度到扩展中的第一阶，我们计算由于二阶项而产生的误差场。
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 $\nabla\vec{B}$ and $\nabla\nabla\vec{B}$ 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 to 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.
