仿星器永磁体排列的计算：线性最小二乘法
Calculation of permanent magnet arrangements for stellarators: A linear least-squares method
摘要：
在一些工程领域中出现的问题是在体积外部设计磁体以在其内部产生所需的磁场。这个问题的一个实例是仿星器设计，其中最近已经表明永磁体可以提供所需的磁场形状。在这里，我们展示了一个强大的和有效的算法REGCOIL_PM来计算这些永磁体的空间分布。该过程涉及少量的定点迭代，在每一步都解决了线性最小二乘问题。该方法利用毕奥-萨伐尔定律的精确线性磁化密度和近似线性的磁体尺寸，远离目标区域的磁体。没有对磁化方向施加约束，因此自然地找到Halbach解，并且可以使磁化的幅度均匀地等于目标值。
英文摘要：
A problem arising in several engineering areas is to design magnets outside a volume that produce a desired magnetic field inside it. One instance of this problem is stellarator design, where it has recently been shown that permanent magnets can provide the required shaping of the magnetic field. Here we demonstrate a robust and efficient algorithm REGCOIL_PM to calculate the spatial distribution of these permanent magnets. The procedure involves a small number of fixed-point iterations, with a linear least-squares problem solved at each step. The method exploits the Biot-Savart Law's exact linearity in magnetization density and approximate linearity in magnet size, for magnets far from the target region. No constraint is placed on the direction of magnetization, so Halbach solutions are found naturally, and the magnitude of the magnetization can be made uniformly equal to a target value.
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