论文标题
恒星的永久磁体布置的计算：线性最小二乘法
Calculation of permanent magnet arrangements for stellarators: A linear least-squares method
论文作者
论文摘要
在几个工程领域产生的一个问题是在体积之外设计磁铁，该磁铁在其内部产生所需的磁场。这个问题的一个实例是恒星设计，最近已经证明永久磁铁可以提供磁场所需的形状。在这里，我们演示了一种强大，有效的算法regcoil_pm来计算这些永久磁体的空间分布。该过程涉及少量的定点迭代，每个步骤都解决了线性最小二乘问题。该方法利用了远离目标区域的磁体，利用了磁化密度的生物 - 萨瓦特定律的精确线性和近似线性的线性。没有约束在磁化方向上放置，因此自然而然地发现了Halbach溶液，并且可以使磁化强度均匀地等于目标值。
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.
