arXiv 2012.092782020-12-16physics.plasm-ph

等离子体-线圈组合优化算法

Combined plasma-coil optimization algorithms

Sophia A. Henneberg, Stuart R. Hudson, David Pfefferlé, Per Helander

备注：: to be submitted to JPP
DOI：: 10.1017/S0022377821000271

摘要：

讨论了仿星器等离子体线圈组合优化设计方法，提出了一种新的自由边界平衡计算方法。仿星器优化有四种不同的类型，其中两种是新的方法，它们是固定边界优化、广义固定边界优化、准自由边界优化和自由边界（线圈）优化。这些都是使用多区域弛豫磁流体动力学（MRxMHD）的能量功能，Biot-Savart积分，线圈惩罚功能和虚拟套管积分，及其衍生物。所提出的自由边界平衡计算不同于现有的方法中的边界值问题是如何提出的，并为新的方法，似乎没有一个相关的能量最小化原则，因为一个非对称的功能出现。我们建议解决这个问题的弱制定使用谱Galerkin方法，这将减少自由边界平衡计算的东西可比的固定边界计算。在我们的讨论组合等离子体线圈优化算法，我们强调的重要性，稳定性矩阵。

英文摘要：

Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi free-boundary optimization, and the free-boundary (coil) optimization. These are described using the multi-region relaxed magnetohydrodynmics (MRxMHD) energy functional, the Biot-Savart integral, the coil-penalty functional and the virtual casing integral, and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma-coil optimization algorithms, we emphasize the importance of the stability matrix.

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