The fundamental concept of magnetically confined nuclear fusion devices is the magnetohydrodynamic (MHD) equilibrium: the pressure gradient due to highly energetic charged particles is balanced by the Lorenz force due to strong magnetic fields. Hence, numerical methods for MHD equilibria are also fundamental for fusion engineering applications. We rely here on a finite element method on composite meshes for the simulation of axisymmetric equilibria in tokamaks, torus-shaped nuclear fusion devices. One mesh with Cartesian quadrilaterals covers the domain accessible by the plasma and one mesh with triangles discretizes the region outside the chamber. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the principal unknown, the poloidal magnetic flux, while preserving accurate meshing of the geometric details in the exterior. We show that higher order regularity allows to formulate appropriate optimal control problems that help to find a special type of equilibria, called snowflake equilibria, that are a very promising concept to mitigate high heat loads due to plasma escaping particles.

中文翻译：

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复合网格上的有限元方法用于调整托卡马克中的等离子体平衡

磁约束核聚变装置的基本概念是磁流体动力学（MHD）平衡：由于高能带电粒子所引起的压力梯度被强磁场所产生的洛伦兹力所平衡。因此，用于MHD平衡的数值方法也是融合工程应用的基础。我们在这里依靠复合网格上的有限元方法来模拟托卡马克，圆环形核聚变装置中的轴对称平衡。带有笛卡尔四边形的一个网格覆盖了等离子体可访问的区域，带有三角形的一个网格离散了腔室外的区域。这两个网格在狭窄的区域内重叠。这种方法提供了灵活性，可以轻松地以低成本实现较高的阶正则性，以近似主未知数，极向磁通，同时保持外部几何细节的精确啮合。我们表明，较高阶的规则性允许制定适当的最佳控制问题，以帮助找到一种特殊类型的平衡，即雪花平衡，这是一个非常有希望的概念，可以缓解由于等离子体逸出颗粒而产生的高热负荷。