论文标题
计算相对于等离子体边界的恒星线圈复杂性的形状梯度
Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary
论文作者
论文摘要
线圈复杂性是恒星设计中的关键考虑。传统的两步优化方法，在该方法中，血浆边界针对物理性质进行了优化，并且线圈随后优化以与该边界一致，可以导致血浆形状无法用足够简单的线圈产生。为了应对这一挑战，我们提出了一种将线圈复杂性考虑在等离子体边界的优化中的方法。线圈复杂度指标是从使用Regcoil代码获得的当前潜在解决方案计算的（Landreman 2017Nucl。Fusion57 046003）。我们使用形状梯度来计算这些指标相对于等离子体边界扰动的局部灵敏度（Landreman＆Paul 2018nucl。Fusion。58076023）。我们扩展了对描述血浆边界的参数的计算这些指标的衍生物。为了与先前对绕组表面优化的研究保持一致（Paul等人，2018Nucl。Fusion58 076015），使用离散的伴随方法计算形状衍生物。与先前的工作相反，衍生物是根据等离子体而不是绕组表面参数计算的。为了进一步降低所需的分辨率，我们使用单个傅立叶级数提出了血浆表面的更有效表示，以描述与坐标轴和光谱凝结的螺状角的径向距离。与VMEC代码中使用的标准圆柱表示相比（Hirshman＆Whitson 1983年流体物理学26 3553-3568）相比，该表示形式是有利的，因为它提供了独特定义的螺状角，消除了等化表面优化的空空间。所得的形状梯度突出显示了与简单线圈一致的等离子体边界的特征，可用于将线圈和固定边界优化搭配。
Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman 2017 Nucl. Fusion 57 046003). We compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul 2018 Nucl. Fusion 58 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al. 2018 Nucl. Fusion 58 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma rather than the winding surface parameters. To further reduce the required resolution, we present a more efficient representation of the plasma surface using a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson 1983 The Physics of Fluids 26 3553-3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. The resulting shape gradient highlights features of the plasma boundary consistent with simple coils and can be used to couple coil and fixed-boundary optimization.
