论文标题
基于梯度的3D MHD平衡优化
Gradient-based optimization of 3D MHD equilibria
论文作者
论文摘要
使用最近开发的伴随方法来计算依赖于MHD平衡的功能的形状衍生物（Antonsen等，2019; Paul等，2020），我们介绍了基于分析梯度的优化固定体性恒星平衡的第一个例子。我们利用梯度信息来优化与恒星设计相关性的优点图，包括轴附近的旋转变换，磁孔和准对称性。使用伴随方法的应用，我们通过优化空间（$ \ sim 50-500 $）的维度减少了平衡评估的数量，而基于有限差异梯度的方法。我们讨论了与固定边界优化相关性的正则目标，包括一种防止等离子体边界自我交流的新方法。我们提出了几个优化的平衡，包括在整个体积中具有非常低磁剪切的真空场。
Using recently developed adjoint methods for computing the shape derivatives of functions that depend on MHD equilibria (Antonsen et al. 2019; Paul et al. 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well, and quasisymmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ($\sim 50-500$) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.
