We present the first single-stage optimization of islands in finite-$β$ stellarator equilibria. Stellarator optimization is traditionally performed as a two-stage process; in the first stage, an optimal equilibrium is calculated which balances a set of competing constraints, and in the second stage a set of coils is found that supports said equilibrium. Stage one is generally performed using a representation for the equilibrium that assumes nestedness of flux surfaces, even though this is not warranted and occasionally undesired. The second stage optimization of coils is never perfect, and the mismatch leads to worse performing equilibria, and further deteriorates if additional constraints such as force minimization, coil torsion or port access are included. The higher fidelity of single-stage optimization is especially important for the optimization of islands as these are incredibly sensitive to changes in the field. In this paper we demonstrate an optimization scheme capable of optimizing islands in finite $β$ stellarator equilibria directly from coils. We furthermore develop and demonstrate a method to reduce the dimensionality of the single-stage optimization problem to that of the first stage in the two-stage approach.
Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing
Analytic non-axisymmetric 3D MHD equilibria without stellarator symmetry
Google DeepMind（谷歌DeepMind）；Department of Mechanical and Aerospace Engineering, University of California San Diego（加州大学圣地亚哥分校机械与航空航天工程系）；University of Maryland, College Park（马里兰大学帕克学院）
Omnigenous stellarators with improved ideal and kinetic ballooning stability
Princeton University（普林斯顿大学）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；University of York（约克大学）；University of Maryland, College Park（马里兰大学帕克分校）
Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry
提出了一种优化仿星器几何结构的方法，在消除磁岛的同时，实现了仿星器的其他物理特性。对于许多已经在仿星器优化中使用的物理量，包括准对称性，新古典输运和磁流体动力学稳定性，使用确保磁表面存在的磁平衡表示是方便的。然而，这种表示隐藏了磁岛的可能存在，这通常是不希望的。为了在单个优化中包括基于表面的目标和岛宽度，在优化的每次迭代中运行两个固定边界平衡计算：一个是强制磁表面的存在（VMEC [S.赫什曼和J. C. Whitson，Phys.Fluids 26，3553（1983）]），和一种不这样（SPEC [S. R. Hudson等人，Phys.Plasmas 19，112502（2012）]）。通过惩罚目标函数中的岛残基，在优化期间使两个磁场表示一致。一个例子中，特别是在表面上的准对称的目标，准对称实现更准确地比以前公布的例子。
Stochastic single-stage stellarator optimization using fixed-boundary equilibria
Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）；Max-Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）；Department of Physics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校物理系）；Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院等离子体与核聚变研究所）
Stellarator optimization for nested magnetic surfaces at finite $β$ and toroidal current
良好的磁表面，相对于磁岛和混乱的场线，通常是仿星器所需要的。在以前的工作中，M。Landreman等人[Phys. of Plasmas 28，092505（2021）]表明，通过步进压力平衡代码（SPEC）[S. P. Hudson等人，等离子体19，112502（2012）]可以优化用于真空中的良好磁性表面。在本文中，我们建立在他们的工作，以显示第一个有限的$β$，固定和自由边界优化的SPEC平衡良好的磁性表面。目标函数由选取的有理曲面的Greene残数构造，优化过程由SIMSOPT框架驱动[M. Landreman等人，J. Open Source Software 6，3525（2021）]。我们表明，在一个经典的仿星器的几何形状，通过优化注入的环形电流分布，一个完美的导电壁周围的等离子体的形状（固定边界的情况下），或线圈（自由边界的情况下），在一个合理的计算时间量的磁岛的大小和随之而来的区域所占据的混乱的场线可以最小化。这项工作表明，SPEC可以用作两步或单步仿星器优化循环的平衡代码。
Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis
1 Max-Planck-Institute for Plasma Physics, 17491 Greifswald, Germany 2 Institute for Research in Electronics \& Applied Physics, University of Maryland, MD 20742, USA 3 Mechanical；Aerospace Engineering, Princeton University, NJ 08544, USA
How Does The Magnetic Gradient Scale Length Influence Complexity of Filamentary Coils in Stellarators?
Institute for Research in Electronics and Applied Physics, University of Maryland（马里兰大学电子研究与应用物理研究所）；Proxima Fusion（普罗克西玛聚变）；Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）
A Variational Framework for Guiding-Center Kinetics, Anisotropic Equilibria, and Quasisymmetry in Stellarators
Courant Institute School of Mathematics, Computing, and Data Science, New York University（纽约大学库朗数学科学研究所）；Department of Astrophysical Sciences, Princeton University（普林斯顿大学天体物理科学系）
AI-Accelerated Gyrokinetic Predictions of Turbulent Transport for Stellarator Design Optimization and Experimental Planning
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；University of Maryland, College Park（马里兰大学帕克分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；Type One Energy；California Institute of Technology（加州理工学院）；Argonne National Laboratory（阿贡国家实验室）；Princeton University（普林斯顿大学）；University of Wisconsin, Madison（威斯康星大学麦迪逊分校）
Relaxed magnetohydrodynamics with cross-field flow
Mathematical Sciences Institute, Australian National University（澳大利亚国立大学数学科学研究所）；Proxima Fusion（普罗克西玛聚变）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数理科学学院）
SPECTRE: A robust solver for 3D equilibria with arbitrary topology
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Proxima Fusion GmbH（Proxima Fusion有限公司）；Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）；York Plasma Institute, School of Physics, University of York（约克大学物理学院约克等离子体研究所）
