2024/11/07 by Maximilian Ruth, R. Jorge, Ruth, Maximilian +3 · 2 citations
Engineering · Materials Science · Physics and Astronomy · #65M30 #FOS: Mathematics #FOS: Physical sciences #G.1.8 #Magnetic Properties of Alloys #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Particle accelerators and beam dynamics #Plasma Physics (physics.plasm-ph)
paper · pdf · doi:10.48550/arxiv.2411.04352
openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When analyzing stellarator configurations, it is common to perform an asymptotic expansion about the magnetic axis. This so-called near-axis expansion is convenient for the same reason asymptotic expansions often are, namely, it reduces the dimension of the problem. This leads to convenient and quickly computed expressions of physical quantities, such as quasisymmetry and stability criteria, which can be used to gain further insight. However, it has been repeatedly found that the expansion diverges at high orders in the distance from axis, limiting the physics the expansion can describe. In this paper, we show that the near-axis expansion diverges in vacuum due to ill-posedness and that it can be regularized to improve its convergence. Then, using realistic stellarator coil sets, we demonstrate numerical convergence of the vacuum magnetic field and flux surfaces to the true values as the order increases. We numerically find that the regularization improves the solutions of the near-axis expansion under perturbation, and we demonstrate that the radius of convergence of the vacuum near-axis expansion is correlated with the distance from the axis to the coils.