Simons Hour Talk

Taking the Near-Axis Expansion to Arbitrary Order: Ill-Posedness and Regularization
Aug 15, 2024, 10:00 am11:00 am



Event Description

Abstract: The near-axis expansion (NAE) has been used widely within the Simons Collaboration on Hidden Symmetries and Nuclear Fusion. For theorists, its asymptotic nature is useful for analyzing properties of quasisymmetry and stability criteria. For those who compute, the low-dimensional structure of the NAE allows for efficient exploration of the space of stellarators without relying on full 3D MHS solvers. Unfortunately, it has been found by many that the NAE tends to diverge at higher orders, leading to limitations on its ability to resolve important objectives (such as corrections to the magnetic shear and curvature).
In this talk, we focus on the vacuum problem, where we show that one explanation for the NAE’s divergence is that the underlying problem is ill-posed. To fix this, we introduce a regularization term to the expansion and show that we can achieve improved convergence of the magnetic field in high orders of the magnetic expansion. Using a coil set optimized to the Landreman-Paul stellarator configuration, we find asymptotic agreement of both flux surfaces and rotational transform to 9 orders.

Talk time in other timezones:
AEST 12:00 AM Fri 16 Aug,
JST  11:00 PM Thu 15 Aug,
CEST  4:00 PM Thu 15 Aug,
BST   3:00 PM Thu 15 Aug,
UTC  14:00    Thu 15 Aug,
EDT  10:00 AM Thu 15 Aug,
CDT   9:00 AM Thu 15 Aug,
MDT   8:00 AM Thu 15 Aug,
MST   7:00 AM Thu 15 Aug,
PDT   7:00 AM Thu 15 Aug
Simons Foundation