Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface

Abstract

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic PDE for a function $\eta$ such the field strength satisfies $B=B(\eta )$. Closed-form solutions are obtained in cylindrical, slab, and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasi-helical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side.

References in corpus (10)

• Necessary and Sufficient Conditions for Quasisymmetry
• Near-Axis Expansion of Stellarator Equilibrium at Arbitrary Order in the Distance to the Axis
• Magnetic well and Mercier stability of stellarators near the magnetic axis
• Construction of Quasisymmetric Stellarators Using a Direct Coordinate Approach
• Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance
• On quasisymmetric plasma equilibria sustained by small force
• The Use of Near-Axis Magnetic Fields for Stellarator Turbulence Simulations
• Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions. II. Circular axis stellarators
• Optimized quasisymmetric stellarators are consistent with the Garren-Boozer construction
• Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

Cited by in corpus (4)

• Generalized Boozer coordinates: a natural coordinate system for quasisymmetry
• Adjoint methods for quasisymmetry of vacuum fields on a surface
• Existence of weakly quasisymmetric magnetic fields in asymmetric toroidal domains with non-tangential quasisymmetry
• Quasisymmetric magnetic fields in asymmetric toroidal domains