Exact non-symmetric closed line vacuum magnetic fields in a topological torus

Abstract

Non-symmetric vacuum magnetic fields with closed magnetic field lines are of interest in the construction of stellarator equilibria. Beyond the result of D.Lortz (ZAMP \textbf{21}, 196 (1970)), few results are available. This work presents a closed-form expression for a class of vacuum magnetic fields in a topological torus with closed field lines. We explicitly obtain the invariants of such a field. We finally show that a three-dimensional low beta magnetohydrodynamic (MHD) equilibrium may be constructed in a topological torus starting with these closed line vacuum magnetic fields.

References in corpus (5)

• Direct construction of optimized stellarator shapes. I. Theory in cylindrical coordinates
• Constructing stellarators with quasisymmetry to high order
• Study of the interplay between magnetic shear and resonances using Hamiltonian models for the magnetic field lines
• Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equlibrium
• Low-shear three-dimensional equilibria and vacuum magnetic fields with flux surfaces

Cited by in corpus (3)

• Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface
• Symmetric Ideal Magnetofluidostatic Equilibria with Non-Vanishing Pressure Gradients in Asymmetric Confinement Vessels
• Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines