Numerical tests of formulae for volume enclosed by flux surfaces of integrable magnetic fields

2025/10/02 by Martinez-del-Rio, David, MacKay, Robert S.
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Plasma Physics (physics.plasm-ph)

paper · doi:10.48550/arxiv.2510.01957

Abstract

Numerical tests of volume formulae are presented to compute efficiently the volume enclosed between flux surfaces for integrable 3D vector fields with various degrees of symmetry. In the process, a new case is proposed and tested.

Citations

• Computation of Magnetohydrodynamic Equilibria with Voigt Regularization
• Conefield approach to identifying regions without flux surfaces for magnetic fields
• Volume enclosed by a flux surface
• Regions without flux surfaces of given class for magnetic fields in toroidal geometry
• Some mathematics for quasi-symmetry
• Numerical Integration of Periodic Functions: A Few Examples

Related

• Volume enclosed by a flux surface
• Magnetic flux surfaces and magnetic curves with Bishop frame in Euclidean 3-space
• Method of Relative Magnetic Helicity Computation II: Boundary Conditions for the Vector Potentials
• Flux ruled surfaces and the magnetic curves obtained from the curvature theory
• Magnetic spherical indicatrix of a ruled surface