Winding and Helicity in Periodic Domains

Daining Xiao (Durham University)

Wednesday 22nd November, 2023 15:00-16:00 Maths 309

Abstract

Periodic boundary conditions are commonly used for computation in numerical magnetohydrodynamical studies. However, it has been a challenge to geometrically interpret magnetic helicity (an ideal invariant) in this configuration, given the classical result that magnetic helicity in magnetically closed domains is equivalent to the Gauss linking number of field lines. Continuing from our earlier studies in spherical geometry (Xiao, Prior & Yeates, 2023, J. Phys. A.), we propose an analogous winding-based definition of magnetic helicity that is both mathematically rigorous and efficiently computable from magnetic fields. We prove its properties as a physically meaningful quantity, and compare it with the existing literature, e.g., the topological approach (MacTaggart & Valli, 2023, J. Phys. A.) and Fourier methods (Yang et al., 2020, Astrophy. J.).

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