Conserving Local Magnetic Helicity in Numerical Simulations

TL;DR

This paper introduces an algorithm to enforce strict local conservation of magnetic helicity in numerical simulations, improving their accuracy in modeling astrophysical magnetic phenomena.

Contribution

The paper presents a novel algorithm that ensures local magnetic helicity conservation in simulations, addressing limitations of previous methods that suffered from numerical errors and resistivity effects.

Findings

Algorithm effectively enforces local magnetic helicity conservation.

Improved simulation fidelity in modeling astrophysical magnetic systems.

Reduces unphysical helicity loss due to numerical errors.

Abstract

Magnetic helicity is robustly conserved in systems with very large magnetic Reynolds numbers, including most systems of astrophysical interest, and unlike kinetic and magnetic energy is not dissipated at small scales. This plays a major role in suppressing the kinematic large-scale dynamo and may also be responsible for driving the large-scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. In these simulations, magnetic helicity is lost either through numerical errors or through the action of an unrealistically large resistivity. Errors in the internal distribution of magnetic helicity are equally important and typically larger. Here we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations so that their evolution more closely approximates that of real systems.