Relative field-line helicity in bounded domains

Abstract

Models for astrophysical plasmas often have magnetic field lines that leave the boundary rather than closing within the computational domain. Thus, the relative magnetic helicity is frequently used in place of the usual magnetic helicity, so as to restore gauge invariance. We show how to decompose the relative helicity into a relative field-line helicity that is an ideal-magnetohydrodynamic invariant for each individual magnetic field line, and vanishes along any field line where the original field matches the reference field. Physically, this relative field-line helicity is a magnetic flux, whose specific definition depends on the gauge of the reference vector potential on the boundary. We propose a particular `minimal' gauge that depends only on the reference field and minimises this boundary contribution, so as to reveal topological information about the original magnetic field. We illustrate the effect of different gauge choices using the Low-Lou and Titov-Demoulin models of solar active regions. Our numerical code to compute appropriate vector potentials and relative field-line helicity in Cartesian domains is open source and freely available.

21 pages, 9 figures, accepted for publication in J Plasma Phys (will appear in revised form after editorial input by Cambridge University Press)

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Cited by in corpus (10)

• Relative field line helicity of a large eruptive solar active region
• Relative magnetic field line helicity
• Two Classes of Eruptive Events During Solar Minimum
• Magnetic Helicity and Free Magnetic Energy as Tools to Probe Eruptions in two Differently Evolving Solar Active Regions
• Comparison of magnetic energy and helicity in coronal jet simulations
• Spatial Scales and Locality of Magnetic Helicity: Part 1
• The Minimal Helicity of Solar Coronal Magnetic Fields
• Magnetic field extrapolation in active region well comparable with observations in multiple layers
• Evolution of Field Line Helicity in Magnetic Relaxation
• The Properties of Non-Potential Magnetic Field Parameters in a Super-Active Region with Complex Structures and Strong Solar Flares