Spatial Scales and Locality of Magnetic Helicity: Part 1

Abstract

Magnetic helicity is approximately conserved in resistive MHD models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both the dynamo in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement.There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. We apply a multiresolution wavelet decomposition to the magnetic field and demonstrate how it can be applied to various quantities associated with magnetic helicity, including the field line helicity. We use a geometrical definition of helicity which allows these quantities to be calculated for fields with arbitrary boundary conditions. It is shown that the multiresolution decomposition of helicity has the crucial property of local additivity and demonstrate a general linear energy-topology conservation law which is a significant generalisation of the two point correlation decomposition used in the analysis of homogeneous turbulence and periodic fields. The localisation property of the wavelet representation is shown to characterise inhomogeneous distributions which a Fourier representation cannot. Using an analytic representation of a resistive braided field relaxation we demonstrate a clear correlation between the variations in energy at various length scales and the variations in helicity at the same spatial scales. Its application to helicity flows in a surface flux transport model show how various contributions to the global helicity input from active region field evolution and polar field development are naturally separated by this representation.

arXiv commentSubmitted to Astronomy and Astrophysics

References in corpus (24)

• Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results
• Magnetic Helicity Conservation and Astrophysical Dynamos
• Doubly Helical Coronal Ejections from Dynamos and their Role in Sustaining the Solar Cycle
• The solar magnetic field since 1700: I. Characteristics of sunspot group emergence and reconstruction of the butterfly diagram
• Galactic dynamos supported by magnetic helicity fluxes
• Scale-dependence of magnetic helicity in the solar wind
• Magnetic helicity density and its flux in weakly inhomogeneous turbulence
• The variation of relative magnetic helicity around major flares
• The invariant Twist of Magnetic Fields in the Relativistic Jets of Active Galactic Nuclei
• Magnetic Braiding and Quasi-Separatrix Layers
• Threshold of non-potential magnetic helicity ratios at the onset of solar eruptions
• On the Helicity of Open Magnetic Fields
• Evolution of field line helicity during magnetic reconnection
• Heating of braided coronal loops
• Magnetic Helicity and Large Scale Magnetic Fields: A Primer
• Photospheric Injection of Magnetic Helicity: Connectivity--based Flux Density Method
• Unique Topological Characterization of Braided Magnetic Fields
• Two-scale analysis of solar magnetic helicity
• Relative field-line helicity in bounded domains
• The critical role of magnetic helicity in astrophysical large-scale dynamos
• Relative magnetic field line helicity
• Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops
• How Spectral Shapes of Magnetic Energy and Magnetic Helicity Influence their Respective Decay Time Scales
• Interpreting magnetic helicity flux in solar flux emergence

Cited by in corpus (3)

• Differences in periodic magnetic helicity injection behaviour between flaring and non-flaring Active Regions: Case Study
• On the differences in the periodic behaviour of magnetic helicity flux in flaring active regions with and without X-class events
• Inferring magnetic helicity spectrum in spherical domains: the method and example applications