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Spatial scales and locality of magnetic helicity

Prior, Christopher; Hawkes, Gareth; Berger, M.

Spatial scales and locality of magnetic helicity Thumbnail


Authors

Gareth Hawkes

M. Berger



Abstract

Context: Magnetic helicity is approximately conserved in resistive magnetohydrodynamic models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both dynamo development in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement. Aims: There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. Spectral helicity decompositions can be used in periodic domains and is fruitful for the analysis of homogeneous phenomena. This paper aims to develop methods for analysing the evolution of magnetic field topology in non-homogeneous systems. Methods: The method of multi-resolution wavelet decomposition is applied to the magnetic field. It is demonstrated how this decomposition can further 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. Results: It is shown that the multi-resolution decomposition of helicity has the crucial property of local additivity. We demonstrate a general linear energy-topology conservation law, which significantly generalises 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. Conclusions: The multi-resolution wavelet decomposition can be used to analyse the evolution of helicity in magnetic fields in a manner which is consistently additive. This method has the advantage over more established spectral methods in that it clearly characterises the inhomogeneous nature of helicity flows where spectral methods cannot. Further, its applicability in aperiodic models significantly increases the range of potential applications.

Citation

Prior, C., Hawkes, G., & Berger, M. (2020). Spatial scales and locality of magnetic helicity. Astronomy & Astrophysics, 635, Article A95. https://doi.org/10.1051/0004-6361/201936675

Journal Article Type Article
Acceptance Date Dec 8, 2019
Online Publication Date Mar 13, 2020
Publication Date Mar 31, 2020
Deposit Date Dec 10, 2019
Publicly Available Date Mar 28, 2024
Journal Astronomy and astrophysics.
Print ISSN 0004-6361
Electronic ISSN 1432-0746
Publisher EDP Sciences
Peer Reviewed Peer Reviewed
Volume 635
Article Number A95
DOI https://doi.org/10.1051/0004-6361/201936675
Related Public URLs https://arxiv.org/abs/1909.07838

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Copyright Statement
Prior, Christopher, Hawkes, Gareth & Berger, M. (2020). Spatial scales and locality of magnetic helicity. Astronomy and Astrophysics 635: A95 reproduced with permission, © ESO.






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