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A Comparison of Sparse and Non-sparse Techniques for Electric-Field Inversion from Normal-Component Magnetograms

Mackay, D. H. and Yeates, A. R. (2021) 'A Comparison of Sparse and Non-sparse Techniques for Electric-Field Inversion from Normal-Component Magnetograms.', Solar Physics, 296 (12). p. 178.


An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm’s law. Yeates (Astrophys. J. 836(1), 131, 2017) put forward a new “sparse” technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm’s law compared to previously used “non-sparse” techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J. 729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise.

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Publisher statement:Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Date accepted:09 November 2021
Date deposited:25 January 2022
Date of first online publication:08 December 2021
Date first made open access:25 January 2022

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