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Sparse reconstruction of electric fields from radial magnetic data

Yeates, A.R.

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Accurate estimates of the horizontal electric field on the Sun's visible surface are important not only for estimating the Poynting flux of magnetic energy into the corona but also for driving time-dependent magnetohydrodynamic models of the corona. In this paper, a method is developed for estimating the horizontal electric field from a sequence of radial-component magnetic field maps. This problem of inverting Faraday's law has no unique solution. Unfortunately, the simplest solution (a divergence-free electric field) is not realistically localized in regions of non-zero magnetic field, as would be expected from Ohm's law. Our new method generates instead a localized solution, using a basis pursuit algorithm to find a sparse solution for the electric field. The method is shown to perform well on test cases where the input magnetic maps are flux balanced, in both Cartesian and spherical geometries. However, we show that if the input maps have a significant imbalance of flux - usually arising from data assimilation - then it is not possible to find a localized, realistic, electric field solution. This is the main obstacle to driving coronal models from time sequences of solar surface magnetic maps.


Yeates, A. (2017). Sparse reconstruction of electric fields from radial magnetic data. Astrophysical Journal, 836(1), Article 131.

Journal Article Type Article
Acceptance Date Jan 27, 2017
Online Publication Date Feb 14, 2017
Publication Date Feb 14, 2017
Deposit Date Jan 27, 2017
Publicly Available Date Jan 27, 2017
Journal Astrophysical Journal
Print ISSN 0004-637X
Electronic ISSN 1538-4357
Publisher American Astronomical Society
Peer Reviewed Peer Reviewed
Volume 836
Issue 1
Article Number 131
Related Public URLs


Accepted Journal Article (1 Mb)

Copyright Statement
© 2017. The American Astronomical Society. All rights reserved.

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