Sparse Reconstruction of Electric Fields from Radial Magnetic Data
Abstract
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 timedependent magnetohydrodynamic models of the corona. In this paper, a method is developed for estimating the horizontal electric field from a sequence of radialcomponent magnetic field maps. This problem of inverting Faraday’s law has no unique solution. Unfortunately, the simplest solution (a divergencefree electric field) is not realistically localized in regions of nonzero 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.
 Authors:

 Department of Mathematical Sciences, Durham University, Durham, DH1 3LE (United Kingdom)
 Publication Date:
 OSTI Identifier:
 22663799
 Resource Type:
 Journal Article
 Journal Name:
 Astrophysical Journal
 Additional Journal Information:
 Journal Volume: 836; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004637X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASSIMILATION; ELECTRIC FIELDS; EVOLUTION; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PHOTOSPHERE; SPHERICAL CONFIGURATION; SUN; SURFACES; TIME DEPENDENCE
Citation Formats
Yeates, Anthony R. Sparse Reconstruction of Electric Fields from Radial Magnetic Data. United States: N. p., 2017.
Web. doi:10.3847/15384357/AA5C84.
Yeates, Anthony R. Sparse Reconstruction of Electric Fields from Radial Magnetic Data. United States. doi:10.3847/15384357/AA5C84.
Yeates, Anthony R. Fri .
"Sparse Reconstruction of Electric Fields from Radial Magnetic Data". United States. doi:10.3847/15384357/AA5C84.
@article{osti_22663799,
title = {Sparse Reconstruction of Electric Fields from Radial Magnetic Data},
author = {Yeates, Anthony R.},
abstractNote = {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 timedependent magnetohydrodynamic models of the corona. In this paper, a method is developed for estimating the horizontal electric field from a sequence of radialcomponent magnetic field maps. This problem of inverting Faraday’s law has no unique solution. Unfortunately, the simplest solution (a divergencefree electric field) is not realistically localized in regions of nonzero 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.},
doi = {10.3847/15384357/AA5C84},
journal = {Astrophysical Journal},
issn = {0004637X},
number = 1,
volume = 836,
place = {United States},
year = {2017},
month = {2}
}