# Sparse reconstruction of electric fields from radial magnetic data

## TL;DR

This paper introduces a sparse reconstruction method for estimating localized horizontal electric fields on the Sun's surface from radial magnetic data, improving modeling of solar corona energy transfer.

## Contribution

A novel sparse basis pursuit algorithm is developed to produce localized electric field estimates from magnetic maps, addressing the non-uniqueness of the inverse problem.

## Key findings

- Performs well on flux-balanced magnetic maps in Cartesian and spherical geometries.
- Localization fails with flux-imbalanced maps common in data assimilation.
- Main obstacle is flux imbalance in input data, affecting realistic electric field estimation.

## 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 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.