A Practical Approach to Coronal Magnetic Field Extrapolation Based on the Principle of Minimum Dissipation Rate

TL;DR

This paper introduces a new method for extrapolating the solar coronal magnetic field using the Principle of Minimum Dissipation Rate, which generalizes force-free models and is validated against simulation data.

Contribution

The paper develops a novel MDR-based extrapolation method that decomposes the magnetic field into linear force-free and potential components, suitable for open, driven systems like the solar corona.

Findings

Quantitative accuracy in magnetic energy estimates within a few percent

Successful recovery of strong perpendicular current density structures

Both approaches yield good results when tested against 3D MHD simulations

Abstract

We present a newly developed approach to solar coronal magnetic field extrapolation from vector magnetograms, based on the Principle of Minimum Dissipation Rate (MDR). The MDR system was derived from a variational problem that is more suitable for an open and externally driven system, like the solar corona. The resulting magnetic field equation is more general than force-free. Its solution can be expressed as the superposition of two linear (constant-$\alpha$) force-free fields (LFFFs) with distinct $\alpha$ parameters, and one potential field. Thus the original extrapolation problem is decomposed into three LFFF extrapolations, utilizing boundary data. The full MDR-based approach requires two layers of vector magnetograph measurements on solar surface, while a slightly modified practical approach only requires one. We test both approaches against 3D MHD simulation data in a finite volume. Both yield quantitatively good results. The errors in the magnetic energy estimate are within a few percents. In particular, the main features of relatively strong perpendicular current density structures, representative of the non-force freeness of the solution, are well recovered.