A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory

TL;DR

This paper presents an analytical approximation for nonlinear force-free magnetic fields that enables rapid forward-fitting to solar magnetic data, facilitating efficient modeling of coronal phenomena.

Contribution

The authors develop a second-order accurate analytical NLFFF approximation suitable for fast fitting to various types of solar magnetic data, improving modeling efficiency.

Findings

Provides explicit expressions for magnetic field components and current density.

Achieves second-order accuracy in the nonlinear force-free parameter.

Enables quick and accurate forward-fitting to observational data.

Abstract

We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components $B_x({\bf x})$, $B_y({\bf x})$, $B_z({\bf x})$, the force-free parameter $\alpha({\bf x})$, the electric current density ${\bf j}({\bf x})$, and are accurate to second-order (of the nonlinear force-free $\alpha$-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.