Self-consistent equilibrium of a force-free magnetic flux rope

TL;DR

This paper derives an exact, self-consistent equilibrium solution for a force-free magnetic flux rope using magnetostatic equations, providing new analytical profiles without phenomenological assumptions.

Contribution

It introduces a novel nonlinear equation for axial current density and obtains analytical magnetic field and current profiles for the flux rope.

Findings

Analytical radial profiles of magnetic field components

New nonlinear equation for axial current density

Self-consistent equilibrium solution

Abstract

We present an exact solution to the problem of a self-consistent equilibrium force-free magnetic flux rope. Unlike other approaches, we use magnetostatic equations and assume only a relatively rapid decrease in the axial magnetic field at infinity. For the first time we obtain a new nonlinear equation for the axial current density, the derivation of which does not require any phenomenological assumptions. From the resulting nonlinear equation, we analytically find the radial profiles of the components of the magnetic field strength and current density.