Writhed Analytical Magnetic Flux Rope Model

TL;DR

This paper introduces a novel analytical model for magnetic flux ropes with writhed, non-cylindrical geometries, enabling more realistic descriptions of interplanetary magnetic clouds that account for deformations along their axes.

Contribution

The authors develop a writhed flux rope model with variable curvature and torsion, expanding beyond traditional cylindrical or toroidal assumptions to better represent deformed magnetic structures.

Findings

The model produces a class of solutions with varying magnetic twist.

It generates new magnetic field profiles differing from classical models.

The approach captures deformations along the flux rope axis.

Abstract

Observations of magnetic clouds, within interplanetary coronal mass ejections (ICMEs), are often well described by flux rope models. Most of these assume either a cylindrical or toroidal geometry. In some cases, these models are also capable of accounting for non-axisymmetric crosssections but they generally all assume axial invariance. It can be expected that any ICME, and its flux rope, will be deformed along its axis due to influences such as the solar wind. In this work, we aim to develop a writhed analytical magnetic flux rope model which would allow us to analytically describe a flux rope structure with varying curvature and torsion so that we are no longer constrained to a cylindrical or toroidal geometry. In this first iteration of our model we will solely focus on a circular cross-section of constant size. We describe our flux rope geometry in terms of a parametrized flux rope axis and a parallel transport frame. We derive expressions for the axial and poloidal magnetic field components under the assumption that the total axial magnetic flux is conserved. We find an entire class of possible solutions, which differ by the choice of integration constants, and present the results for a specific example. In general, we find that the twist of the magnetic field locally changes when the geometry deviates from a cylinder or torus. This new approach also allows us to generate completely new types of in situ magnetic field profiles which strongly deviate from those generated by cylindrical or toroidal models.