Writhed Analytical Magnetic Flux Rope Model
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 nonaxisymmetric 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 crosssection 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.
 Publication:

Journal of Geophysical Research (Space Physics)
 Pub Date:
 December 2022
 DOI:
 10.1029/2022JA030898
 arXiv:
 arXiv:2202.10096
 Bibcode:
 2022JGRA..12730898W
 Keywords:

 flux rope modeling;
 ICMEs;
 flux ropes;
 Earth Science;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Space Physics
 EPrint:
 19 pages, 4 figures