Writhed Magnetic Flux Rope Model

We present our latest developments for a writhed, or bent, magnetic flux rope model, which allows 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. The mathematical framework is based on previous work from Nieves-Chinchilla et al., where we now describe the current and the magnetic field in terms of a coefficient series with shifted Legendre polynomials instead of a power series. We derive expressions for the axial and poloidal magnetic field components under the assumption that the total axial magnetic flux is conserved. The model also supports arbitrary twist distributions. We present a fully analytical solution for the case of an arbitrarily curved flux rope within a plane. In the case of a writhed flux rope, with arbitrary curvature and torsion, we find an approximate solution that is valid for small curvature. In both cases we find that the twist of the magnetic field changes locally when the geometry deviates from a cylinder or torus. We also show how this model can be numerically implemented for the purpose of modelling large-scale ICME flux rope structures, which are key for interpreting multi-point ICME spacecraft measurements at large separations.