Generally Curved Magnetic Flux Rope Structures

We present a new analytical approach with the aim to describe generally curved and twisted magnetic flux rope structures, that are embedded within interplanetary coronal mass ejections, under the constraint of invariant axial flux. In this paper we showcase the simplest case of a generally curved flux rope with a circular cross-section which can be described in terms of the curvature and the torsion of the Frenet-Serret equations. The magnetic field configuration, for the axial and poloidal field components, are described in terms of a radial expansion using a Legendre basis. We further derive equations that allow us to configure our model for any arbitrary magnetic twist and also evaluate the force distribution. We show the effects and differences of our proposed model compared to a purely cylindrical or toroidal geometry using an arbitrarily twisted exemplary flux rope structure with an uniformly twisted magnetic field configuration. In order to indirectly compare our model with real in-situ measurements we generate two synthetic in-situ profiles using virtual spacecraft trajectories, realistically simulating apex and flank encounters of an interplanetary coronal mass ejection. This proposed model presents an intermediate steps towards describing more complex flux rope structures with arbitrary cross-section shapes.