Distorted-Toroidal Flux Rope Model

The 3D characterization of magnetic flux ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitations on inferring the 3D global topology and physical properties from the 1D time series from any spacecraft. To advance our understanding of magnetic flux ropes whose configuration departs from the typical stiff geometries, here we present an analytical solution for a 3D flux rope model with an arbitrary cross section and a toroidal global shape. This constitutes the next level of complexity following the elliptic-cylindrical (EC) geometry. The mathematical framework was established by Nieves-Chinchilla et al. with the EC flux rope model, which describes a magnetic topology with an elliptical cross section as a first approach to changes in the cross section. In the distorted-toroidal flux rope model, the cross section is described by a general function. The model is completely described by a nonorthogonal geometry and the Maxwell equations can be consistently solved to obtain the magnetic field and relevant physical quantities. As a proof of concept, this model is generalized in terms of the radial dependence of current density components. The last part of this paper is dedicated to a specific function, F(φ) = δ (1 - λ cosφ), to illustrate possibilities of the model. This model paves the way toward the investigation of complex distortions of magnetic structures in the solar wind. Future investigations will explore these distortions in depth by analyzing specific events; studying implications for physical quantities, such as magnetic fluxes, helicity, or energy; and evaluating the force balance with the ambient solar wind that allows such distortions.