Distorted-toroidal Flux Rope Model for Heliospheric Flux Ropes

The three-dimensional characterization of magnetic flux-ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to limitation infer 3D global topology and physical properties from 1D time series any spacecraft. To advance our understanding whose configuration departs typical stiff geometries, here we present analytical solution flux-rope model with an arbitrary cross-section toroidal shape. constitutes next level complexity following elliptic-cylindrical (EC) geometry. mathematical framework was established by Nieves-Chinchilla et al. (2018) ApJ, EC that describes elliptical as first approach changes cross-section. In distorted-toroidal flux rope model, described general function. completely non-orthogonal geometry Maxwell equations can be consistently solved obtain field relevant quantities. As proof concept, this generalized terms radial dependence current density components. last part paper dedicated specific function, $F(\varphi)=\delta(1-\lambda\cos\varphi)$, illustrate possibilities model. paves way investigate complex distortions structures solar wind. Future investigations will in-depth explore these analyzing events, implications quantities, such fluxes, heliciy or energy, evaluating force balance ambient wind allows distortions.