Elliptic-cylindrical analytical flux-rope model for ICMEs

We present an analytical flux-rope model for realistic magnetic structures embedded in Interplanetary Coronal Mass Ejections. The framework of this model was established by Nieves-Chinchilla et al. (2016) with the circular-cylindrical analytical flux rope model and under the concept developed by Hidalgo et al. (2002). Elliptic-cylindrical geometry establishes the first-grade of complexity of a series of models. The model attempts to describe the magnetic flux rope topology with distorted cross-section as a possible consequence of the interaction with the solar wind. In this model, the flux rope is completely described in the non-euclidean geometry. The Maxwell equations are solved using tensor calculus consistently with the geometry chosen, invariance along the axial component, and with the only assumption of no radial current density. The model is generalized in terms of the radial dependence of the poloidal current density component and axial current density component. The misalignment between current density and magnetic field is studied in detail for the individual cases of different pairs of indexes for the axial and poloidal current density components. This theoretical analysis provides a map of the force distribution inside of the flux-rope. The reconstruction technique has been adapted to the model and compared with in situ ICME set of events with different in situ signatures. The successful result is limited to some cases with clear in-situ signatures of distortion. However, the model adds a piece in the puzzle of the physical-analytical representation of these magnetic structures. Other effects such as axial curvature, expansion and/or interaction could be incorporated in the future to fully understand the magnetic structure. Finally, the mathematical formulation of this model opens the door to the next model: toroidal flux rope analytical model.