Elliptic-cylindrical Analytical Flux Rope Model for Magnetic Clouds

In this paper, we present the elliptic-cylindrical analytical flux rope model, which constitutes the first level of complexity above that of a circular-cylindrical geometry. The framework of this series of models was established by Nieves-Chinchilla et al. with the circular-cylindrical analytical flux rope model. The model describes the magnetic flux rope topology with distorted cross section as a possible consequence of the flux rope interaction with the solar wind. In this model, for the first time, a flux rope is completely described by a nonorthogonal geometry. The Maxwell equations can be consistently solved using tensorial analysis, and relevant physical quantities can be derived, such as magnetic fluxes, number of turns, or Lorentz force distribution. The model is generalized in terms of the radial dependence of the poloidal and axial current density components. The circular-cylindrical reconstruction technique has been adapted to the new geometry for a specific case of the model and tested against an interplanetary coronal mass ejection observed by the Wind spacecraft on 2005 June 12. In this specific case, from the comparative analysis between the circular-cylindrical and elliptic-cylindrical models, the inclusion of the cross-section distortion in the 3D reconstruction results in significant changes in the derived axis orientation, size, central magnetic field, magnetic fluxes, and force-freeness. The case studied in this paper exemplifies the use of the model and reconstruction technique developed. Furthermore, the novel mathematical formulation to model flux ropes in heliophysics paves the way to the inclusion of more complex magnetic field configurations.