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Dynamical evolution of a magnetic cloud from the Sun to 5.4 AU

Magnetic Clouds (MCs) are a particular subset of Interplanetary Coronal Mass Ejections (ICMEs), forming large scale magnetic flux ropes. In this work we analyze the evolution of a particular MC (observed on March 1998) using {\it in situ} observations made by two spacecraft approximately aligned with the Sun, the first one at 1 AU from the Sun and the second one at 5.4 AU. We study the MC expansion, its consequent decrease of magnetic field intensity and mass density, and the possible evolution of the so-called global ideal-MHD nvariants. We describe the magnetic configuration of the MC at both spacecraft using different models and compute relevant global quantities (magnetic fluxes, helicity and energy) at both helio-distances. We also track back this structure to the Sun, in order to find out its solar source. We find that the flux rope is significantly distorted at 5.4 AU. However, we are able to analyze the data before the flux rope center is over-passed and compare it with observations at 1 AU. From the observed decay of magnetic field and mass density, we quantify how anisotropic is the expansion, and the consequent deformation of the flux rope in favor of a cross section with an aspect ratio at 5.4 AU of $\approx 1.6$ (larger in the direction perpendicular to the radial direction from the Sun). We quantify the ideal-MHD invariants and magnetic energy at both locations, and find that invariants are almost conserved, while the magnetic energy decays as expected with the expansion rate found. The use of MHD invariants to link structures at the Sun and the interplanetary medium is supported by the results of this multispacecraft study. We also conclude that the local dimensionless expansion rate, that is computed from the velocity profile observed by a single spacecraft, is very accurate for predicting the evolution of flux ropes in the solar wind.