Investigating Magnetic Clouds through Velocity-Modified Flux Rope Models

Magnetic clouds (MCs) have been identified as a type of well organized magnetic field structures in space plasmas. They are usually fitted with models which are static such as Lundquist's force free cylindrically-symmetric flux rope solution. But MCs usually expand when propagating away from the Sun so we need a better model which includes it. In this study, we expand on the work of Farrugia et al., 1993, and we investigate the expansion only for the component perpendicular to the MCs axes. We introduce velocity-modified analytical flux rope models for non-force-free solutions of magnetic clouds, and compare the results of expanding models with those that do not expand. We fit several MCs by these expanding circular cylindrical flux rope models, in order to qualitatively analyze their expansion speed.