Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs) characterized primarily by a smooth rotation in the magnetic field direction indicative of the presence of a magnetic flux rope. Energetic particle signatures suggest MC flux ropes remain magnetically connected to the Sun at both ends, leading to widely used model of global MC structure as an extended flux rope, with a loop-like axis stretching out from the Sun into the heliosphere and back to the Sun. The time of flight of energetic particles, however, suggests shorter magnetic field line lengths than such a continuous twisted flux rope would produce. In this study, two simple models are compared with observed flux rope axis orientations of 196 MCs to show that the flux rope structure is confined to the MC leading edge. The MC "legs," which magnetically connect the flux rope to the Sun, are not recognizable as MCs and thus are unlikely to contain twisted flux rope fields. Spacecraft encounters with these non-flux rope legs may provide an explanation for the frequent observation of non-MC ICMEs.
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