Coronal mass ejections (CMEs) are the main drivers of geomagnetic disturbances, but the effects of their interaction with Earths magnetic field depend on their magnetic configuration and orientation. Fitting and reconstruction techniques have been developed to determine the important geometrical and physical CME properties. In many instances, there is disagreement between such different methods but also between fitting from in situ measurements and reconstruction based on remote imaging. Here, we compare three methods based on different assumptions for measurements of thirteen CMEs by the Wind spacecraft from 1997 to 2015. These CMEs are selected from the interplanetary coronal mass ejections catalog on https://wind.nasa.gov/ICMEindex.php due to their simplicity in terms of 1) small expansion speed throughout the CME and 2) little asymmetry in the magnetic field profile. This makes these thirteen events ideal candidates to compare codes that do not include expansion nor distortion. We find that, for these simple events, the codes are in relatively good agreement in terms of the CME axis orientation for six out of the 13 events. Using the Grad-Shafranov technique, we can determine the shape of the cross-section, which is assumed to be circular for the other two models, a force-free fitting and a circular-cylindrical non-force-free fitting. Five of the events are found to have a clear circular cross-section, even when this is not a pre-condition of the reconstruction. We make an initial attempt at evaluating the adequacy of the different assumptions for these simple CMEs. The conclusion of this work strongly suggests that attempts at reconciling in situ and remote-sensing views of CMEs must take in consideration the compatibility of the different models with specific CME structures to better reproduce flux ropes.
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