  Coronal mass ejections (CMEs) are the main drivers of geomagnetic
disturbances, but the effects of their interaction with Earth's 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.
