This study aims to provide a reference to different magnetic field models and reconstruction methods for interplanetary coronal mass ejections (ICMEs). In order to understand the differences in the outputs of those models and codes, we analyze 59 events from the Coordinated Data Analysis Workshop (CDAW) list, using four different magnetic field models and reconstruction techniques; force-free fitting (Goldstein,1983,Burlaga,1988,Lepping et al.,1990), magnetostatic reconstruction using a numerical solution to the Grad-Shafranov equation (Hu and Sonnerup, 2001), fitting to a self-similarly expanding cylindrical configuration (Marubashi and Lepping, 2007) and elliptical, non-force free fitting (Hidalgo,2003). The resulting parameters of the reconstructions for the 59 events are compared statistically, as well as in selected case studies. The ability of a method to fit or reconstruct an event is found to vary greatly: the Grad-Shafranov reconstruction is successful for most magnetic clouds (MCs) but for less than 10% of the non-MC ICMEs; the other three methods provide a successful fit for more than 65% of all events. The differences between the reconstruction and fitting methods are discussed, and suggestions are proposed as to how to reduce them. We find that the magnitude of the axial field is relatively consistent across models but not the orientation of the axis of the ejecta. We also find that there are a few cases for which different signs of the magnetic helicity are found for the same event when we do not fix the boundaries, illustrating that this simplest of parameters is not necessarily always well constrained by fitting and reconstruction models. Finally, we look at three unique cases in depth to provide a comprehensive idea of the different aspects of how the fitting and reconstruction codes work.
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