Aims. The magnetic field of coronal mass ejections (CMEs) determines their structure, evolution, and energetics, as well as their geoeffectiveness. However, we currently lack routine diagnostics of the near-Sun CME magnetic field, which is crucial for determining the subsequent evolution of CMEs. Methods. We recently presented a method to infer the near-Sun magnetic field magnitude of CMEs and then extrapolate it to 1 AU. This method uses relatively easy to deduce observational estimates of the magnetic helicity in CME-source regions along with geometrical CME fits enabled by coronagraph observations. We hereby perform a parametric study of this method aiming to assess its robustness. We use statistics of active region (AR) helicities and CME geometrical parameters to determine a matrix of plausible near-Sun CME magnetic field magnitudes. In addition, we extrapolate this matrix to 1 AU and determine the anticipated range of CME magnetic fields at 1 AU representing the radial falloff of the magnetic field in the CME out to interplanetary (IP) space by a power law with index aB. Results. The resulting distribution of the near-Sun (at 10 Rs ) CME magnetic fields varies in the range [0.004, 0.02] G, comparable to, or higher than, a few existing observational inferences of the magnetic field in the quiescent corona at the same distance. We also find that a theoretically and observationally motivated range exists around aB = -1.6 +-0.2, thereby leading to a ballpark agreement between our estimates and observationally inferred field magnitudes of magnetic clouds (MCs) at L1. Conclusions. In a statistical sense, our method provides results that are consistent with observations.
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