Deriving the Topological Properties of the Magnetic Field of Coronal Mass Ejections from In Situ Measurements: Techniques

Coronal mass ejections (CMEs) are magnetized plasma systems with highly complex magnetic topology and evolution. Methods developed to assess their magnetic configuration have primarily focused on reconstructing three-dimensional representations from one-dimensional time series measurements taken in situ using techniques based on the "highly twisted magnetic flux rope" approximations. However, the magnetic fields of CMEs is know to have more complicated geometries. Their structure can be quantified using measures of field line topology, which have been primarily used for solar physics research. In this work, we introduce a novel technique of directly quantifying the various form of magnetic helicity within a CME in the interplanetary space using synthetic in situ measurements. We use a relatively simple three-dimensional simulation of a CME initiated with a highly-twisted flux rope. We find that a significant portion of the magnetic helicity near 1~au is contained in writhe and mutual helicity rather than just in twist. We discuss the implications of this finding for fitting and reconstruction techniques.