Evidence of the origin of the Hall magnetic field for reconnection: Hall MHD reconstruction results from Cluster observations

Using reconstruction results from Cluster observations in the magnetotail, we present observational evidence for the electron‐current loops responsible for generating the out‐of‐plane Hall magnetic field during reconnection. This reconstruction is the first successful application to actual spacecraft data of a newly developed reconstruction technique (Sonnerup and Teh, 2009) based on Hall MHD equations in a steady state, two‐dimensional (2‐D) geometry. Maps from our reconstructions show that the regions of the Hall magnetic field are surrounded by electron‐current loops, which is confirmed by direct observations from Cluster 2 of the electrons that flow in and out of the reconnection site within the Hall field region. From the observational perspective our results show that the Hall magnetic field is generated by the Hall electron‐current loop as predicted by reconnection theory. Comparison of the reconstructed magnetic field maps from Cluster 1 and Cluster 3 shows that the current sheet is being temporarily distorted, indicating a wavy motion along the current sheet during the event, as suggested by Volwerk et al. (2003). Also, the reconstruction maps help us interpret the observations in more detail. The proper frame for the reconstruction is obtained by optimizing the correlation coefficient between predictions from the map on the basis of Cluster 1 and measurements from the other three spacecraft not otherwise used in the reconstruction. The resulting frame velocity is consistent with that obtained from the timing analysis method for single X line reconnection configuration. In addition, we use Grad‐Shafranov reconstruction for force‐free conditions together with higher‐resolution magnetic field data to derive a 2‐D magnetic field map of a secondary magnetic island structure seen by Cluster 3 within the Hall field region and first identified by Eastwood et al. (2007). Key Points Reconstructions show Hall magnetic fields surrounded by electron‐current loops Observational evidence of the origin of the Hall magnetic field for reconnection First application of Hall‐MHD reconstruction to actual spacecraft data