Physical Origin of the Quadrupole Out-of-Plane Magnetic Field in Hall-MHD Reconnection

A quadrupole pattern of the out-of-plane component of the magnetic field inside a reconnection region is seen as an important signature of the Hall-magnetohydrodynamic (Hall-MHD) regime of reconnection. It has been first observed in numerical simulations and just recently confirmed in the MRX (Magnetic Reconnection Experiment) [M. Yamada, H. Ji, S. Hsu, T. Carter, R. Kulsrud, N. Bertz, F. Jobes, Y. Ono, and F. Perkins, Phys. Plasmas 4, 1936 (1997)] and also seen in spacecraft observations of Earth's magnetosphere. In this study, the physical origin of the quadrupole field is analyzed and traced to a current of electrons that flows along the lines in and out of the inner reconnection region to maintain charge neutrality. The role of the quadrupole magnetic field in the overall dynamics of the reconnection process is discussed. In addition, the bipolar poloidal electric field is estimated and its effect on ion motions is emphasized.