  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.
