  With the neutron star rotating under a stationary magnetic field generating
unipolar induction, charges are driven to the pulsar surface according to their
signs, and are uploaded to the magnetosphere along the magnetic field lines. In
the presence of an electron-positron plasma, the pulsar magnetosphere is
represented by a unique magnetohydrodynamic (MHD) plasma. The pulsar equation
of force-free equilibrium is solved analytically for two configurations. The
first one is a light cylinder guided jet-like open magnetosphere, and the
second one is a closed magnetosphere within the light cylinder. The Goldreich
Julian condition for the stability of the closed magnetosphere (dead zone) is
reconsidered which indicates transition of the closed magnetosphere to the open
one as the electron-positron plasma density builds up. This suggests that the
pulsar period could be the result of magnetosphere dynamics rather than the
pulsar rotation.
