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The Pulsating Pulsar Magnetosphere

Following the basic principles of a charge separated pulsar magnetosphere \citep{goldreich1969}, we consider the magnetosphere be stationary in space, instead of corotating, and the electric field be uploaded from the potential distribution on the pulsar surface, set up by the unipolar induction. Consequently, the plasma of the magnetosphere undergoes guiding center drifts of the gyro motion due to the transverse forces to the magnetic field. These forces are the electric force, magnetic gradient force, and field line curvature force. Since these plasma velocities are of drift nature, there is no need to introduce an emf along the field lines, which would contradict the $E_{\parallel}=\vec E\cdot\vec B=0$ plasma condition. Furthermore, there is also no need to introduce the critical field line separating the electron and ion open field lines. We present a self-consistent description where the magnetosphere is described in terms of electric and magnetic fields and also in terms of plasma velocities. The fields and velocities are then connected through the space charge densities self-consistently. We solve the pulsar equation analytically for the fields and construct the standard steady state pulsar magnetosphere. By considering the unipolar induction inside the pulsar and the magnetosphere outside the pulsar as one coupled system, and under the condition that the unipolar pumping rate exceeds the Poynting flux in the open field lines, plasma pressure can build up in the magnetosphere, in particular in the closed region. This could cause a periodic openning up of the closed region, leading to a pulsating magnetosphere, which could be an alternative for pulsar beacons. The closed region can also be openned periodically by the build-up of toroidal magnetic field through a positive feedback cycle.