The role of reconnection in the pulsar magnetosphere
  The present work is our first attempt to understand the role of reconnection in the pulsar magnetosphere. Our discussion is based on the observationaly infered fact that, as the pulsar spins down, the region of closed corotating dipolar field lines grows with time. This implies that reconnection must take place in the magnetosphere. We argue that non-dissipative reconnection along the equatorial current sheet allows for the continuous channeling of pulsar spindown energy into particle energy, all the way from the light cylinder to the pulsar wind termination shock, and we propose that this effect may account for the low \sigma values inferred by observations. We present a simple model that allows us to relate the magnetic diffusivity in the equatorial current sheet to an observable pulsar parameter, the braking index n. When n~1, the global structure of the magnetosphere approaches that of a relativistic split monopole where the pulsar spindown energy is carried by the electromagnetic field. However, for values of n>1.5, almost all field lines close inside the pulsar wind termination shock, and thus most of the electromagnetic pulsar spindown energy flux is effectively transformed into particle energy in the equatorial current sheet. 
Ioannis Contopoulos