  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.
