The present work is our first attempt to understand the role of reconnection in the pulsar magnetosphere .
Our discussion is based on the observationaly inferred 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 _ { shock } 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 \sim 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 \lower 2.0 pt \hbox { $ \buildrel { \scriptstyle > } \over { \scriptstyle \sim } $ } 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 .