Using the exact solution of the axisymmetric pulsar magnetosphere derived in a previous publication and the conservation laws of the associated MHD flow , we show that the Lorentz factor of the outflowing plasma increases linearly with distance from the light cylinder .
Therefore , the ratio of the Poynting to particle energy flux , generically referred to as \sigma , decreases inversely proportional to distance , from a large value ( typically \lower 2.0 pt \hbox { $ \buildrel { \scriptstyle > } \over { \scriptstyle \sim } $ } 10 ^ { 4 } ) near the light cylinder to \sigma \simeq 1 at a transistion distance R _ { trans } .
Beyond this distance the inertial effects of the outflowing plasma become important and the magnetic field geometry must deviate from the almost monopolar form it attains between R _ { lc } and R _ { trans } .
We anticipate that this is achieved by collimation of the poloidal field lines toward the rotation axis , ensuring that the magnetic field pressure in the equatorial region will fall-off faster than 1 / R ^ { 2 } ( R being the cylindrical radius ) .
This leads both to a value \sigma = \sigma _ { s } \ll 1 at the nebular reverse shock at distance R _ { s } ( R _ { s } \gg R _ { trans } ) and to a component of the flow perpendicular to the equatorial component , as required by observation .
The presence of the strong shock at R = R _ { s } allows for the efficient conversion of kinetic energy into radiation .
We speculate that the Crab pulsar is unique in requiring \sigma _ { s } \simeq 3 \times 10 ^ { -3 } because of its small translational velocity , which allowed for the shock distance R _ { s } to grow to values \gg R _ { trans } .

\keywords magnetic fields — MHD — pulsars : general