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tokens: also that, if we assume that is roughly proportional to as suggested by observations (Thompson 2008 ; Grenier Harding 2015 ), then . A final comment is in order here before we move on to the next section. As we saw in the calculation below equation ( 5 ), near the surface of the star the separatrix electric charge fails to account for the separatrix return current by a factor ( r pc / r lc ) 2 ≪ 1. The same calculation near the Y-point yields the separatrix surface charge density σ lc near the light cylinder R → r lc , (see Uzdensky 2003 ; Timokhin 2006 , for details). Here, B lc ≡ B * ( r * / r lc ) 3 /2 is the value of the dipole magnetic field at the light cylinder. In the above estimate, ‘IN’ and ‘OUT’ at the Y-point refers to the region just outside and inside the light cylinder, respectively. Obviously, the separatrix electric charge is sufficient to support the separatrix return current. The only way to reconcile this result with the inefficiency of the separatrix electric charge to carry the same electric current near the surface of the star is the following: The separatrix must contain an extra amount of distributed corotating positive electric charge with surface charge density σ + ( R ) > 0 such that, at all distances, from the polar cap at r pc to the light cylinder. Here, σ − ( R ) ∼ − I pc /2π Rc is the negative charge density carried by the electrons that inflow from the dissipation zone. Clearly, which is in absolute terms much greater than σ pc . Consequently, σ + pc ≈ |σ − pc |. It is conceivable that these corotating positrons are the result of pair formation by the inflowing separatrix electrons. Note that the concept of one particle population of the ‘right’ type flowing through another stationary (corotating) population of the ‘wrong’ type needed to support both the electric charge and electric current distributions in the pulsar magnetosphere was first proposed in section 4 of Contopoulos ( 2016 ). 3 HIGH-ENERGY RADIATION If we know the accelerating electric field and the trajectory of particles in the equatorial dissipation region, it is straightforward to calculate the asymptotic particle Lorentz factor Γ in the curvature radiation reaction limit, Here, E acc is the accelerating electric field in the dissipation region. We have assumed here that the radius of curvature around the Y-point is equal to r lc . We can estimate E acc if we make the simplifying assumption that the magnetic flux that crosses the equatorial dissipation zone does so in a dipole-like configuration. In that case, the width Δ of that region is equal to and hence, the accelerating electric field in that region is equal to We have thus shown that the accelerating electric field is approximately equal to the value of the magnetic field near the light cylinder. One can easily check that, with this accelerating electric field, where, P is the pulsar period. This will be reached within an acceleration distance on the order of Obviously, the