The Power of Axisymmetric Pulsar

Stationary force-free magnetosphere of an axisymmetric pulsar is shown to have a separatrix inclination angle of 77.3${}^{\circ }$. The electromagnetic field has an $R^{-1\mathrm{/}2}$ singularity inside the separatrix near the light cylinder. A numerical simulation of the magnetosphere which crudely reproduces these properties is presented. The numerical results are used to estimate the power of an axisymmetric pulsar: $L=(1\pm 0.1){\mu }^2{\mathrm{\Omega }}^4\mathrm{/}{c}^3$. A need for a better numerical simulation is pointed out.