Self-Consistent Equilibria in the Pulsar Magnetosphere

For a ‘collisionless’ pulsar magnetosphere the self-consistent equilibrium particle distribution functions are functions of the constants of the motion only. Reasons are given for concluding that to a good approximation they will be functions of the rotating frame Hamiltonian only. This is shown to result in rigid rotation of the plasma, which therefore becomes trapped inside the velocity of light cylinder. The self-consistent field equations are derived, and a method of solving them is illustrated. The axial component of the magnetic field decays to zero at the plasma boundary. In practice, some streaming of particles into the wind zone may occur as a second-order effect. Acceleration of such particles to very high energies is expected when they approach the velocity of light cylinder, but they cannot be accelerated to very high energies near the star.