Acceleration of relativistic plasma in the magnetosphere of an axisymmetric rotator

The flow of relativistic plasma in the magnetosphere of an axisymmetrical rotator is considered analytically aswell as numerically. The selfconsistent solution of the plasma outflow in a monopole-like poloidal magnetic field is obtained accurately up to terms proportional to σ/U 3 0 , where σ is Michel’s magnetization parameter, U0 = γ0v0/c, while γ0 and v0 are the initial Lorentz-factor and the velocity of the plasma. It is shown that under the condition σ/U 3 0 1 typical for real radio pulsars, the plasma is not accelerated and is not collimated in the subsonic region. Numerical simulation of the time dependent version of this problem shows that the stationary flow of relativistic plasma is apparently unstable when σ/U0 > 1. This instability of the flow leads to the acceleration of the plasma.