On the MHD effects on the force-free monopole outflow

The stationary axisymmetric outflow from a rotating sphere with a (split) monopole magnetic field is considered. The stream equation describing the outflow is linearized in terms of the Michel magnetization parameter σ−1 ≪ 1, which allows a self-consistent analysis of the direct problem. It is shown that for a finite σ the fast magnetosonic surface is located at a finite distance ∼ σ1/3RL (RL = c/ΩF is the light cylinder). We have also found that the particle energy at the fast surface is just equal to the Michel value γ ∼ σ1/3. The particle acceleration and magnetic field collimation are shown to become ineffective outside the fast magnetosonic surface.