The effective acceleration of plasma outflow in the paraboloidal magnetic field

The problem of the efficiency of particle acceleration for a paraboloidal poloidal magnetic field is considered within the approach of steady axisymmetric magnetohydrodynamic (MHD) flow. For the large Michel magnetization parameter σ it is possible to linearize the stream equation near the force-free solution and to solve the problem self-consistently as was done by Beskin, Kuznetsova & Rafikov for a monopole magnetic field. It is shown that, on the fast magnetosonic surface (FMS), the particle Lorentz factor γ does not exceed the standard value σ1/3. On the other hand, in the supersonic region, the Lorentz factor grows with the distance z from the equatorial plane as γ≈ (z/RL)1/2 up to the distance z≈σ2RL, where RL=c/ΩF is the radius of the light cylinder. Thus, the maximal Lorentz factor is γmax≈σ, which corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one.