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 sigma 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 gamma does not exceed the standard value sigma(1/3). On the other hand, in the supersonic region, the Lorentz factor grows with the distance z from the equatorial plane as gamma approximate to (z/R-L)(1/2) up to the distance z approximate to sigma R-2(L), where R-L=c/Omega(F) is the radius of the light cylinder. Thus, the maximal Lorentz factor is gamma(max)approximate to sigma, which corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one.