On the effective particle acceleration in the paraboloidal magnetic   field
  The problem of the efficiency of particle acceleration for parabolic poloidal magnetic field is considered within the approach of steady axisymmetric MHD flow. For the large Michel magnetization parameter 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 and Rafikov (1998) for monopole magnetic field. It is shown that on the fast magnetosonic surface the particle Lorentz factor does not exceed the standard value. On the other hand, in the supersonic region the Lorentz factor grows linearly with the distance from the rotational axis, reaching almost its maximal value. This corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one. 
V. S. Beskin (1), E. E. Nokhrina (2) ((1) P.N.Lebedev Physical   Institute,(2) Moscow Institute of Physics and Technology)