On the effective particle acceleration in the paraboloidal magnetic field

The problem of the efficiency of particle acceleration for paraboloidal poloidal magnetic field is considered within the approach of steady axisymmetric 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 (1998) for monopole magnetic field. It is shown that on the fast magnetosonic surface the particle Lorentz factor γ does not exceed the standard value σ. 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.