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.

Observational studies of collimation in jets in active galactic nuclei (AGN) are a key to understanding their formation and acceleration processes. We have performed an automated search for jet shape transitions in a sample of 367 AGN using VLBA data at 15 and 1.4 GHz. This search has found 10 out of 29 nearby jets at redshifts z < 0.07 with a transition from a parabolic to conical shape, while the full analysed sample is dominated by distant AGN with a typical z ≈ 1. The ten AGN are UGC 00773, NGC 1052, 3C 111, 3C 120, TXS 0815−094, Mrk 180, PKS 1514+00, NGC 6251, 3C 371, and BL Lac. We conclude that the geometry transition may be a common effect in AGN jets. It can be observed only when sufficient linear resolution is obtained. Supplementing these results with previously reported shape breaks in the nearby AGN 1H 0323+342 and M87, we estimate that the break occurs at 105–106 gravitational radii from the nucleus. We suggest that the jet shape transition happens when the bulk plasma kinetic energy flux becomes equal to the Poynting energy flux, while the ambient medium pressure is assumed to be governed by Bondi accretion. In general, the break point may not coincide with the Bondi radius. The observational data support our model predictions on the jet acceleration and properties of the break point.

The analysis of the frequency dependence of the observed shift of the cores of relativistic jets in active galactic nuclei (AGN) allows us to evaluate the number density of the outflowing plasma n e and, hence, the multiplicity parameter λ = n e /n GJ , where n GJ is the Goldreich-Julian number density. We have obtained the median value for λ med = 3 · 10 13 and the median value for the Michel magnetization parameter σ M,med = 8 from an analysis of 97 sources. Since the magnetization parameter can be interpreted as the maximum possible Lorentz factor Γ of the bulk motion which can be obtained for relativistic magnetohydrodynamic (MHD) flow, this estimate is in agreement with the observed superluminal motion of bright features in AGN jets. Moreover, knowing these key parameters, one can determine the transverse structure of the flow. We show that the poloidal magnetic field and particle number density are much larger in the center of the jet than near the jet boundary. The MHD model can also explain the typical observed level of jet acceleration. Finally, casual connectivity of strongly collimated jets is discussed.

Magnetic fields are fundamental to the dynamics of both accretion disks and the jets that they often drive. We review the basic physics of these phenomena, the past and current efforts to model them numerically with an emphasis on the jet-disk connection, and the observational constraints on the role of magnetic fields in the jets of active galaxies on all scales.

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