|Annu. Rev. Astron. Astrophys. 1988. 36:
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4.2. Global Electrodynamics of Confined Jets
The basic assumption in magnetic confinement of large-scale jets is that magnetic flux is advected by the flow that originates from accretion disks, although more flux can be added by entrainment of external magnetized matter or by internal stresses. From the solutions of the previous section, both poloidal Bp and toroidal B magnetic components are supported by the dynamics of accretion disks and extend to large scales. A poloidal component actually increases internal jet pressure and loosens collimation, while the toroidal component pinches the flow toward the axis, although it may then favor instabilities. In an expanding jet, magnetic fields are expected to decay owing to expansion, as Bp R-2 and B R-1, where R is the jet radius. This behavior agrees qualitatively with typical observations showing the initial part of the jet dominated by longitudinal (poloidal) fields and later by the perpendicular (toroidal) component. On the other hand, synchrotron luminosity does not decay as rapidly as the simple adiabatic expansion law would predict, L R-(5+4) ( spectral index). Thus, magnetic flux must be added along the flow, most likely through entrainment, turbulent shear amplification, or dynamo effects (De Young 1980).
An analytic study of the structure of magnetized jets outside the acceleration and collimation zone is performed by looking for solutions of the asymptotic MHD wind equations. The classical self-similar solution by Heyvaerts & Norman (1989) shows that jets after the acceleration phase are recollimated by the toroidal field generated by the disk rotation and become cylindrically confined. Chiueh et al (1991) extended the study to relativistic flow speeds, showing that flux surfaces either collimate to current-carrying cylinders or to current-free paraboloids. Similarly, Lovelace et al (1987) showed that, by including a rotating force-free magnetosphere outside a Keplerian disk, jets can be self-pinched.
The confinement of the flow is governed by the Grad-Shafranov equation (Appl & Camenzind 1993a), in which currents and current gradients are essential in the structure of jets. While collective effects in plasmas are very efficient in maintaining charge neutrality, jets may carry a net current, especially when considering a plasma with both thermal and suprathermal relativistic components (Sol et al 1989). The idea of self-confinement by the tension of toroidal field lines in current-carrying jets was originally proposed by Benford (1978). He showed that the total net current involved in an axisymmetric jet solution is I ~ 1017 P-121/2 dkpc Amp in typical units (P is the pressure). Confinement can be achieved by a radial field profile B 1 / R so that magnetic stresses reach equilibrium with the external medium at some radius.
Appl & Camenzind (1993a, b) discussed force-free relativistic magnetized jets in terms of the radial distribution of poloidal current I(R) = cRB / 2. They solved the Grad-Shafranov equation for given current distributions, which can take into account variations of the jet radius. Equilibrium solutions are found for jets with a current-carrying core [Rc = (v/c) RL , where RL is the light cylinder radius] enveloped in a current-free envelope. The jet core is electromagnetically dominated, as the Poynting flux is concentrated on the jet axis. In dense regions close to the AGN core, the shape of the jet is determined by the ambient pressure. Any amount of current inside the jet is compensated by a return current on the jet surface. Once the ambient pressure drops below the electromagnetic pressure on the jet, boundary self-confinement begins and the shape of the jet becomes cylindrical. Various current radial distributions have been studied, and in a cylindrical force-free jet, it has been proven that only part of the current and return current can flow inside the beam.
Other studies of magnetic self-confinement refer to fields generated by surface currents at the interface between the jet and a surrounding cocoon (Cohn 1983). Others focus on helical equilibria, although without a consistent explanation of the origin of ordered longitudinal fields that are linked to predefined boundary conditions (Chan & Henriksen 1980, Villata & Ferrari 1995, Trussoni et al 1996).