Magnetic acceleration of relativistic AGN jets

We present numerical simulations of axisymmetric, magnetically driven relativistic jets. To eliminate the dissipative effects induced by a free boundary with an ambient medium we assume that the flow is confined by a rigid wall of a prescribed shape, which we take to be $z\propto r^a$ (in cylindrical coordinates, with $a$ ranging from 1 to 3). The outflows are initially cold, sub-Alfv\'enic and Poynting flux-dominated, with a total--to--rest-mass energy flux ratio $\mu \sim 15$. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. The acceleration process is very efficient: on the outermost scale of the simulation as much as $\sim 77%$ of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approaches its maximum possible value ($\Gamma_\infty \simeq \mu$). We also find a high collimation efficiency: all our simulated jets develop a cylindrical core. We argue that this could be the rule for current-carrying outflows that start with a low initial Lorentz factor ($\Gamma_0 \sim 1$). Our conclusions on the high acceleration and collimation efficiencies are not sensitive to the particular shape of the confining boundary or to the details of the injected current distribution, and they are qualitatively consistent with the semi-analytic self-similar solutions derived by Vlahakis & K\"onigl. We apply our results to the interpretation of relativistic jets in AGNs: we argue that they naturally account for the spatially extended accelerations inferred in these sources ($\Gamma_\infty \ga 10$ attained on radial scales $R\ga 10^{17} {\rm cm}$) and are consistent with the transition to the matter-dominated regime occurring already at $R\ga 10^{16} {\rm cm}$.