Poynting Jets from Accretion Disks

We give further considerations on the problem of the evolution of a coronal, force-free magnetic field which threads a differentially rotating, conducting Keplerian disk, extending the work of Li {\it et al.} (2001). This situation is described by the force-free Grad-Shafranov (GS) equation for the flux function $\Psi(r,z)$ which labels the poloidal field lines (in cylindrical coordinates). The GS equation involves a function $H(\Psi)$ describing the distribution of poloidal current which is determined by the differential rotation or {\it twist} of the disk which increases linearly with time. We numerically solve the GS equation in a sequence of volumes of increasing size corresponding to the expansion of the outer perfectly conducting boundaries at ($R_{m}, Z_{m}$). The outer boundaries model the influence of an external non-magnetized plasma. The sequence of GS solutions provides a model for the dynamical evolution of the magnetic field in response to (1) the increasing twist of the disk and (2) the pressure of external plasma. We find solutions with {\it magnetically collimated} Poynting jets where there is a {\it continuous} outflow of energy, angular momentum, and toroidal magnetic flux from the disk into the external space.