  The turbulence driven by gravitational instabilities (GIs) can amplify
magnetic fields in massive gaseous disks. This GI dynamo may appear in young
circumstellar disks, whose weak ionization challenges other amplification
routes, as well as in active galactic nuclei. Although regarded as a
large-scale dynamo, only local simulations have so far described its kinematic
regime. We study the GI dynamo in global magnetohydrodynamic (MHD) models of
accretion disks, focusing on its kinematic phase. We perform resistive MHD
simulations with the Pluto code for different radiative cooling times and
electrical resistivities. A weak magnetic field seeds the dynamo, and we adopt
mean-field and heuristic models to capture its essence. We recover the same
induction process leading to magnetic field amplification as previously
identified in local simulations. The dynamo is, however, global in nature,
connecting distant annuli of the disk via a large-scale dynamo mode of a fixed
growth rate. This large-scale amplification can be described by a mean-field
model that does not rely on conventional alpha-Omega effects. When varying the
disk parameters we find an optimal resistivity that facilitates magnetic
amplification, whose magnetic Reynolds number, Rm < 10, is substantially
smaller than in local simulations. Unlike local simulations, we find an optimal
cooling rate and the existence of global oscillating dynamo modes. The
nonlinear saturation of the dynamo puts the disk in a strongly magnetized
turbulent state on the margins of the effective range of GI. In our
simulations, the accretion power eventually exceeds the threshold required by
local thermal balance against cooling, leaving the long-term nonlinear outcome
of the GI dynamo uncertain.
