  We examine the conditions under which the disks of gas and dust orbiting
young gas giant planets are sufficiently conducting to experience turbulence
driven by the magneto-rotational instability. By modeling the ionization and
conductivity in the disk around proto-Jupiter, we find that turbulence is
possible if the X-rays emitted near the Sun reach the planet's vicinity and
either (1) the gas surface densities are in the range of the minimum-mass
models constructed by augmenting Jupiter's satellites to Solar composition,
while dust is depleted from the disk atmosphere, or (2) the surface densities
are much less, and in the range of gas-starved models fed with material from
the Solar nebula, but not so low that ambipolar diffusion decouples the neutral
gas from the plasma. The results lend support to both minimum-mass and
gas-starved models of the protojovian disk: (1) The dusty minimum-mass models
have internal conductivities low enough to prevent angular momentum transfer by
magnetic forces, as required for the material to remain in place while the
satellites form. (2) The gas-starved models have magnetically-active surface
layers and a decoupled interior "dead zone". Similar active layers in the Solar
nebula yield accretion stresses in the range assumed in constructing the
circumjovian gas-starved models. Our results also point to aspects of both
classes of models that can be further developed. Non-turbulent minimum-mass
models will lose dust from their atmospheres by settling, enabling gas to
accrete through a thin surface layer. For the gas-starved models it is crucial
to learn whether enough stellar X-ray and ultraviolet photons reach the
circumjovian disk. Additionally the stress-to-pressure ratio ought to increase
with distance from the planet, likely leading to episodic accretion outbursts.
