LOCAL MAGNETOHYDRODYNAMIC INSTABILITIES AND THE WAVE-DRIVEN DYNAMO IN ACCRETION DISKS

In this paper we consider the consequences of magnetic buoyancy and the magnetic shearing instability (MSI) on the strength and organization of the magnetic field in a thin accretion disk. We discuss a model in which the wave-driven dynamo growth rate is balanced by the dissipative effects of the MSI. As in earlier work, the net helicity is due to small advective motions driven by nonlinear interactions between internal waves. Assuming a simple model of the internal wave spectrum generated from the primary m = 1 internal waves, we find that the magnetic energy density saturates at approximately (H/r)4/3 times the local pressure (where H is the disk thickness and r is its radius). On very small scales (approximately V(A)/OMEGA where V(A) is the Alfven velocity and OMEGA is the local rotational frequency) the shearing instability will produce an (approximately) isotropic fluctuating field with V(A) approximately V(A) and an (approximately) isotropic strong MHD turbulence with velocities of order V(A). For a stationary disk this is equivalent to a dimensionless "viscosity" alpha approximately (H/r)4/3. The vertical and radial diffusion coefficients will be comparable to each other. Magnetic buoyancy will be largely suppressed by the turbulence due to the MSI. We present a rough estimate of its effects and find that it removes magnetic flux from the disk at a rate comparable to that caused b turbulent diffusion.