A saturation mechanism of magnetorotational instability due to ohmic dissipation

The nonlinear saturation of the magnetorotational instability due to ohmic dissipation is investigated with two-dimensional magnetohydrodynamic simulations of accretion disks. We adopt a local disk model in which the physical quantities are assumed to be spatially uniform except for the shear velocity in the azimuthal direction. Starting with a weak vertical field, the magnetorotational instability is saturated in the nonlinear regime when the magnetic Reynolds number R-m is less than unity. In the saturated turbulent state, the growth of the magnetic field for the instability and the damping by the ohmic dissipation are almost balanced. The efficiency of angular momentum transport a! is of the order of 10(-2) to 10(-3), and alpha is found to be inversely proportional to the initial beta value. When R-m greater than or similar to 1, channel solutions appear and the magnetic energy continues growing even with the dissipation process. We can roughly explain these features with the help of the results obtained by the linear analysis. Our conclusion is that the magnetic dissipation is one of the most important precesses that determine the saturation level of the magnetorotational instability.