Turbulent transport and its effect on the dead zone in protoplanetary   discs
  Protostellar accretion discs have cool, dense midplanes where externally originating ionisation sources such as X-rays or cosmic rays are unable to penetrate. This suggests that for a wide range of radii, MHD turbulence can only be sustained in the surface layers where the ionisation fraction is sufficiently high. A dead zone is expected to exist near the midplane, such that active accretion only occurs near the upper and lower disc surfaces. Recent work, however, suggests that under suitable conditions the dead zone may be enlivened by turbulent transport of ions from the surface layers into the dense interior.   In this paper we present a suite of simulations that examine where, and under which conditions, a dead zone can be enlivened by turbulent mixing. We use three-dimensional, multifluid shearing box MHD simulations, which include vertical stratification, ionisation chemistry, ohmic resistivity, and ionisation due to X-rays from the central protostar. We compare the results of the MHD simulations with a simple reaction-diffusion model.   The simulations show that in the absence of gas-phase heavy metals, such as magnesium, turbulent mixing has essentially no effect on the dead zone. The addition of a relatively low abundance of magnesium, however, increases the recombination time and allows turbulent mixing of ions to enliven the dead zone completely beyond a distance of 5 AU from the central star, for our particular disc model. During the late stages of protoplanetary disc evolution, when small grains have been depleted and the disc surface density has decreased below its high initial value, the structure of the dead zone may be significantly altered by the action of turbulent transport. 
Martin Ilgner and Richard P. Nelson