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Keywords:

  • diffusion;
  • instabilities;
  • MHD;
  • turbulence;
  • protoplanetary discs

ABSTRACT

The interaction between settling of dust grains and magnetorotational instability (MRI) turbulence in protoplanetary discs is analysed. We use a reduced system of coupled ordinary differential equations to represent the interaction between the diffusion of grains and the inhibition of the MRI. The coupled equations are styled on a Landau equation for the turbulence and a Fokker–Planck equation for the diffusion. The turbulence–grain interaction is probably most relevant near the outer edge of the disc’s quiescent, or ‘dead’ zone. Settling is most pronounced near the mid-plane, where a high dust concentration can self-consistently suppress the MRI. Under certain conditions, however, grains can reach high altitudes, a result of some observational interest. Finally, we show that the equilibrium solutions are linearly stable.