Effect of ambipolar diffusion on the nonlinear evolution of magnetorotational instability in weakly ionized disks

Xue Ning Bai, James McLellan Stone

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We study the role of ambipolar diffusion (AD) on the nonlinear evolution of the magnetorotational instability (MRI) in protoplanetary disks using the strong coupling limit, which applies in very weakly ionized gas with electron recombination time much shorter than the orbital time so that a single-fluid treatment is sufficient. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency at which neutral particles collides with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the MRI turbulence depends on the magnetic geometry and increases with the net magnetic flux. There is an upper limit to the net flux for sustained turbulence, corresponding to the requirement that the most unstable vertical wavelength be less than the disk scale height. Correspondingly, at a given Am, there exists a maximum value of the turbulent stress αmax. For Am ≲ 1, the largest stress is associated with a field geometry that has both net vertical and toroidal flux. In this case, we confirm the results of linear analyses that show the fastest growing mode has a non-zero radial wavenumber with a growth rate exceeding that of the pure vertical field case. We find there is a very tight correlation between the turbulent stress α and the plasma 〈β〉 ≡ Pgas/Pmag ≈ 1/2α at the saturated state of the MRI turbulence regardless of field geometry, and αmax rapidly decreases with decreasing Am. In particular, we find αmax ≈ 7 × 10-3 for Am = 1 and αmax ≈ 6 × 10-4 for Am = 0.1.

Original languageEnglish (US)
Article number144
JournalAstrophysical Journal
Issue number2
StatePublished - Aug 1 2011

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • instabilities
  • magnetohydrodynamics (MHD)
  • methods: numerical
  • protoplanetary disks
  • turbulence


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