On the Properties of Velikhov-Chandrasekhar MRI in Ideal and Non-ideal Plasmas

Part of the Astrophysics and Space Science Library book series (ASSL, volume 454)


In this chapter, conditions of the Velikhov-Chandrasekhar magneto-rotational instability (MRI) in ideal and non-ideal plasmas are examined. A linear WKB analysis of hydromagnetic axially symmetric flows shows that in the Rayleigh-unstable hydrodynamic case where the angular momentum decreases with radius, the MRI branch becomes stable, and the magnetic field suppresses the Rayleigh instability at small wavelengths. We investigate the limiting transition from hydromagnetic flows to hydrodynamic flows. The Rayleigh mode smoothly transits to the hydrodynamic case, while the Velikhov-Chandrasekhar MRI mode completely disappears without the magnetic field. The effects of viscosity and magnetic diffusivity in the plasma on the MRI conditions in thin accretion discs are studied. We find the limits on the mean free-path of ions allowing MRI to operate in such discs.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Sternberg Astronomical InstituteLomonosov Moscow State UniversityMoscowRussia
  2. 2.Kazan Federal UniversityKazanRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia

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