Large Scale Magnetic Field Growth and Stability in Hall-MHD Simulations of Quasi-Keplerian Flows

Understanding the self-generation of large-scale magnetic fields in plasmas and their relation to magnetorotational instability and momentum transport is an outstanding problem in plasma astrophysics. One hypothesis is that large-scale dynamo magnetic fields could cause the magnetorotational instability to enter the stable regime and therefore suppress turbulence in the plasma. Here, we examine this behavior in quasi-keplerian cylindrical flows. 

We employ the NIMROD code to conduct nonlinear numerical simulations of the plasmas at different ion inertial lengths, di, to examine the dominance of the principal modes in the magnetic behavior of the plasma. We follow this with our investigation of the Hall and MHD dynamo terms in the induction equation and the WKB derivation of a dispersion relation for perturbations of the system. We find that in the Hall regime a large-scale vertical magnetic field is generated with larger ion inertial lengths. We also provide analytic evidence for the alteration of the MRI stability condition in the Hall regime, suggesting that the Hall effect may cause laminar behavior. This work is relevant to weakly ionized accretion disks.