Linear and Nonlinear Simulations of Magnetorotational Instability for the Upcoming DRESDYN-MRI Experiment

Magnetorotational instability (MRI) is considered as the most likely mechanism driving angular momentum transport in astrophysical disks. We conduct a linear and nonlinear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor–Couette (TC) flow with a purely axial background magnetic field. This study is intended as preparatory for the upcoming large-scale liquid sodium MRI experiments planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so we explore these instability types for typical values of the main parameters: the magnetic Reynolds number (Rm), the Lundquist number (Lu), and the ratio of the angular velocities of the cylinders (µ), which are attainable in these experiments. In contrast to previous attempts at detecting MRI in the laboratory, our results demonstrate that MRI can in principle be detected in the DRESDYN-TC device for the range of the above parameters, including the astrophysically most important Keplerian rotation, despite the extremely small magnetic Prandtl number of liquid sodium. In the present work, we show that the transition of MRI from exponential growth phase to saturated (or steady) state occurs via magnetic reconnection. In the saturated state, magnetic energy and normalized torque exhibit a consistent power-law behavior for all sets of (Lu, Rm).