Speaker
Description
Magnetorotational instability (MRI) is the most likely candidate driving angular momentum transport in astrophysical disks. Due to its great importance, there have been considerable efforts to capture MRI in the laboratory. Despite recent promising results, a definitive experimental evidence of MRI is, however, still elusive. I will present our preparatory theoretical study for upcoming large-scale DRESDYN-MRI experiments at HZDR aiming to detect various types of MRI in a laboratory Taylor-Couette (TC) flow of liquid sodium threaded by a background magnetic field, including standard MRI (SMRI) in the presence of a purely axial field. We first carried out a linear analysis of axisymmetric and non-axisymmetric SMRI, exploring typical values of the parameters in the DRESDYN-TC device: the Reynolds ($Re$) and magnetic Reynolds ($Rm$) numbers, the Lundquist number ($Lu$) and the ratio of the angular velocities of the cylinders. We demonstrated that axisymmetric SMRI is most unstable and can be detected in the DRESDYN-TC device owing to higher $Rm\leq 40$ and $Lu\leq 10$ reached there than those in previous MRI-experiments despite the small magnetic Prandtl number of sodium, $Pm=Rm/Re\sim 10^{-5}$. Then, we focused on the nonlinear dynamics and saturation of SMRI assuming infinitely long cylinders. It was shown that saturation occurs through the formation of current sheets and resulting magnetic reconnection process. The saturated state appears to be most sensitive to $Re$ with the perturbation magnetic energy and torque on the cylinders, which characterizes angular momentum transport, exhibiting power-law scalings $Re^{-1/2}$ and $Re^{1/2}$, respectively. Based on these scalings, the magnitudes of velocity and magnetic field perturbations were estimated that can be expected in the upcoming DRESDYN-MRI experiments. These scaling laws will be instrumental in the subsequent analysis of more realistic finite-length TC flows and comparison of numerical results with those obtained from the DRESDYN-MRI experiments in order to conclusively identify SMRI. I will conclude with some preliminary results for TC flows with finite-length cylinders taking into account endcap effects and future work.
