Magnetorotational instability in liquid metal Taylor-Couette flows — experimental and numerical studies for the DRESDYN and Princeton MRI-experiments

• Applicant: Dr. George Mamatsashvili
• Subject Area: Fluid Mechanics ; Astrophysics and Astronomy
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 558120280

The magnetorotational instability (MRI) arising from the interplay between a magnetic field and differential rotation in electrically conducting flows is of great importance in astrophysics. It renders astrophysical disks turbulent, driving accretion of matter by transporting its angular momentum outward. MRI can also play an important role in stars and planets. There have been significant interest and experimental efforts to detect MRI in the laboratory using liquid metal Taylor-Couette (TC) setups that mimic disks. Nevertheless, a definitive experimental confirmation of MRI has remained elusive for a long time due to very small magnetic Prandtl numbers Pm=10^(-6)-10^(-5) (ratio of viscosity to magnetic diffusivity) of liquid metals that in turn require very high Reynolds numbers Re>10^6 of the TC flow, yielding magnetic Reynolds numbers Rm=PmRe>1 sufficient for exciting MRI. At such high Re, the basic effects due to the endcaps of the TC device - poloidal Ekman circulation, Ekman-Hartmann and Stewartson-Shercliff layers (EHLs and SSLs) - largely affect the onset and evolution of MRI, leading to the dynamics that is fundamentally new compared to that at lower Re studied before. The recent experiments by the group at the Princeton Plasma Physics Laboratory (PPPL) with their upgraded TC device have reported the first results on the MRI detection. These preliminary findings, however, necessitate further investigation and validation, which is our main motivation. A basic problem is that the parameters in the present simulations and experiments are quite different not allowing a systematic quantitative comparison between them. Another motivation is to carry out a preparatory theoretical analysis of MRI for upcoming MRI-experiments in the DRESDYN facility. In close collaboration with the PPPL group, we will carry out an in-depth study of MRI in magnetized TC flows to address the key unresolved questions: How do Ekman circulation, EHLs and SSLs determine the onset (bifurcation) and structure of MRI and how do these depend on the parameters of a TC setup as well as on the configuration and electrical conductivity of the endcaps? What are the saturation mechanism and dynamics of the saturated MRI state? How do the velocity and magnetic field in the latter state depend on the system parameters and compare to those in the experiments? To this end, we will carry out numerical simulations of MRI both for the DRESDYN and Princeton TC setups, which have different parameters, geometry, endcap configuration and electrical conductivity. These simulations will be systematically compared with the existing and new MRI-experiments in the high-Rm regimes conducted by the PPPL group. In contrast to previous studies, we put emphasis on high Re>10^4 regime, closer to the experimental one. Investigating MRI in TC flows in this regime with a combined experimental and simulation approach, we will gain deeper insights into the dynamical processes behind MRI-experiments.

• DFG Programme: Research Grants
• International Connection: USA
• Co-Investigator: Dr. Frank Stefani
• Cooperation Partners: Professor Hantao Ji, Ph.D.; Dr. Yin Wang