From helical to standard magnetorotational instability: predictions for upcoming liquid sodium experiments

TL;DR

This paper analyzes different types of magnetorotational instability (MRI) in liquid sodium flows, predicting their detectability in upcoming experiments and exploring the transition between helical and standard MRI regimes.

Contribution

It provides a linear analysis of SMRI, H-SMRI, and HMRI in liquid sodium, predicting experimental conditions for their detection and characterizing the transition between regimes.

Findings

SMRI and H-SMRI can be detected in DRESDYN experiments.

H-SMRI exhibits overstability with a non-zero frequency increasing with azimuthal field.

The transition between HMRI and SMRI is continuous and monotonic.

Abstract

We conduct a linear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard version (SMRI) with a purely axial background magnetic field and two further types -- helically modified SMRI (H-SMRI) and helical MRI (HMRI) -- in the presence of combined axial and azimuthal magnetic fields. This study is intended as preparatory for 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, the Lundquist number and the ratio of the angular velocities of the cylinders, which are attainable in these experiments. In contrast to previous attempts at detecting MRI in the lab, our results demonstrate that SMRI and its helically modified version 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. Since in the experiments we plan to approach (H-)SMRI from the previously studied HMRI regime, we characterise the continuous and monotonous transition between the both regimes. We show that H-SMRI, like HMRI, represents an overstability (travelling wave) with non-zero frequency linearly increasing with azimuthal field. Because of its relevance to finite size flow systems in experiments, we also analyse the absolute form of H-SMRI and compare its growth rate and onset criterion with the convective one.