Magnetorotational Instability in a Swirling Partially Ionized Gas

TL;DR

This paper proposes a laboratory experiment using swirling, weakly-ionized argon gas to study non-ideal magnetorotational instability (MRI), including effects like Hall, resistivity, and ambipolar diffusion, relevant to astrophysical discs.

Contribution

It introduces a new experimental setup to observe non-ideal MRI effects, deriving the relevant dispersion relation and demonstrating feasibility through initial hydrodynamic tests.

Findings

Hall effect can enhance MRI growth rate in the experiment.

Hydrodynamic prototype shows a measurable alpha-parameter.

Numerical solutions suggest MRI can be produced in the proposed setup.

Abstract

The magnetorotational instability (MRI) has been proposed as the method of angular momentum transport that enables accretion in astrophysical discs. However, for weakly-ionized discs, such as protoplanetary discs, it remains unclear whether the combined non-ideal magnetohydrodynamic (MHD) effects of Ohmic resistivity, ambipolar diffusion, and the Hall effect make these discs MRI-stable. While much effort has been made to simulate non-ideal MHD MRI, these simulations make simplifying assumptions and are not always in agreement with each other. Furthermore, it is difficult to directly observe the MRI astrophysically because it occurs on small scales. Here, we propose the concept of a swirling gas experiment of weakly-ionized argon gas between two concentric cylinders threaded with an axial magnetic field that can be used to study non-ideal MHD MRI. For our proposed experiment, we derive the hydrodynamic equilibrium flow and a dispersion relation for MRI that includes the three non-ideal effects. We solve this dispersion relation numerically for the parameters of our proposed experiment. We find it should be possible to produce non-ideal MRI in such an experiment because of the Hall effect, which increases the MRI growth rate when the vertical magnetic field is anti-aligned with the rotation axis. As a proof of concept, we also present experimental results for a hydrodynamic flow in an unmagnetized prototype. We find that our prototype has a small, but non-negligible, $\alpha$-parameter that could serve as a baseline for comparison to our proposed magnetized experiment, which could be subject to additional turbulence from the MRI.