Numerical simulations of the Princeton magneto-rotational instability experiment with conducting axial boundaries

TL;DR

This paper numerically investigates the Princeton MRI experiment with conducting endcaps, revealing higher saturation levels of MRI that could enable experimental detection beyond previous theoretical and numerical limits.

Contribution

It demonstrates that conducting axial boundaries significantly increase MRI saturation levels, providing new insights into boundary effects in MRI experiments.

Findings

Higher MRI saturation with conducting endcaps

Saturation level becomes independent of Reynolds number at high Re

Potential for first positive experimental detection of MRI

Abstract

We investigate numerically the Princeton magneto-rotational instability (MRI) experiment and the effect of conducting axial boundaries or endcaps. MRI is identified and found to reach a much higher saturation than for insulating endcaps. This is probably due to stronger driving of the base flow by the magnetically rather than viscously coupled boundaries. Although the computations are necessarily limited to lower Reynolds numbers ($\Re$) than their experimental counterparts, it appears that the saturation level becomes independent of $\Re$ when $\Re$ is sufficiently large, whereas it has been found previously to decrease roughly as $\Re^{-1/4}$ with insulating endcaps. The much higher saturation levels will allow for the first positive detection of MRI beyond its theoretical and numerical predictions.