Nonlinear simulations of magnetic Taylor-Couette flow with current-free helical magnetic fields

Abstract

The magnetorotational instability (MRI) in cylindrical Taylor-Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with time-dependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from $O(10^6)$ (axial field only) to $O(10^3)$ for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field $\sim 50$ Gauss and axial current $\sim 4$ kA for the toroidal field. It is sufficient that the vertical velocity $u_z$ of the flow can be measured with a precision of 0.1mm/s. We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards.