Axisymmetric helical magnetorotational instability in a Taylor-Couette flow with sufficiently large positive shear

Yurong Zhao¹ - Rainer Hollerbach² - Wenpeng Hong¹ - Yang Yu¹ - Jianjun Tao³

¹ School of Energy and Power Engineering, Northeast Electric Power University, Jilin 132012, China
² School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
³ Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China

Abstract
The range of parameters is explored for the axisymmetric helical magnetorotational instability in a Taylor-Couette flow with high enough positive shear. The magnetic Prandtl number has a wide range from 10⁻⁶ to 100. The ratio of the azimuthal magnetic field to the axial magnetic field β is equal to 20, 50, 70 and 100. In different parameters, the stability curves are computed and shown in the plane for the Lundquist numbers S on the x-axis and for the magnetic Reynolds numbers Rm on the y-axis. The computed results can help find or avoid the instability in the corresponding flows. Figs 6, Refs 29.