cylinders) magnetic field [@Velikhov59; @Chandrasekhar60] – a setup which is also best suited and most frequently used nowadays for experimental investigations. The conducting medium filling the gap between cylinders is usually a liquid metal (sodium, gallium) characterized by an extremely small ratio of viscosity to Ohmic resistivity, or magnetic Prandtl number, $Pm=\nu/\eta \sim 10^{-6}-10^{-5}$. By suitably adjusting the rotation rates of outer and inner cylinders, the TC flow profile can be made very close to the Keplerian one [@Ji_etal06; @Schartman_etal12; @Edlund_Ji15; @Lopez_Avila17], offering a unique possibility to study the disk MRI problem in laboratory as well, which has been up to now mostly carried out both via analytical means and numerical simulations.

First experimental efforts to study MRI in the laboratory were made at the University of Maryland [@Sisan_etal04], at Princeton University [@Nornberg_etal10; @Roach_etal12], and at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) [@Stefani_etal06; @Stefani_etal09; @Seilmayer_etal14]. The liquid sodium spherical Couette experiment in Maryland had produced coherent velocity/magnetic field fluctuations showing up in a parameter region reminiscent of MRI [@Sisan_etal04]. The liquid GaInSn TC experiments in Princeton was designed to investigate the standard version of MRI (SMRI) with only an axial magnetic field being imposed. In this case, the azimuthal magnetic field (which is 