is believed to operate in a vast variety of cosmic objects, ranging from astrophysical disks and stars to liquid-metal cores of planets. While discovered as early as 1959 [@Velikhov59], the astrophysical significance of MRI was first recognized only three decades later by Balbus & Hawley [@Balbus_Hawley91], who demonstrated that weak magnetic fields can destabilize Keplerian accretion disks around such diverse objects as supermassive black holes, black holes in X-ray binaries and young stellar objects, which would otherwise be linearly stable according to Rayleigh’s criterion. The linear growth of MRI, which taps into the free energy of differential rotation, eventually breaks down into magnetohydrodynamic (MHD) turbulence [@Hawley_etal95; @Fromang13]. This turbulence transports angular momentum outward and, as a consequence, matter inward in the disk, yielding mass accretion rates onto the central object close to observationally inferred values. More recently, MRI has also been discussed for explaining angular momentum transport in the Sun, massive stars and neutron stars [@Kagan_Wheeler14; @Wheeler_etal15; @Masada_etal15; @Spada_etal16] and also in the context of the geodynamo [@Petitdemange_etal08; @Petitdemange_etal13].

The MRI was originally discovered theoretically in a classical Taylor-Couette (TC) flow of a conducting fluid between two concentric rotating cylinders threaded by an external vertical (along the common axis of 