point of view. The linear analysis identified critical magnetic Reynolds numbers for the onset of the instability and discussed possibilities for its experimental detection (e.g., [@Ji_etal01; @Ruediger_Zhang01; @Goodman_Ji02; @Kirillov_Stefani10]). In particular, it was shown that the linear growth rate is determined by magnetic Reynolds number and Lundquist number (i.e., ratio of the magnetic diffusion time to the Alfvén crossing time), which should be both larger than unity for SMRI to operate. The saturation properties of SMRI following its exponential growth was investigated both in the weakly nonlinear regime, i.e., near the instability threshold, [@Umurhan_etal07a; @Umurhan_etal07b; @Clark_Oishi16a; @Clark_Oishi16b] and in the fully nonlinear regime [@Knobloch_Julien05; @Liu_etal06a; @Liu08; @Ebrahimi_etal09; @Gissinger_etal12; @Gellert_etal12; @Wei_etal16]. It was demonstrated that SMRI saturates on the resistive time scale by modifying (reducing) the background velocity shear responsible for it and strengthening the background field. The dependence of the saturation level on the imposed field as well as on the magnetic Reynolds number, Prandtl number and Lundquist number was explored in greater detail.

While SMRI has been explored quite extensively both in TC flows and astrophysical disk context since the 1990s, its relative – helical magnetorotational instability (HMRI) – has become a subject of active theoretical and experimental research 