only in the last decade. These studies were initiated by Hollerbach & R[ü]{}diger [@Hollerbach_Ruediger05], who realized that adding an azimuthal magnetic field to the axial field can destabilize highly resistive flows at much smaller field strengths and at several orders of magnitude smaller Reynolds numbers, reducing the critical value from $Re\sim 10^6$ needed for SMRI with purely axial field to $Re\sim
10^3$. Because this instability takes place in the presence of helical magnetic field, composed of azimuthal and axial components, it was termed HMRI. Like the SMRI, the HMRI also draws free energy from the background shear flow and transports angular momentum outward. Subsequently, HMRI has been widely studied theoretically by means of linear modal stability analysis [@Liu_etal06; @Priede_etal07; @Priede_Gerbeth09; @Kirillov_Stefani10; @Priede11; @Kirillov_Stefani13; @Kirillov_etal14; @Ruediger_etal06]. It was shown that HMRI represents a destabilized inertial wave [@Liu_etal06] and its growth rate is governed by the Reynolds number and the Hartmann number, $Ha$, characterizing the magnetic field strength. As a result, HMRI can persist even at extremely small magnetic Prandtl numbers typical to liquid metals, in contrast to SMRI, which is generally suppressed under this condition. Another difference with SMRI is that HMRI is restricted to rotational profiles with comparably steep negative 