Inductionless instabilities in rotational MHD flows: A comprehensive short-wavelength analysis

We perform a local stability analysis of rotational ows in the presence of a constant vertical magnetic eld and an azimuthal magnetic eld with a general radial dependence characterized by an appropriate magnetic Rossby number. Employing the short-wavelength approximation we develop a unied framework for the investigation of the standard, the helical, and the azimuthal version of the magnetorotational instability, as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers which applies, e.g., to liquid metal experiments but also to the colder parts of accretion disks. We show in particular that the inductionless versions of MRI that were previously thought to be restricted to comparably steep rotation proles extend well to the Keplerian case if only the azimuthal eld slightly deviates from its current-free prole.