  We conduct a linear analysis of axisymmetric magnetorotational instability
(MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard
version (SMRI) with a purely axial background magnetic field and two further
types -- helically modified SMRI (H-SMRI) and helical MRI (HMRI) -- in the
presence of combined axial and azimuthal magnetic fields. This study is
intended as preparatory for upcoming large-scale liquid sodium MRI experiments
planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so
we explore these instability types for typical values of the main parameters:
the magnetic Reynolds number, the Lundquist number and the ratio of the angular
velocities of the cylinders, which are attainable in these experiments. In
contrast to previous attempts at detecting MRI in the lab, our results
demonstrate that SMRI and its helically modified version can in principle be
detected in the DRESDYN-TC device for the range of the above parameters,
including the astrophysically most important Keplerian rotation, despite the
extremely small magnetic Prandtl number of liquid sodium. Since in the
experiments we plan to approach (H-)SMRI from the previously studied HMRI
regime, we characterise the continuous and monotonous transition between the
both regimes. We show that H-SMRI, like HMRI, represents an overstability
(travelling wave) with non-zero frequency linearly increasing with azimuthal
field. Because of its relevance to finite size flow systems in experiments, we
also analyse the absolute form of H-SMRI and compare its growth rate and onset
criterion with the convective one.
