  We consider a Taylor-Dean-type flow of an electrically conducting liquid in
an annulus between two infinitely long perfectly conducting cylinders subject
to a generally helical magnetic field. The cylinders are electrically connected
through a remote, perfectly conducting endcap, which allows a radial electric
current to pass through the liquid. The radial current interacting with the
axial component of magnetic field gives rise to the azimuthal electromagnetic
force, which destabilizes the base flow by making its angular momentum decrease
radially outwards. This instability, which we refer to as the
pseudo--magnetorotational instability (MRI), looks like an MRI although its
mechanism is basically centrifugal. In a helical magnetic field, the radial
current interacting with the azimuthal component of the field gives rise to an
axial electromagnetic force, which drives a longitudinal circulation. First,
this circulation advects the Taylor vortices generated by the centrifugal
instability, which results in a traveling wave as in the helical MRI (HMRI).
However, the direction of travel of this wave is opposite to that of the true
HMRI. Second, at sufficiently strong differential rotation, the longitudinal
flow becomes hydrodynamically unstable itself. For electrically connected
cylinders in a helical magnetic field, hydrodynamic instability is possible at
any sufficiently strong differential rotation. In this case, there is no
hydrodynamic stability limit defined in the terms of the critical ratio of
rotation rates of inner and outer cylinders that would allow one to distinguish
a hydrodynamic instability from the HMRI. These effects can critically
interfere with experimental as well as numerical determination of MRI.
