  We analyze a linear perturbation scheme for a two-dimensional background
plasma, which is rotating with a differential frequency and is embedded in a
poloidal magnetic field. The main two assumptions of the present study, which
in turn are related, are that the plasma profile is axially symmetric, both in
the background and the perturbation approximation, where the azimuthal magnetic
field is requested to vanish identically and secondly the angular frequency on
the magnetic surface function only still holds in the non-stationary regime,
which, on the steady background equilibrium, is ensured by the validity of the
corotation theorem (Ferraro 1937). Indeed, such a restriction of the model is
rather natural and it implies that the azimuthal component of the linear plasma
shift is reabsorbed in the expression for the non stationary electric field (in
principle, at any order of approximation) and can no longer provide a non-zero
azimuthal component of the magnetic tension field. As a result, the
Magneto-rotational instability is suppressed and the magnetic field has the
effect to stabilize the plasma configuration with respect to the pure
hydrodynamical case.
