  Global stationary configurations of both aligned and logarithmic spiral MHD
perturbations are constructed analytically within an axisymmetric background
ofrazor-thin scale-free gas disc, which is embedded in an axisymmetric
gravitational potential of a dark matter halo and involves an isopedic magnetic
field almost vertically threaded through the disc plane. The scale-free index
$\beta$ of the disc rotation speed $v_{\theta}\propto R^{-\beta}$ falls in the
rangeof $(-1/2 , 1/2)$ where $R$ is the cylindrical radius. With the
holding-back of a deep background dark matter halo potential, the isopedic
magnetic field may be strong enough to allow for the magnetic tension force
overtaking the disc self-gravity, which can significantly influence global
stationary MHD perturbation configurations and stability properties of the
scale-free disc system. Only for stationary logarithmic spiral MHD
perturbations with a perturbation scale-free index $\beta_1=1/4$ or for aligned
stationary MHD perturbations, can the MHD disc maintain a constant radial flux
of angularmomentum. The variable radial flux of angular momentum in the radial
direction corresponds to a complex dispersion relation. The marginal
instabilities foraxisymmetric MHD disturbances are also examined for a special
case as an example. When the magnetic tension force overtakes the disc
self-gravity, the scale-free disc can be completely stable against axisymmetric
MHD disturbances of all wavelengths. We predict the possible existence of an
isopedicallymagnetized gas disc system in rotation primarily confined by a
massive dark matter halo potential.
