  We investigate a theoretical MHD disc problem involving a composite disc
system of gravitationally coupled stellar and gaseous discs with a coplanar
magnetic field in the presence of an axisymmetric dark matter halo. The two
discs are expediently approximated as razor-thin, a ring-like magnetic field,
and a power-law rotation curve in radius . By imposing the scale-free
condition, we construct analytically stationary global MHD perturbation
configurations for both aligned and logarithmic spiral patterns. MHD
perturbation configurations in a composite system of partial discs in the
presence of an axisymmetric dark matter halo are also considered. We derive
analytically the stationary MHD dispersion relations for both aligned and
unaligned perturbation structures and analyze the corresponding phase
relationships between surface mass densities and the magnetic field. Compared
with earlier results, we obtain three solution branches corresponding to super
fast MHD density waves, fast MHD density waves and slow MHD density waves,
respectively. By evaluating the unaligned $m=0$ case, we determine the marginal
stability curves where the two unstable regimes corresponding to Jeans collapse
instability and ring fragmentation instability are identified. We find that the
aligned $m=0$ case is simply the limit of the unaligned $m=0$ case with the
radial wavenumber $\xi\to0$. We further show that a composite system of partial
discs behaves much differently from a composite system of full discs in certain
aspects. Our formalism provides a useful theoretical framework in the study of
stationary global perturbation configurations for MHD disc galaxies with bars,
spirals and barred spirals.
