  Hydromagnetic stresses in accretion discs have been the subject of intense
theoretical research over the past one and a half decades. Most of the disc
simulations have assumed a small initial magnetic field and studied the
turbulence that arises from the magnetorotational instability. However, gaseous
discs in galactic nuclei and in some binary systems are likely to have
significant initial magnetisation. Motivated by this, we performed ideal
magnetohydrodynamic simulations of strongly magnetised, vertically stratified
discs in a Keplerian potential. Our initial equilibrium configuration, which
has an azimuthal magnetic field in equipartion with thermal pressure, is
unstable to the Parker instability. This leads to the expelling of magnetic
field arcs, anchored in the midplane of the disc, to around five scale heights
from the midplane. Transition to turbulence happens primarily through
magnetorotational instability in the resulting vertical fields, although
magnetorotational shear instability in the unperturbed azimuthal field plays a
significant role as well, especially in the midplane where buoyancy is weak.
High magnetic and hydrodynamical stresses arise, yielding an effective
$\alpha$-value of around 0.1 in our highest resolution run. Azimuthal magnetic
field expelled by magnetic buoyancy from the disc is continuously replenished
by the stretching of a radial field created as gas parcels slide in the linear
gravity field along inclined magnetic field lines. This dynamo process, where
the bending of field lines by the Parker instability leads to re-creation of
the azimuthal field, implies that highly magnetised discs are astrophysically
viable and that they have high accretion rates.
