A disc of plasma, orbiting around a central object, and threaded by a weak
magnetic field is highly unstable. Indeed different studies have shown that,
in few orbital time scales, the nonlinear development of the so-called
magnetorotational instability drives a turbulent transport of angular momentum
as well as a dynamo.

In order to define the properties of this unusual dynamo --- the turbulence
which provides the growth of magnetic energy relies on the magnetic field
itself --- we wish to perform global MHD simulations of an incompressible
accretion disc. Our approach in this dynamo study will require an explicit
control of the dissipation of both the magnetic field and the velocity field
because of the lack of knowledge of the properties of numerical dissipation.
Moreover, in contrast with other studies, our equilibrium state includes an
inflow driven by the viscous torque.

We have started this project by the linear study of the global MRI modes; we
would like to address here some of their properties, pointing out the
dependence on the definition of a set of boundary conditions consistent with
the incompressible nonlinear regime.