Global structure of self-excited magnetic fields arising from the magneticshear instability

The global structure of a self-excited magnetic field arising from the magn etic shear instability has been simulated in spherical geometry by a 3D ful ly non-linear approach. In order to model the structure of an accretion dis c we prescribe a rotation profile of the Brandt type which is Keplerian in the outer regions but yields rigid rotation at the inner core. We performed a whole series of runs at different dynamo numbers with an increasing numb er of modes in spectral space, thereby checking the influence of the numeri cal resolution in our simulations. Starting from arbitrary small perturbati ons, the magnetic and kinetic energies grow by several orders of magnitude as soon as a certain azimuthal resolution of at least m=15 was used at a dy namo number of order C-Omega=10(5). Several phases of the transition to tur bulence are realized and interpretations are given for the respective effec ts occurring at each stage. The resulting magnetic field is highly non-axis ymmetric and possesses a pronounced inhomogeneous vortex structure of twist ed flux tubes. The flow is almost axisymmetric but shows a Kolmogorov-like behaviour for small scales. The outer surface of the shell is penetrated by magnetic field lines in spot-like regions, which are located mainly in the equatorial plane. For very high dynamo numbers we find a cyclic behaviour of the averaged magnetic field amplitude. The problem of angular momentum t ransport is discussed in terms of the Shakura-Sunyaev viscosity alpha, whic h depends exponentially on the radial distance and adopts values in the ran ge 10(-3)-10(-5).