Magnetic fields are present in many different astrophysical objects, such as accretion discs, stars, and planets. They influence the evolution and dominate the interior dynamics of these objects, in particular their evolutionary stages. The presence of a weak (subthermal) magnetic field plays a crucial role to drive turbulence in accretion discs thus leading to the stresses needed for accretion and angular momentum transport. This instability is known as the Magneto Rotational Instability (MRI) and it has been studied intensively for the last two decades. Recent numerical results show the importance of understanding the dynamo process in accretion discs. Small-scale dynamo action could prevent the saturation of MRI modes whereas the generation of large-scale magnetic fields provides a suitable coherent field for the angular-momentum transport by MRI modes. Observations show a huge variety of stellar and planetary magnetic fields. Cosmic magnetic fields differ in their magnitude, topology and time dependence. Of particular interest is the understanding of cyclic field variations, as known from the Sun. They are often explained by an important Ω effect, i.e., by the stretching of field lines because of strong differential rotation. We computed the dynamo coefficients for an oscillatory dynamo model with the help of the so-called test-field method. We argue that this example is of α2Ω-type and here the Ω-effect alone is not responsible for its cyclic time variation. More general conditions which lead to dynamo waves in global direct numerical simulations are presented. Zonal flows driven by convection in planetary interiors may lead to secondary instabilities. We showed that a simple, modified version of the MRI (so-called MSMRI) can develop in the Earth's outer liquid core (Petitdemange, Dormy, Balbus, GRL,35, 2008). The force balance in the Earth's core and in classical astrophysical applications of the MRI (such as gaseous discs around stars) is different. The weak differential rotation in planetary interiors yields an instability by its constructive interaction with the much larger rotation rate of the planets. The resulting destabilizing mechanism is just strong enough to counteract the stabilizing resistive effects, and to produce growth on geophysically interesting time scales. MRI and dynamo action are both interesting in their own right, however, their interaction is crucial in order to understand the dynamics of accretion discs, stellar and planetary interiors.
Times Cited: 0 Workshop on Waves and Instabilities in Space and Astrophysical Plasmas JUN 19-24, 2011 Ben Gurion Univ Negev, Eilat Campus, Eilat, ISRAEL French Embassy, Off Sci & Technol; Lab Cassiopee, Observ Cote Azur