Differential rotation and magnetic fields in stellar interiors

The processes contributing to the evolution of an initially weak magnetic f ield in a differentially rotating star are reviewed. These include rotation al smoothing (akin to convective expulsion) and a list of about 5 instabili ties, among them magnetorotational instability, buoyancy instability, and p inch-type instabilities. The important effects of thermal and magnetic diff usion on these instabilities are analyzed in some detail. The first instabi lity to set in is a pinch-type instability. It becomes important in modifyi ng the field configuration before magnetic buoyancy-driven instabilities se t in. The evolution of an initially strong field remains a more open questi on, including the old problem whether dynamically stable magnetic equilibri a exist in stars.