GLOBAL MAGNETIC SHEAR INSTABILITY IN SPHERICAL GEOMETRY

This paper concerns the global stability of a differentially rotating magnetized sphere of an incompressible fluid. Rotation laws subcritica l to the Rayleigh stability criterion produce the instability in the f inite interval B(min)less than or equal to B less than or equal to B-m ax of the magnetic field amplitudes. The upper, B-max, and the lower, B-min, bounds are imposed by the finite size of the system and by fini te diffusivities (magnetic resist ivity and viscosity), respectively. For high rotation rates, B-max grows linearly with the angular velocit y gradient while B-min approaches a constant value. The global modes w ith different types of symmetry relative to the equatorial plane are i dentified. The modes with symmetric magnetic field and antisymmetric f low are always dominating. Nonaxisymmetric excitations are preferred w hen rotation is not too slow and the field strength is close to B-max. The possibility of a hydromagnetic dynamo produced by the instability in stellar radiative cores is briefly discussed.