On the Stability of a General Magnetic Field Topology in Stellar Radiative Zones

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. In particular, a purely magnetic instability can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations as originally studied in Tayler (1973), Markey & Tayler (1973), and Tayler (1980). However, most of the magnetic field configurations observed at the surface of massive stars are non- axisymmetric. Thus, extending earlier studies of the axisymmetric Tayler instability in spherical geometry (Goossens, 1980), we introduce a formulation for the global change in the potential energy contained in a convectively-stable region given an arbitrary Lagrangian perturbation, which permits the inclusion of both axisymmetric and non-axisymmetric magnetic fields. With this tool in hand, a path is shown by which more general stability criterion can be established.