Topological Properties of Magnetic and Vorticity Fields

The interior media of stars and planets are often virtually perfect conductors and possess magnetic fields. These fields are said to be “frozen" into the medium (for instance, plasma or magma) in spite of temperatures of a million degrees. Mathematically this means that any motion of the medium transports the fields by a diffeomorphism action preserving the mutual alocation of the fields' trajectories. Such a transform may diminish the field magnetic energy. The topological structure of the field provides obstacles to the full dissipation of the magnetic energy of the star or planet.