Mirror Asymmetry and Helicity Invariants in Astrophysical Dynamos

Abstract

The mirror asymmetry of hydrodynamics flows and magnetic fields plays a crucial role in magnetic field evolution in various celestial bodies including the Earth, Sun and Milky Way galaxy. A natural measure of the mirror asymmetry is associated with the Gauss invariant, i.e. the linkage number of vortex and magnetic lines. We consider the relation between magnetic field generation and the knotting of vortex and magnetic lines in terms of hydrodynamic and magnetic helicities. Higher helicity invariants known in topology generalize in various ways the Gauss invariant. We argue that these higher helicities are less important for magnetic field evolution than the classical Gauss invariant.