Helicity as a lower bound for the energy of magnetic fields in plasmas

In 1974, V.I. Arnold showed in a classical paper that the energy of a magnetic field is bounded from below by its total magnetic helicity. His inequality contains a constant C, which is the smallest possible eigenvalue of the curl operator in the magnetically closed domain. The corresponding eigenstate is a state of maximum helicity for a given energy.  

However, the original formula by Arnold was derived for simply connected and magnetically closed domains. This severely restricts the range of applications. We explore how one can extend Arnold’s result to other domains and boundary conditions, what the corresponding maximum helicity states look like and the relation between helicity and the Calabi invariant. 

Venue: Fulton G20