Higher helicity invariants and solar dynamo

Modern models of nonlinear dynamo saturation in celestial bodies (specifically, on the Sun) are largely based on the consideration of the balance of magnetic helicity. This physical variable has also a topological meaning: it is associated with the linking coefficient of magnetic tubes. In addition to magnetic helicity, magnetohydrodynamics has a number of topological integrals of motion (the so-called higher helicity moments). We have compared these invariants with magnetic helicity properties and concluded that they can hardly serve as nonlinear constraints on dynamo action.