Magnetic helicity evolution in a periodic domain with imposed field

In helical hydromagnetic turbulence with an imposed magnetic field the magnetic helicity of the field within a periodic domain is no longer an invariant of the ideal equations. There is a generalized magnetic helicity that is an invariant of the ideal equations, but it is not gauge invariant and can therefore not be used. Instead, the evolution equation of the magnetic helicity of the field describing the deviation from the imposed field is shown to be a useful tool and is used to determine steady state quenching of the alpha-effect and to derive a simple three-scale model to describe the evolution of the magnetic helicity. The results of the model agree favorably with simulations