Simulations of a magnetic fluctuation driven large-scale dynamo and comparison with a two-scale model

Abstract

Models of large-scale (magnetohydrodynamic) dynamos (LSDs) which couple large-scale field growth to total magnetic helicity evolution best predict the saturation of LSDs seen in simulations. For the simplest so-called 'α2' LSDs in periodic boxes, the electromotive force driving LSD growth depends on the difference between the time-integrated kinetic and current helicity associated with fluctuations. When the system is helically kinetically forced (KF), the growth of the large-scale helical field is accompanied by growth of small-scale magnetic (and current) helicity which ultimately quench the LSD. Here, using both simulations and theory, we study the complementary magnetically forced (MF) case in which the system is forced with an electric field that supplies magnetic helicity. For this MF case, the kinetic helicity and turbulent diffusion terms comprise the backreaction that saturates the LSD. Simulations of both MF and KF cases can be approximately modelled with the same equations of magnetic helicity evolution, but with complementary initial conditions. A key difference between KF and MF cases is that the helical large-scale field in the MF case grows with the same sign of injected magnetic helicity, whereas the large- and small-scale magnetic helicities grow with opposite sign for the KF case. The MF case can arise even when the thermal pressure is approximately smaller than the magnetic pressure, and requires only that helical small-scale magnetic fluctuations dominate helical velocity fluctuations in LSD driving. We suggest that LSDs in accretion discs and Babcock models of the solar dynamo are actually MF LSDs. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.