Preliminary Measurement of the Turbulent Magnetic Diffusivity in Three Dimensions

Abstract

Turbulent transport plays an important role in the evolution of astrophysical magnetic fields. The underlying idea is that the small-scale, turbulent motions increase the magnetic diffusivity above the value due to the molecular diffusion . However, it has been shown that in two dimensions the turbulent diffusion of large-scale magnetic fields is reduced significantly once the large-scale field strength exceeds a critical value, which can be much less than equipartition. The question that naturally arises is whether this holds true in three dimensions or whether magnetic fields of equipartition energy are required in order to suppress the effective turbulent diffusion. In order to elucidate this question we performed numerical calculations based on the full, incompressible MHD equations, that allow us to measure the effective magnetic diffusivity for different values of the large-scale magnetic field strength.