On the Inverse Cascade of Magnetic Helicity

We study the inverse cascade of magnetic helicity in conducting fluids, as pertinent to the generation and dynamics of magnetic fields as observed, e.g., in the solar corona, by investigating the detailed transfer of helicity between different spherical shells in Fourier space in direct numerical simulations of three-dimensional magnetohydrodynamics (MHD). Two different numerical simulations are used, one in which the system is forced with an electromotive force in the induction equation and one in which the system is forced mechanically with an ABC flow and the magnetic field is solely sustained by a dynamo action. The magnetic helicity cascade at the initial stages of both simulations is observed to be inverse and local (in scale space) at large scales and direct and local at small scales. When saturation is approached, most of the helicity is concentrated at large scales and the cascade is nonlocal. Helicity is transferred directly from the forced scales to the largest scales. At the same time, a smaller in amplitude direct cascade is observed from the largest scale to small scales.