Magnetic helicity fluxes in an α² dynamo embedded in a halo

Abstract

We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical α quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic helicity, so that the total magnetic helicity can reach a steady state value only through fluxes through the boundary, which are themselves suppressed by the velocity boundary conditions. Even with such a set up, the small-scale magnetic helicity is found to reach a steady state. In agreement with the earlier work, the magnetic helicity fluxes of small-scale fields are found to be turbulently diffusive. By comparing results with and without halos, we show that artificial constraints on magnetic helicity at the boundary do not have a significant impact on the evolution of the magnetic helicity, except that “softer” (halo) boundary conditions give a lower energy of the saturated mean magnetic field.

Keywords:

• Solar dynamo
• Turbulence simulations
• Alpha effect
• Alpha quenching
• Magnetic helicity

Acknowledgements

We thank Petri Käpylä for detailed suggestions that have helped to improve this article. We acknowledge the allocation of computing resources provided by the Swedish National Allocations Committee at the Center for Parallel Computers at the Royal Institute of Technology in Stockholm and the National Supercomputer Centers in Linköping as well as the Norwegian National Allocations Committee at the Bergen Center for Computational Science. This work was supported in part by the European Research Council under the AstroDyn Research Project No. 227952 and the Swedish Research Council Grant No. 621-2007-4064.