Diffusion of large-scale magnetic fields by reconnection in MHD turbulence

The rate of magnetic field diffusion plays an essential role in several astrophysical plasma processes. It has been demonstrated that the omnipresent turbulence in astrophysical media induces fast magnetic reconnection, which consequently leads to large-scale magnetic flux diffusion at a rate independent of the plasma microphysics. This process is called 'reconnection diffusion' (RD) and allows for the diffusion of fields, which are dynamically important. The current theory describing RD is based on incompressible magnetohydrodynamic (MHD) turbulence. In this work, we have tested quantitatively the predictions of the RD theory when magnetic forces are dominant in the turbulence dynamics (Alfvenic Mach number M-A < 1). We employed the Pencil Code to perform numerical simulations of forced MHD turbulence, extracting the values of the diffusion coefficient eta(RD) using the test-field method. Our results are consistent with the RD theory (eta(RD) similar to M-A(3) for M-A < 1) when turbulence approaches the incompressible limit (sonic Mach number M-S less than or similar to 0.02), while for larger M-S the diffusion is faster (eta(RD) similar to M-A(2)). This work shows for the first time simulations of compressible MHD turbulence with the suppression of the cascade in the direction parallel to the mean magnetic field, which is consistent with incompressible weak turbulence theory. We also verified that in our simulations the energy cascading time does not follow the scaling with M-A predicted for the weak regime, in contradiction with the RD theory assumption. Our results generally support and expand the RD theory predictions.

Automated summary

The diffusion rate of magnetic fields is crucial in astrophysical plasma processes, with turbulence inducing fast magnetic reconnection and consequently large-scale magnetic flux diffusion. In this study, quantitative tests were conducted to verify predictions of the reconnection diffusion (RD) theory, showing generally consistent results and expanding on the theory.