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 (Alfv{e}nic Mach number $M_A < 1$). We employed the textsc{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 ($eta_{RD} sim M_A^{3}$ for $M_A < 1$) when turbulence approaches the incompressible limit (sonic Mach number $M_S lesssim 0.02$), while for larger $M_S$ the diffusion is faster ($eta_{RD} sim M_A^{2}$). 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.
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