### abstract

- We study a nonlinear quenching of turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a developed two-dimensional MHD turbulence at large magnetic Reynolds numbers. We show that transport of the mean-square magnetic potential strongly changes quenching of turbulent magnetic diffusion. In particularly, the catastrophic quenching of turbulent magnetic diffusion does not occur for the large-scale magnetic fields $B\ensuremath{\gg}{B}_{\mathrm{eq}}∕\sqrt{\mathrm{Rm}}$ when a divergence of the flux of the mean-square magnetic potential is not zero, where ${B}_{\mathrm{eq}}$ is the equipartition mean magnetic field determined by the turbulent kinetic energy and $\mathrm{Rm}$ is the magnetic Reynolds number. In this case the quenching of turbulent magnetic diffusion is independent of magnetic Reynolds number. The situation is similar to three-dimensional MHD turbulence at large magnetic Reynolds numbers whereby the catastrophic quenching of the $\ensuremath{\alpha}$ effect does not occur when a divergence of the flux of the small-scale magnetic helicity is not zero.