Dynamics and Statistics of Inverse Cascade Processes in 2D Magnetohydrodynamic Turbulence

The inverse cascade of the mean square potential $A$ in a 2D magnetofluid randomly forced at small scales is studied by numerical simulations. One finds the spectrum $A_k\simeq 2.6{\epsilon }_A^{\frac{2}{3}}{k}^{\frac{-7\mathrm{}}{3}}$. The cascade proceeds by coalescence of current filaments, which is a fast reconnection process owing to high turbulent resistivity. Statistics of $\delta {\nu }_l$ and $\delta B_l$ are strictly Gaussian, also in the condensation phase of $A_k$ at $k=1\mathrm{}$. Only when the coherent magnetic field intensity exceeds that of the fluctuations, non-Gaussian statistics in $\delta B_l$ occur, which are, however, entirely due to the static magnetic structure and not associated with intermittency of the small-scale turbulence, the latter remaining Gaussian.