Universal Nonlinear Small-Scale Dynamo

We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds numbers (Re). We argue that it is universal in a sense that magnetic energy grows at a rate which is a constant fraction C-E of the total turbulent dissipation rate. On the basis of locality bounds we claim that this efficiency of the small-scale dynamo, C-E, is a true constant for large Re and is determined only by strongly nonlinear dynamics at the equipartition scale. We measured C-E in numerical simulations and observed a value around 0.05 in the highest resolution simulations. We address the issue of C-E being small, unlike the Kolmogorov constant which is of order unity.