arXiv:2509.09949v1 Announce Type: new
Abstract: Small-scale dynamos (SSDs) amplify magnetic fields in turbulent plasmas. Theory predicts nonlinear magnetic energy growth $E_mathrm{mag} propto t^{p_mathrm{nl}}$, but this scaling has not been tested across flow regimes. Using a large ensemble of SSD simulations spanning sub- to supersonic turbulence, we find linear growth ($p_mathrm{nl} = 1$) in subsonic flows and quadratic growth ($p_mathrm{nl} = 2$) in supersonic flows. In all cases, we find a dynamo efficiency of $sim 1/100$ and a duration $Delta t approx 20,t_0$, with $t_0$ the turnover time, establishing the universal timescales and efficiencies of the nonlinear SSD across astrophysical and laboratory plasmas.