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 subsonic to supersonic turbulence, we measure linear growth ($p_{\mathrm{nl}}=1$) in subsonic flows and quadratic growth ($p_{\mathrm{nl}}=2$) in supersonic flows. In all cases, the nonlinear dynamo converts a nearly constant fraction approximately equal to $1/100$ of the turbulent kinetic energy flux into magnetic energy, and the nonlinear phase has a characteristic duration $\mathrm{\Delta }t\approx 20t_0$, where $t_0$ is the outer-scale turnover time. By isolating the onset of magnetic backreaction in SSDs, our statistical ensemble approach identifies a robust efficiency and duration for the nonlinear SSD that can be used to interpret more complex astrophysical and laboratory plasmas.

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• Dynamo theory
• Magnetic field generation & plasma dynamo
• Magnetohydrodynamic turbulence
• Space & astrophysical plasma