The growth of magnetic energy during the nonlinear phase of the subsonic and supersonic small-scale dynamo

Small-scale dynamos (SSDs) amplify magnetic fields in turbulent plasmas. Theory predicts nonlinear magnetic energy growth Eₘag ∝ tpₙl, 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 (pₙl = 1) in subsonic flows and quadratic growth (pₙl = 2) in supersonic flows. In all cases, we find a dynamo efficiency of ~ 1/100 and a duration Δt ≈ 20\,t₀, with t₀ the turnover time, establishing the universal timescales and efficiencies of the nonlinear SSD across astrophysical and laboratory plasmas.