Since turbulence can amplify a seed magnetic field very efficiently, turbulence plays important roles in the origin of cosmic magnetism. The seed magnetic field can be either spatially uniform or localized. If coherence length of a seed magnetic field is larger than the system size, we can treat it as a uniform seed field. It is well known that turbulence can efficiently amplify a uniform/homogeneous seed field. Numerical simulations show that the saturation stage is reached in ~15 large-eddy turnover times (L/v), where L is the driving scale and v is the r.m.s. velocity. On the other hand, when a seed magnetic field is ejected from an astrophysical object, we expect that the seed field is highly localized in space. Simulations show that turbulence can also efficiently amplify a localized seed field. Based on the simulations, we can construct a model for fast magnetization of the universe. Our model suggests that a localized seed magnetic field can fill the whole system in ~L_(sys)/L times the large-eddy turnover time and that growth of the magnetic field stops in ~max(15,L_(sys)/L) times the large-eddy turnover time. Our finding implies that, regardless of the shape of the seed field, fast magnetization is possible in turbulent systems, such as large-scale structure of the universe or galaxies.
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