Figure 20: Four snapshots representing the temporal evolution of MRI from the linear to the nonlinear phase. Panels (a), (b), (c) and (d) correspond to the time slice , , , and respectively. The color bar indicates the size of the toroidal magnetic field normalized by the strength of the initial vertical magnetic field (  G). Note that the vertical and horizontal are normalized by the typical spatial scale of the local portion in the protoneutron stars which is selected as km in the fiducial run. Three typical evolutionary stages are observed, (i) exponential growth stage, (ii) transition stage, and (iii) nonlinear turbulent stage (compare with Figure 19).