  A relatively modest value of the initial rotation of the iron core, a period
of ~ 6-31 s, will give a very rapidly rotating protoneutron star and hence
strong differential rotation with respect to the infalling matter. Under these
conditions, a seed field is expected to be amplified by the MRI and to grow
exponentially. Exponential growth of the field on the time scale Omega^{-1} by
the magnetorotational instability (MRI) will dominate the linear growth process
of field line "wrapping" with the same characteristic time. The shear is
strongest at the boundary of the newly formed protoneutron star. Modest initial
rotation velocities of the iron core result in sub-Keplerian rotation and a
sub-equipartition magnetic field that nevertheless produce substantial MHD
luminosity and hoop stresses: saturation fields of order 10^{15} - 10^{16} G
develop ~ 300 msec after bounce with an associated MHD luminosity of ~ 10^{49}
- 10^{53} erg s^{-1}. Bi-polar flows driven by this MHD power can affect or
even cause the explosions associated with core-collapse supernovae. If the
initial rotation is too slow, then there will not be enough rotational energy
to power the supernova despite the high luminosities. The MRI should be active
and may qualitatively alter the flow if a black hole forms directly or after a
fall-back delay.
