We investigate the action of the magnetorotational instability (MRI) in the
context of iron-core collapse. Exponential growth of the field on the rotation
time scale by the MRI will dominate the linear growth process of field line
"wrapping" with the same characteristic time. We examine a variety of initial
rotation states, with solid body rotation or a gradient in rotational velocity,
that correspond to models in the literature. A relatively modest value of the
initial rotation, a period of ~ 10 s, will give a very rapidly rotating PNS and
hence strong differential rotation with respect to the infalling matter. We
assume conservation of angular momentum on spherical shells. Results are
discussed for two examples of saturation fields, a fiducial field that
corresponds to Alfven velocity = rotational velocity and a field that
corresponds to the maximum growing mode of the MRI. 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 within 300 msec after bounce with an associated MHD luminosity of about
10^{52} erg/s. Bi-polar flows driven by this MHD power can affect or even cause
the explosions associated with core-collapse supernovae.Comment: 42 pages, including 15 figures. Accepted for publication in ApJ. We
have revised to include an improved treatment of the convection, and some
figures have been update
