  We present here the first 2D rotating, multi-group, radiation
magnetohydrodynamics (RMHD) simulations of supernova core collapse, bounce, and
explosion. In the context of rapid rotation, we focus on the dynamical effects
of magnetic stresses and the creation and propagation of MHD jets. We find that
a quasi-steady state can be quickly established after bounce, during which a
well-collimated MHD jet is maintained by continuous pumping of power from the
differentially rotating core. If the initial spin period of the progenitor core
is $\sles$ 2 seconds, the free energy reservoir in the secularly evolving
protoneutron star is adequate to power a supernova explosion, and may be enough
for a hypernova. The jets are well collimated by the infalling material and
magnetic hoop stresses, and maintain a small opening angle. We see evidence of
sausage instabilities in the emerging jet stream. Neutrino heating is
sub-dominant in the rapidly rotating models we explore, but can contribute
10$-$25% to the final explosion energy. Our simulations suggest that even in
the case of modest or slow rotation, a supernova explosion might be followed by
a secondary, weak MHD jet explosion, which, because of its weakness may to date
have gone unnoticed in supernova debris. Furthermore, we suggest that the
generation of a non-relativistic MHD precursor jet during the early
protoneutron star/supernova phase is implicit in both the collapsar and
"millisecond magnetar" models of GRBs. The multi-D, multi-group, rapidly
rotating RMHD simulations we describe here are a start along the path towards
more realistic simulations of the possible role of magnetic fields in some of
Nature's most dramatic events.
