All recent numerical simulations agree that stars in the main sequence mass range of 9-40 solar masses do not produce a prompt hydrodynamic ejection of the outer layers after core collapse and bounce. Rather they suggest that stellar core collapse and supernova explosion are dynamically distinct astrophysical events, separated by an unspectacular accretion phase of at least ~40 ms duration. As long as the neutrinospheres remain convectively stable, the explosion dynamics is determined by the neutrons, protons, electrons and neutrinos in the layer of impact-heated matter piling up on the protoneutron star. The crucial role of neutrino transport in this regime has been emphasized in many previous investigations. Here, we search for efficient means to address the role of magnetic fields and fluid instabilities in stellar core collapse and the postbounce phase.

4 pages, contribution to Nuclei in the Cosmos VIII, Jul. 19-23, submitted to Nucl. Phys. A