\[fig:momspace\] shows map projections of the momentum space angular neutrino distribution at different radii in a supernova core. In the dense protoneutron star, neutrinos are trapped and in equilibrium with matter. Their radiation field is isotropic. They gradually diffuse out and decouple from matter at the *neutrinosphere* (the neutrino equivalent of the photosphere). This decoupling is gradual and marked by the transition of the angular distribution into the forward (radial) direction. In the outer decoupling region, neutrino heating is expected to occur and the heating rates are sensitive to the angular distribution of the radiation field (cf. [@ott:08]). Eventually, at radii of a few hundred kilometers, the neutrinos have fully decoupled and are free streaming. Neutrino interactions with matter (and thus the decoupling process) are very sensitive to neutrino energy, since weak-interaction cross-sections scale with the square of the neutrino energy. This is why neutrino transport needs to be *multi-group*, with typically a minimum of $10-20$ energy groups covering supernova neutrino energies of $1 -
      \mathcal{O}(100)\,\mathrm{MeV}$. Typical mean energies of electron neutrinos are around $10-30\,\mathrm{MeV}$. Energy exchanges between matter and radiation occur via the collision terms in the Boltzmann equation. These are stiff sources/sinks that must be handled time-implicitly with 