  Development of large mass detectors for low-energy neutrinos and dark matter
may allow supernova detection via neutrino-nucleus elastic scattering. An
elastic-scattering detector could observe a few, or more, events per ton for a
galactic supernova at 10 kpc ($3.1 \times 10^{20}$ m). This large yield, a
factor of at least 20 greater than that for existing light-water detectors,
arises because of the very large coherent cross section and the sensitivity to
all flavors of neutrinos and antineutrinos. An elastic scattering detector can
provide important information on the flux and spectrum of $\nu_\mu$ and
$\nu_\tau$ from supernovae. We consider many detectors and a range of target
materials from $^4$He to $^{208}$Pb. Monte Carlo simulations of low-energy
backgrounds are presented for the liquid-neon-based Cryogenic Low Energy
Astrophysics with Noble gases (CLEAN) detector. The simulated background is
much smaller than the expected signal from a galactic supernova.
