  Theoretical work has shown that intermediate mass (0.01Msun<M_He<0.1Msun)
Helium shells will unstably ignite on the accreting white dwarf (WD) in an AM
CVn binary. For more massive (M>0.8Msun) WDs, these helium shells can be dense
enough (5x10^5 g/cc) that the convectively burning region runs away on a
timescale comparable to the sound travel time across the shell; raising the
possibility for an explosive outcome. The nature of the explosion (i.e.
deflagration or detonation) remains ambiguous. In the case of detonation, this
causes a laterally propagating front whose properties in these geometrically
thin and low density shells we begin to study here. Our calculations show that
the radial expansion time of <0.1 s leads to incomplete helium burning, in
agreement with recent work by Sim and collaborators, but that the nuclear
energy released is still adequate to realize a self-sustaining detonation
propagating laterally at slower than the Chapman-Jouguet speed. Our simulations
resolve the subsonic region behind the front and are consistent with a direct
computation of the reaction structure from the shock strength. The ashes are
typically He rich, and consist of predominantly Ti-44, Cr-48, along with a
small amount of Fe-52, with very little Ni-56 and with significant Ca-40 in
carbon-enriched layers. If this helium detonation results in a Type Ia
Supernova, its spectral signatures would appear for the first few days after
explosion. (abridged)
