Carbon detonation is a characteristic event of Type 1a Supernova (EDIT: where an accreting white dwarf near the Chandrashankar limit of 1.4 solar masses explodes), an extremely important standard candle for cosmology. An area of active research is designing computer simulations to model supernova spectra and light curves and fit these to ones obtained observationally to better understand the effect of trace elements and characteristics of the explosion (asymmetry, companion star properties, etc) in order to provide better distance estimates to get more accurate constraints on cosmological parameters (Hubble constant, Dark Energy equation of state, etc).
But it would be very interesting (and extremely cool) if there was a way of generating carbon detonations in a laboratory situation in order to study these effects. What sort of temperature/pressure range is necessary to generate a carbon detonation? Would it be in the range of experimental apparati? Or, on the extreme sides of things, a large thermonuclear device?