Carbon detonation is a characteristic event of Type 1a Supernova, where an accreting white dwarf near the Chandrashankar limit of 1.4 solar masses explodes, which is 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?
Answer
In stars, carbon-carbon fusion gets going around $5\times10^8\,\text{K}$. From a quick glance at a relevant stellar model I have lying around, it looks like the relevant pressure in the core of a $12M_\odot$ star is on the order of $10^{22}\,\text{dyne.cm}^{-2}$ or $10^{21}\,\text{Pa}$. But the densities are also very large: around $10^6\,\text{g.cm}^{-3}$ and the reaction rate scales with $\rho^2$.
As far as I know, the temperatures and densities achieved in the National Ignition Facility are around $10^8\,\text{K}$ and $10^3\,\text{g.cm}^{-3}$. So while it doesn't seem that the temperatures are that hard to reach, the densities probably are.
Our current knowledge of these reaction is built on detailed calculations and collider experiments with small numbers of particles. These collisions aren't nearly enough to produce energy but we can learn something about the reaction cross-sections based on what happens.
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