Gamma-ray images show where the carbon is, during DT burn in NIF capsules

For carbon-ablator capsules imploded at NIF, inelastic scattering of DT neutrons on ¹²C nuclei produces intense gamma radiation, via the process ¹²C(n,n') -> γ(4.4 MeV). Images of the escaping gamma rays allow us to infer the spatial distribution of carbon near the core of the implosion, since the volume emissivity of 4.4-MeV gamma rays depends only on the product of DT neutron flux and carbon density. Often the images are fairly symmetric, and can be explained as resulting from a 1D spherical distribution of carbon. For such cases, we have developed a 5-parameter static 1D model of the “carbon cloud”, computed the resulting model gamma-ray image (including DT gamma rays) with MCNP6^® transport simulations, and used Markov-chain Monte Carlo with Bayesian inference to determine probable values of the model parameters, along with their uncertainties. Some useful outputs of this procedure include the maximum density of compressed carbon during burn, and the mass and density of carbon mixed into the burning core.