Determining the yield amplification of Bigfoot shots with Bayesian methods and Stochastic Collocation

Several NIF campaigns have recently demonstrated the ability to consistently reach neutron yields of 10¹⁶ and above. With such yields we are approaching the burning plasma regime where the energy deposition of the 3.5 MeV alpha particle into the hotspot and cold fuel is significant such that it raises the temperature of the plasma and the DT reactivity. If enough alpha particles deposit their kinetic energy into the DT fuel a sustained burn-wave is formed in the ice layer eventually leading to fusion ignition. The yield amplification due to alpha-particle energy deposition serves as a metric to judge the progress along the path to fusion ignition. We study the yield amplification for a series of Bigfoot shots in which pairs of hydrodynamically similar shots were performed with DT or THD fuel fractions that produce or inhibit alpha particle production, respectively. Two recent developments have enabled us to provide an estimate of the mean and the variance of the yield-amplification. The Bayesian-Super-Postshot (BSPS) analysis infers the posterior-predictive set of 9 input parameters to the radiation-hydrodynamics code HYDRA that are consistent with several experimentally observed quantities for each Bigfoot shot. The Stochastic Collocation (SC) technique then exploits properties of orthogonal polynomials with respect to the BSPS input probability distribution to form a "small" set of simulation nodes in carefully placed locations that provide a reliable estimate of the mean and variance of an experimental observable. The yield amplification mean and variance determined by the BSPS and SC is found to be in good agreement with one-dimensional models. Lastly, this methodology is not limited to yield amplification and can be extended to other observables.