Integrated thermodynamic model for ignition target performance

We have derived a 3-dimensional synthetic model for NIF implosion conditions, by predicting and optimizing fits to a broad set of x-ray and nuclear diagnostics obtained on each shot. By matching x-ray images, burn width, neutron time-of-flight ion temperature, yield, and fuel r, we obtain nearly unique constraints on conditions in the hotspot and fuel in a model that is entirely consistent with the observables. This model allows us to determine hotspot density, pressure, areal density (r), total energy, and other ignition-relevant parameters not available from any single diagnostic. This article describes the model and its application to National Ignition Facility (NIF) tritium-hydrogen-deuterium (THD) and DT implosion data, and provides an explanation for the large yield and r degradation compared to numerical code predictions. To optimize the target and laser parameters for ignition (1, 2), it is important to understand the implosion conditions achieved in a given experiment, independent of the design predictions. To this end, we developed and applied a model to estimate the performance of an implosion and assess temperature, density, and composition distributions within the assembled core, solely from the experimental data taken during the shot. Using radiative, equation of state, nuclear fusion relations for relevant materials, and an approximation of pressure equilibrium within the hotspot (3), we derive a 3-dimensional representation of the capsule density and temperature profiles at stagnation, by predicting and optimizing fits to a broad set of x-ray and nuclear diagnostics. This model allows us to determine hotspot density, pressure, areal density (r), total energy, and other ignition-relevant parameters not available from any single diagnostic. This approach has been validated by comparing results with radiation-hydrodynamic simulations and has produced semi-quantitative (10-20%) agreement. We begin by constructing a 3D model for the temperature and density conditions of the imploded core at neutron bang time, defined as the time of peak neutron and 10-20keV x-ray production in the capsule (4). We further assume that this imploded core, including both hotspot and fuel, is at a uniform pressure Phs. So for a given density profile (r, , ), we derive an associated temperature profile using the hydrogenic equation-of-state, which includes effects of Fermi degeneracy in the dense shell (5). This description produces a relatively complete characterization of the implosion temperature and density distributions, and from this we can calculate the complete properties of the x-ray emission and nuclear fusion processes to predict the ensemble of diagnostic signatures from the implosion. Given an assumed pressure and density profile, we calculate the waist and polar x-ray emission images, using a free-free emissivity derived from the VISTA opacity model, and a Detailed This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.