A Novel Statistical Model to Triple the Fusion Yield in Direct-Drive Laser Fusion

November 2018

Accurate predictive capabilities are essential in the quest for thermonuclear ignition. In support of these predictive models, the Laboratory for Laser Energetics (LLE) has developed a novel statistical approach used to predict and design multiple cryogenic deuterium–tritium (DT) implosions on the OMEGA Laser System. This approach has led to the tripling of the fusion yield to its highest value for direct-drive laser fusion of DT-layered targets.

The design of inertial confinement fusion (ICF) implosions has been historically driven by 1-D and 2-D radiation-hydrodynamic (RH) codes. The use of 3-D codes is mostly limited to post-shot simulations because of the significant computational burden imposed by well-resolved 3-D simulations. LLE uses the 1-D RH code LILAC to design direct-drive implosions with experimentally benchmarked physics models for cross-beam energy transfer (CBET), thermal transport, and first-principles models of the equation of state.

These developments have contributed to experiments with 26 to 28 kJ of laser energy on the OMEGA laser, which have demonstrated core compression that would produce significant fusion alpha-particle self-heating when hydrodynamically scaled to energies of 1.9 MJ at the National Ignition Facility (NIF). Noteworthy performance improvements have also been achieved in indirect-drive ICF with recent layered DT implosions producing over 50 kJ of fusion yield (about 2 × 1016 fusion reactions), greatly exceeding the energy input to the fusion fuel.

Even with this important progress in modeling, it is still not possible to predict, a priori, the results of an ICF experiment with enough accuracy to enable the implementation of iterative design methodologies, which in turn will improve the implosion performance with a high degree of confidence.

LLE, using statistical relationships between RH code outputs and experimental data, has successfully mapped inaccurate code outputs into accurate experimental predictions. The method, as illustrated below, is a stepped-approach making small, incremental changes to either the target or the laser pulse. This process has led to tripling the fusion yield in a focused OMEGA experimental campaign, making possible the highest fusion yield (~1.4 × 1014 fusion reactions) to date in cryogenic DT direct-drive implosions. When scaled to 2-MJ incident laser energies, these targets are predicted to produce a fusion energy output of about 300 kJ, several times higher than the fusion yield achieved on the NIF to date.

This new method's fundamental principle is that although the RH codes are imperfect, the experimental observables Oexp are expected to correlate to the code output variables Osim because both the experiment and the code use the same input—that is, the laser pulse shape and the target geometry. Because the codes do not accurately reproduce the experimental results, the code–experiment relations are no longer one-to-one for each variable. Instead, a more-global relation is assumed to exist for which each experimental observable correlates to a combination of code output variables.

The next step of the direct-drive program on the OMEGA laser will involve applying the same statistical mapping model to increase the areal density while keeping the yields at their highest levels. A modest increase in areal density and/or yield will result in achieving core conditions on OMEGA that scale to megajoule fusion yields at NIF laser energies. This newly acquired predictive capability from statistical mapping offers an accurate and reliable tool, which will spur rapid progress toward the goal of demonstrating thermonuclear ignition and burn in the laboratory for the first time.