An Extended Scaling for the Ignition Threshold Through Statistical Modeling

In laser-driven fusion, determining the ignition margin is an important prerequisite for evaluating the ignition robustness of a target design. The ignition threshold factor (ITF), defined as the shell kinetic energy at the time of maximum implosion velocity divided by the minimum ignition energy of the capsule, is widely adopted as a specific metric of the ignition margin. In this paper, in contrast to previous definitions of ITF, an additional quantity, i.e., the shell aspect ratio (Ar) at the maximum implosion velocity time, is found to have an important influence on the ignition margin. With including the quantity of Ar, we have obtained an extended ITF through the statistical modeling of following two steps with the help of a free available MULTI-IFE code and the PyMC3 Bayesian inference package: first, the sensitivity of the ignition cliff on implosion physical quantities at the maximum implosion velocity time is evaluated and the importance of Ar is revealed; second, an extended ITF that is proportional to Arα(α≈−1.6) is obtained. Our simulations on fusion yields identify a definitive ignition cliff when the extended ITF equals unity. We then conclude that the shell aspect ratio Ar is an important quantity in our extended ITF expression that will be helpful for evaluating and optimizing the ignition target designs and practical implosion experiments.