In inertial confinement fusion, the ignition threshold factor (ITF), defined as the ratio of the available shell kinetic energy to the minimum ignition energy, is an important metric for quantifying how far an implosion is from its performance cliff. We use one-dimensional numerical simulations to develop a dataset with 20 000 targets, in which alpha particle heating magnifies the fusion yield by a factor of 6.5, defined as marginal ignition targets whose ITF equals unity. First, an explicit ITF extended scaling law [1] is found based on analytical theories and statistical modeling and its parameters are obtained by numerically fitting the dataset. Second, some implicit but more reliable ITF expressions [2] are yielded through training machine learning (ML) methods, such as neural networks, support vector machines, and Gaussian processes, to connect the minimum ignition velocity v_igt with other implosion parameters. Then, the ITF extended scaling law and these ML-based ITFs are used to obtain curves of the ignition probability vs the ITF and improved ignition cliffs. For example, Fig. 1 and Fig. 2 compare these results of the neural network-based ITF and the extended scaling law. Subfigures (a) show the predicted data v_igt^net or v_igt^scaling vs the simulation data v_igt, with the black dots representing the 80% training subset and the blue dots representing the 20% testing subset, where the orange diagonal line indicating that the predictions are equal to the simulation results. Subfigures (b) show the probability density function in the ITF-Q_α/Q_(no α) plane, where the black dashed line indicates the ignition criterion Q_α/Q_(no α)=6.5. Subfigures (c) show ignition probability P vs ITF, with the red dotted line indicating the ideal ignition cliff. ML-based ITFs show considerably better accuracy than traditional scaling laws. These results demonstrate that ML methods have promising application prospects for quantifying ignition margins and can be useful in optimizing ignition target designs and practical implosion experiments.

References: [1] Physics of Plasmas 28, 062705 (2021); [2] Physics of Plasmas 29, 082702 (2022).