Hydrodynamic instability is the fundamental physical challenge for inertial confinement fusion. Implosions can compress fusion fuel to the extreme conditions required for thermonuclear reactions, but at the same time, defects in the laser and target pellet can be amplified during the implosion acceleration, disrupting the spherically symmetric structure of the target pellet and leading to fuel mixing or shell breakup. There are two general ideas for suppressing the instability: First, minimize the initial seed of the instability, which includes precision machining of the target pellet, optical smoothing of the spot, beam overlap optimization, and laser-plasma interaction control. Second, improve the ablation of the interface to suppress the growth of instability, which mainly relies on the ablation layer doping and laser pulse shaping to achieve. Laser pulse shaping is relatively easy to implement in terms of engineering, and can achieve nanosecond level dynamic control during the flight of the target pellets, thus becoming the critical means to suppress instabilities.

The Laser Plasma Laboratory of the University of Science and Technology of China (USTC) has proposed a machine-learning-based inertial confinement fusion laser pulse shape optimization method to suppress the development of instabilities by automatically adjusting the pre-pulse and main pulse shapes. It was published in High Power Laser Science and Engineering (Tao, Tao, Guannan Zheng, Qing Jia, Rui Yan, and Jian Zheng. "Laser Pulse Shape Designer for Direct-Drive Inertial Confinement Fusion Implosions." High Power Laser Science and Engineering 11 (2023): e41.).

Graphic description: The optimization method is applied to a double-cone ignition scheme. The total drive energy is 12 kJ, the laser spot power perturbation is ~15%, and the plastic target has an initial radius of 450 μm and a thickness of 50 μm. (a) manually tuned pulse shape and its implosion streamline, (b) pulse shape and its implosion streamline optimized by machine learning, (c)-(d) density perturbation of the shell layer at the imprint stage and at the end of acceleration.

In this paper, machine-learning is used to randomly sample a large number of pulse shapes in fluid simulations, extract imprint and RTI growth rate features, and evaluate pulse shape performance based on final compression areal density and instability amplitude. As the number of samples increases, machine-learning gradually summarizes the potential relationship between pulse shape and implosion performance, and drives shape evolution based on this relationship. In the demo application of the double-cone ignition scheme, machine-learning makes targeted optimization for the specific focal spot and beam overlap of the laser hardware, achieves good synchronization of the implosion wave series, preserves the spectral characteristics of the laser imprint, and considers the coupling evolution of the laser imprint and RTI. Compared to manually tuning the pulse shape, the machine-optimized pulse improves the unmixed fuel layer thickness by a factor of 4 while maintaining a similar compression areal density. This work is a successful application of machine-learning methods, which enables the experiment to achieve fast iterative optimization with high confidence.