Study on the morphology of liquid–gas interface inside inertial confinement fusion target under the condition of temperature gradient based on Young–Laplace equation

Abstract

This study investigates the morphology of the liquid–gas interface inside inertial confinement fusion targets with temperature gradients from the perspective of force balance. The effects of contact angle, liquid volume, temperature gradient, and target size on the interface morphology are discussed. The filling of the fuel and the preparation of the ice layer inside the target are carried out near the deuterium–deuterium triple point at 18.71 K, accompanied by temperature gradient distributions of different magnitudes. The morphology of the liquid–gas interface has a significant impact on the subsequent laser experiments. The differential equation for calculating the morphology of the liquid–gas interface under non-uniform temperature field is derived based on the Young–Laplace equation. In order to verify the accuracy and applicability of the model as well as to provide guidance for practical applications such as process optimization, experimental data within a temperature gradient range of 0.69–1.38 K/cm during the fuel filling process were selected. Image processing techniques, including denoising and edge detection, were applied to the experimental images. The obtained structured data were compared with the numerical solutions of the equation for the liquid–gas interface morphology. The accuracy of the equation was verified by the results. Based on this, the morphology of the liquid–gas interface of deuterium–deuterium inside targets under different experimental conditions was calculated. It was found that a smaller target radius, higher filling temperature, smaller contact angle, and larger temperature gradient are more conducive to subsequent experiments.