He-induced W nanofuzz growth over the W divertor target is one of the main limiting factors affecting the current design and development of fusion reactors. In this paper, based on He reaction rate model in W, we simulate the growth and evolution of He nanobubbles during W nanofuzz formation under fusion-relevant He+ irradiation conditions. Our modeling unveils the existence of He nanobubble-enriched W surface layer (<10 nm), formed due to the He diffusion in W crystal into defect sites. At an elevated temperature, the growth of He bubbles in the W surface layer prevents He atoms diffusing into the deep layer (>10 nm). The formation of W nanofuzz at the surface is attributed to surface bursting of high-density He bubbles with their radius of ~4 nm, and an increase in the surface area of irradiated W. Our findings have been well confirmed by the experimental measurements.

Although W fuzz is formed in the divertor region of the fusion reactor, no theory may clearly explain the W fuzz growth mechanism. In this study, we observe the growth process of W fuzz over W crystal under ITER-relevant He ion irradiations. We propose the tensile stress-driven cracking of nano-structured fuzz during the initial growth of W fuzz. We demonstrate that the existence of tensile stress is due to the swelling of He nano-bubbles in the fuzz. After this cracking, the W fuzz breaks away from the planar network and grows over the W surface, where the micro-stress in the W surface layer acts as the driving force.

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Digital economy has become an important driving force for green economic growth in China. Based on the province-level data of China from 2003 to 2018, this paper constructed the Total-factor Nonradial Directional Distance Function (TNDDF) model to measure the carbon emission efficiency of industrial sector and discussed the impact of digital economy on carbon emission efficiency. Empirical analysis shows that the carbon emission efficiency of China’s industrial sector is low, and there is obvious regional heterogeneity where the carbon emission efficiency of eastern China is higher than that of central and western China. Areas with high level of digital economy development have higher carbon emission efficiency, and digital economy is conducive to promoting energy conservation and pollution reduction in China’s industrial sector. The optimal threshold interval of digital economy for promoting carbon emission efficiency is explored by means of threshold model. In view of this, the Chinese government should vigorously develop the digital economy, promote industrial enterprises to networking and digital evolution, and improve the efficiency of carbon emission as well.

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