Integrated analysis of high-<i>β</i><sub>N</sub> double transport barriers scenario on HL-2A
Authors: Li Zheng-Ji , Chen Wei , Sun Ai-Ping , Yu Li-Ming , Wang Zhuo , Chen Jia-Le , Xu Jian-Qiang , Li Ji-Quan , Shi Zhong-Bing , Jiang Min , Li Yong-Gao , He Xiao-Xue , Yang Zeng-Chen , Li Jian ,   Southwestern Institute of Physics, China National Nuclear Corporation, Chengdu 610041, China,   Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China,   Units of 61287, Chengdu 610000, China
Published: January 2024

Tokamak is considered as the most promising experimental setup for achieving controllable nuclear fusion requirements. The parameter <inline-formula><tex-math id="M20">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M20.png"/></alternatives></inline-formula> is an important parameter for tokamak devices: high <inline-formula><tex-math id="M21">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M21.png"/></alternatives></inline-formula> benefits not only to plasma fusion but also to the enhancement of fusion reaction efficiency and the facilitation of steady-state operation. The HL-2A tokamak device has achieved stable plasma with <inline-formula><tex-math id="M22">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M22.png"/></alternatives></inline-formula> exceeding than 2.5 through neutral beam injection heating, and transiently reached <inline-formula><tex-math id="M23">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M23.png"/></alternatives></inline-formula> = 3.05, with a normalized density (<inline-formula><tex-math id="M24">\begin{document}$n_{\rm{e,l}}/n_{\rm{e,G}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M24.png"/></alternatives></inline-formula>) of about 0.6, stored energy (<inline-formula><tex-math id="M25">\begin{document}$W_{\rm{E}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M25.png"/></alternatives></inline-formula>) of around 46 kJ, and confinement improvement factor (<inline-formula><tex-math id="M26">\begin{document}$H_{98}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M26.png"/></alternatives></inline-formula>) of about 1.65. In this work, the integrated simulation platform OMFIT is used to analyze the plasma at <inline-formula><tex-math id="M27">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M27.png"/></alternatives></inline-formula> = 2.83 and <inline-formula><tex-math id="M28">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M28.png"/></alternatives></inline-formula> = 3.05, and the obtained <inline-formula><tex-math id="M29">\begin{document}$W_ {\rm{E}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M29.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M30">\begin{document}$n_{\rm{e,l}}/n_{\rm{e,G}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M30.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M30.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M31">\begin{document}$H_{98}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M31.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M31.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M32">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M32.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M32.png"/></alternatives></inline-formula>, etc. are consistent with the experimental parameters. The bootstrap current (<inline-formula><tex-math id="M33">\begin{document}$f_{\rm{BS}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M33.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M33.png"/></alternatives></inline-formula>) can reach to <inline-formula><tex-math id="M34">\begin{document}$45{\text{%}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M34.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M34.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M35">\begin{document}$46{\text{%}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M35.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M35.png"/></alternatives></inline-formula>. At both of the above moments, there are ion temperature double transport barrier (DTB) generated by the coexistence of internal transport barrier (ITB) and edge transport barrier (ETB), while high <inline-formula><tex-math id="M36">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M36.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M36.png"/></alternatives></inline-formula> is usually related to DTB. In addition, the formation of ion temperature ITB in the HL-2A device is further analyzed, which is attributed to the dominance of turbulent transport in plasma transport, the suppression of turbulent transport in the core by fast ions and <inline-formula><tex-math id="M37">\begin{document}${\boldsymbol E}\times{\boldsymbol B}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M37.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M37.png"/></alternatives></inline-formula> shear, and the resulting improvement in confinement, thereby ultimately leading to the formation of ion temperature ITB. The ITB of ion temperature and the ETB of H-mode synergistically contribute to the creation of high <inline-formula><tex-math id="M38">\begin{document}$\beta_{\rm{N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M38.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231543_M38.png"/></alternatives></inline-formula> plasma.