中国物理B ›› 2026, Vol. 35 ›› Issue (7): 75201-075201.doi: 10.1088/1674-1056/ae1016

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Numerical studies on the linear and nonlinear evolutions of infernal modes

Jiu-Ying Li(李久瑛)1, Wei Zhang(张威)2,†, Zi-Xi Liu(刘子奚)1,‡, Zhi-Wei Ma(马志为)2, Fei-Fei Long(龙飞飞)1, Cheng-Cheng Deng(邓成成)1, Peng-Cheng Li(厉鹏程)1, Kang-Ning Yang(杨康宁)1, Xiao-Yu Yin(尹晓宇)1, Run-Zhi Hu(胡润志)1, Yi-An Zhao(赵一安)1, Hong Li(李弘)1, Jin-Lin Xie(谢锦林)1, Tao Lan(兰涛)1, Wen-Zhe Mao(毛文哲)1, A-Di Liu(刘阿娣)1, Chu Zhou(周楚)1, Wei-Xing Ding(丁卫星)1, Ge Zhuang(庄革)1, and Wan-Dong Liu(刘万东)1   

  1. 1 Department of Plasma Physics and Fusion Engineering, University of Science and Technology of China, Hefei 230026, China;
    2 Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University, Hangzhou 310027, China
  • 收稿日期:2025-07-07 修回日期:2025-09-25 接受日期:2025-10-07 发布日期:2026-07-10
  • 通讯作者: Wei Zhang, Zi-Xi Liu E-mail:wzhang_ifts@zju.edu.cn;zxliu316@ustc.edu.cn
  • 基金资助:
    Project supported by the National Magnetic Confinement Fusion Program of China (Grant No. 2019YFE03090200) and the National Natural Science Foundation of China (Grant Nos. 12375224, 11975231, 12005185, 11835010, and 12175277).

Numerical studies on the linear and nonlinear evolutions of infernal modes

Jiu-Ying Li(李久瑛)1, Wei Zhang(张威)2,†, Zi-Xi Liu(刘子奚)1,‡, Zhi-Wei Ma(马志为)2, Fei-Fei Long(龙飞飞)1, Cheng-Cheng Deng(邓成成)1, Peng-Cheng Li(厉鹏程)1, Kang-Ning Yang(杨康宁)1, Xiao-Yu Yin(尹晓宇)1, Run-Zhi Hu(胡润志)1, Yi-An Zhao(赵一安)1, Hong Li(李弘)1, Jin-Lin Xie(谢锦林)1, Tao Lan(兰涛)1, Wen-Zhe Mao(毛文哲)1, A-Di Liu(刘阿娣)1, Chu Zhou(周楚)1, Wei-Xing Ding(丁卫星)1, Ge Zhuang(庄革)1, and Wan-Dong Liu(刘万东)1   

  1. 1 Department of Plasma Physics and Fusion Engineering, University of Science and Technology of China, Hefei 230026, China;
    2 Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University, Hangzhou 310027, China
  • Received:2025-07-07 Revised:2025-09-25 Accepted:2025-10-07 Published:2026-07-10
  • Contact: Wei Zhang, Zi-Xi Liu E-mail:wzhang_ifts@zju.edu.cn;zxliu316@ustc.edu.cn
  • Supported by:
    Project supported by the National Magnetic Confinement Fusion Program of China (Grant No. 2019YFE03090200) and the National Natural Science Foundation of China (Grant Nos. 12375224, 11975231, 12005185, 11835010, and 12175277).

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摘要： The present paper numerically investigates the linear and nonlinear evolution of infernal modes through a three-dimensional, toroidal geometric, nonlinear, and full-MHD code CLT. For equilibria with $q_{{\min}}\approx $ 2.0, the development of the infernal modes leads to an elongated high-pressure region. We find that the nonlinear behaviors of the infernal modes can be totally different when the parallel thermal conductivity exceeds a threshold. Below this threshold, the infernal modes experience explosive growth in the nonlinear stage; above this threshold, they finally saturate in the nonlinear phase. For the cases with nonlinearly explosive growth, the patterns of the perturbed pressure are `ballooning-like' and the dominant modes are with $n> 1$, where n is the toroidal mode number. When the parallel thermal conductivity exceeds the threshold, the parallel diffusion along the magnetic field lines is quick enough. Then the nonlinearly explosive growth is suppressed, and the infernal modes will saturate in the nonlinear stage. A two-dimensional (2D) parameter map is provided to illustrate the transition between these distinct nonlinear regimes.

关键词: infernal mode, long-live mode, pressure driven, explosive growth

Abstract: The present paper numerically investigates the linear and nonlinear evolution of infernal modes through a three-dimensional, toroidal geometric, nonlinear, and full-MHD code CLT. For equilibria with $q_{{\min}}\approx $ 2.0, the development of the infernal modes leads to an elongated high-pressure region. We find that the nonlinear behaviors of the infernal modes can be totally different when the parallel thermal conductivity exceeds a threshold. Below this threshold, the infernal modes experience explosive growth in the nonlinear stage; above this threshold, they finally saturate in the nonlinear phase. For the cases with nonlinearly explosive growth, the patterns of the perturbed pressure are `ballooning-like' and the dominant modes are with $n> 1$, where n is the toroidal mode number. When the parallel thermal conductivity exceeds the threshold, the parallel diffusion along the magnetic field lines is quick enough. Then the nonlinearly explosive growth is suppressed, and the infernal modes will saturate in the nonlinear stage. A two-dimensional (2D) parameter map is provided to illustrate the transition between these distinct nonlinear regimes.

Key words: infernal mode, long-live mode, pressure driven, explosive growth

中图分类号:  (Magnetohydrodynamics (including electron magnetohydrodynamics))

  • 52.30.Cv
52.65.-y (Plasma simulation) 52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)) 52.55.Tn (Ideal and resistive MHD modes; kinetic modes)