快粒子对双撕裂模不稳定性的影响

Suppression and control of magnetohydrodynamics(MHD) instability in the reversed magnetic shear plasmas, as one focus issue of tokamak physics, has been extensively studied in theory and experiment. Many energetic-particle-excited MHD modes plays an important role in steady state operation of tokamaks, particular the double tearing mode due to its global mode structure. Until now, there are a few studies on this topic. In this project, we focus on effect of fast particles on the double tearing mode and compare it with observation of experiments. A hybrid model of both MHD and kinetic are used to derive the dispersion relation of the mode in the limits of collision and collisionless. The effects of fast ions on the linear growth and mode coupling are discussed in detail by the numerical solution of dispersion relation. Based on the eigenvalue code and nonlinear model code, we also calculate the dependence of mode structure on the fast ion beta as well as nonlinear evolution of the mode. Comparing the result of experiments, effect of fast ion on the MHD instability at q=1 surfaces is discussed for the neutral beam injecting and off-axis electron-cyclotron resonance heating or electron cyclotron current drive. The results obtained in this project about the interaction of double tearing mode with fast ions in weak/reversed shear configuration are substantial in understanding the basic physics and providing guidance for future advanced devices.

反磁剪切位形下磁流体不稳定性的抑制和控制，一直是受控核聚变理论和实验研究的一个重点课题。快粒子驱动的几种磁流体不稳定性，尤其是具有全局性本征结构的双撕裂模不稳定性，对托卡马克稳态运行具有十分重要的影响，目前国内外研究甚少。本项目立足于理论分析并结合相关实验，研究托卡马克中外部驱动产生的快粒子对双撕裂模不稳定性的影响，主要研究内容有：通过磁流体-动力学混合模型，推导出快粒子存在时线性碰撞/无碰撞双撕裂模的色散关系；数值求解色散关系，明确快粒子在双有理面耦合时对不稳定性线性增长的作用；采用本征值程序和非线性模型程序，数值计算出模式的本征结构对快粒子比压的依赖关系及非线性特征；通过与国内外实验结合（国内装置中性束和离轴ECRH或ECCD放电条件下），进一步解释快粒子对双q=1有理面上磁流体不稳定性在不同实验条件下的作用机制。从而为弱/反磁剪切位形下快粒子与双撕裂模的相关实验提供必要的理论基础。

在托卡马克先进运行模式条件下，快粒子驱动的磁流体不稳定性严重破坏等离子体约束，尤其是q≳2的类鱼骨模(FLM)因具有全局不稳定性和较低的激发临界，因而成为国内外相关领域高度关注的问题。尽管国际上有一些初步的研究，但目前关于FLM的线性激发、波-波和波-粒子非线性相互作用等物理问题却亟待解决。本项目主要研究内容和结果如下：a)反剪切位形下高能量粒子对双撕裂模的影响。分析了快粒子激发MHD不稳定的物理机制。通过该机制，联系双撕裂模已有理论，结合等离子体电阻效应以及模式耦合的影响，进一步揭示了快粒子对不稳定性的激发或抑制的过程。将相应的理论研究结果和实验现象紧密结合，预测出快粒子对双撕裂模的激发以及控制等重要的物理过程；b)通过NIMROD程序模拟双撕裂模的二维模结构，评估模式的不稳定性与快粒子比压的依赖关系；给出不稳定性的时间演化；对比了强、弱反剪切位形下快粒子对不稳定性本征结构的影响，讨论了不同快粒子比压下不稳定性的增长率；c).基于理想情况下双扭曲模的色散关系，以及快粒子电流对扭曲模的影响。进一步推导出在非线性阶段，包含快粒子电流的电阻扭曲模色散关系，同时通过MATLAB编程对色散关系进行了数值解析分析；d)研究了在托卡马克中安全因子剖面（q剖面）局域平化时鱼骨模的基本性质；推导了局域平化的安全因子剖面位形下m=1的鱼骨模不稳定性的线性色散关系和本征模方程；详细讨论了安全因子剖面局域变平时，不同的物理参数对鱼骨模不稳定性线性增长率、频率的影响。本项目的开展解决了上述几个关键的基础物理问题，为实验上等离子体约束水平的改善提供基础理论支撑。