托卡马克中误差场锁模现象的若干问题研究
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摘要
托卡马克金属结构造成的误差场对未来的聚变装置运行有着非常重要的影响。误差场引起的锁模现象可能诱发撕裂模磁岛甚至引起等离子体大破裂。误差场锁模作为托卡马克运行时重要的物理现象,在国际上得到广泛的研究与关注,且实验、理论和模拟都进行了深入的探讨。实验上,国际著名托卡马克装置,诸如JET、DIII-D、COMPASS、 C-Mod等都深入开展了一系列的实验,并与理论进行仔细对比。理论上,误差场锁模物理也得到了国际理论界的广泛研究,核聚变理论界许多国际知名的学者都对误差场的不同形式进行了深入的研究。而模拟研究正在逐步与真实托卡马克等离子体位形接近,即从单纯的研究物理机制的平板几何转向多种耦合的三维实际位形、从磁流体转向双流体以及进一步向动理学的深化。通过二十多年的研究,误差场锁模物理图像越来越清晰和丰满。然而已有理论中仍然存在一些欠缺与不足之处。本文首先对误差场锁模的相关知识进行较全面的介绍,然后深入分析并讨论相关理论和实验,在此基础上解决了其中存在的一些问题。本文大致内容如下：
绪论部分将托卡马克关键物理问题进行了综述性的归纳与概括。并在此基础上重点回顾了误差场锁模研究的研究历史与进展。指出了误差场锁模在托卡马克关键物理问题中的重要性。
第二章,列出了误差场渗透最新理论进展中重要的理论推导,即双流体近似下线性理论、非线性理论,线性动理学理论,并给出双流体近似下线性理论中一些关键细节,作为后继章节工作的基础。
第三章,探讨磁流体近似下误差场渗透的非线性理论。针对磁流体近似下误差场渗透的非线性理论展开了讨论。通过分析得出以前磁流体近似下的非线性理论中,Rutherford机制和Waelbroeck机制间的过渡机制,其一系列参数均没有体现出平滑的过渡趋势,即没有起到很好的过渡作用。在详细分析理论中一些关键细节后,用比较合理的分析(即过渡机制要包含Rutherford机制和Waelbroeck机制间两者的混合性质),修正了以前非线性渗透理论。修改后的机制各个参数基本上都表现出平滑的过渡效果。为了更好地证实该理论分析,通过模拟,从误差场锁定阈值、临界锁定时的磁岛宽度分别与初始速度的定标很好地证实了前面的理论分析。为了更直观地表现其中物理图像,也列出三个机制中达到锁定阈值时的电流分布情况,进一步证实了前面的理论分析。在第三章的最后,针对托卡马克中较受关注的Rutherford机制展开了讨论,分析和模拟讨论得出以前相关模拟文章中的粘性-电阻机制是Rutherford机制。然而从误差场的定标上来说,两者的结论基本一致,因此可以互换使用。通过固定误差场幅值进一步确认了得到的结论。
第四章,讨论误差场渗透理论在托卡马卡中的应用。将以前理论参数定标转化到实验参数定标的两种假设分别进行了讨论。选取比较好的假设,得到的密度定标在非线性的相邻机制之间过渡得比较好。并对自二十世纪九十年代初期以来典型的托卡马克装置中误差场锁模相关实验研究进行了分类及讨论。详细分析了一些装置误差场锁模的实验结果,并得出实验中比较准确的物理机制。通过理论分析,分析了J-TEXT装置参数及最近误差场锁模运行参数,发现目前其锁模实验覆盖了磁流体近似下误差场渗透的全部三种非线性机制。理论分析结果与实验数据拟合吻合。
第五章,通过数值模拟研究反磁剪切位形下的误差场渗透问题。考虑实际托卡马克运行可能包含不同平衡状态,因此在反磁剪切位形下考虑了三种平衡状态,即稳定状态、临界状态及不稳定状态。仔细分析了三种平衡状态下非锁定和锁定情况的主要特征,并讨论了相关机制。模拟结果显示在通常运行双撕裂模稳定情况下,一旦双撕裂模外侧有理面锁定,内侧有理面也会很快锁定,两个有理面上磁岛相互驱动并迅速生长起来,在大范围破坏等离子体约束。这个结果提醒人们要对反磁剪切位形下的误差场锁模有足够的重视。
最后是本论文的结论与展望。
Many investigations indicate that error field will play a significant role in future fusion reactor operations. During the tokamak operation, the error field will still induce the mode locking phenomenon, and further lead to island growth and even major disruption. Meantime, as a remarkable physical phenomenon, error field locked mode receives extensive attention and investigation, and researches are carried out from the points of experiment, theory and simulation. Experimentally, the world's notable tokamakdevices, such as JET, DIII-D, COMPASS, C-Mod etc also took series of investigation. Theoretically, error field locked mode physics also receives extensive studies in the nuclear fusion theoretical cycle. And the simulation was mainly developed in recent years. Nowadays, the simulation are made forward to the real configurations of tokamak plasmas, i.e. from simple study on physical regimes in the slab geometry to coupled three dimensional configuration, and from single fluid to two-fluid and further kinetics. With more than twenty years' studies, error field locked mode physics have become more and more clear. However, revisiting these theories, we still find the necessity of further developments of the existing theories. In this thesis, a comprehensive introduction to error field locked mode is shown at first, and then follows deep analyses to the relevant theory and experiment. On the basis of these, proper answers to these problems are given. The context of this thesis is as follows:
In introduction, the key physics problems in tokamaks in the previous special topic are summarized at first. After then the research history and progress on error field relevant investigation is reviewed. Besides, the significance of error field locked mode in tokamak physics problems is also pointed out.
In chapter2, the newest significant theoretical progress on error field penetration, i.e. linear and nonlinear theories at the two-fluid frame and also linear kinetic theory are present. Some key details in the linear theory under the condition of two-fluid approximation are also shown.
In chapter3, nonlinear error field penetration theories under the condition of magnetohydrodymics (MHD) approximation are reviewed and re-analysed. A discussion on nonlinear error field penetration theory under the condition of MHD approximation is given first. With detailed analysis, the previous transition regime shows little smooth transition characteristic is found. A new transition regime that shows well smooth transition for nearly all parameters is given. To better verify this analysis, a relevant simulation is given. The relation between critical error field amplitude and critical island width, and the detailed scaling results verify our opinion. Besides, we then present the electric current profiles in the three nonlinear regimes at the time of critical error field amplitude. These again verify our theoretical analysis. At the last part of chapter3, extra discussions on the crucial Rutherford regime are shown.
In chapter4, the error field penetration theory is applied in tokamaks. First, a discussion on the two assumptions that are employed when the theoretical scalings transform into experiment parameters is present. On the basis of these, the better assumption is selected, and the more reasonable density scalings are then obtained. Based on these above, an analysis on the error field locked mode relevant experiment investigations is given. After then, follows a comprehensive classification. At the end of chapter4, the theoretical analysis on the very recent error field locked mode experiment results in J-TEXT tokamak is shown. And the present error field locked mode experiments cover all three nonlinear regimes in the frame of MHD. The theoretical result matches well with the experiment data.
In chapter5, error field penetration in reversed magnetic shear configuration is investigated. To give the comprehensive discussion, three states, i.e. stable, marginal and unstable states are considered. The significance is that once error field induces mode locking at the outer rational surface when the double tearing mode is initially stable, the double tearing mode will grow up. This will induce plasma disruption. Hence significant attention should be paid.
At last a summary and prospect ends this thesis.
绪论部分将托卡马克关键物理问题进行了综述性的归纳与概括。并在此基础上重点回顾了误差场锁模研究的研究历史与进展。指出了误差场锁模在托卡马克关键物理问题中的重要性。
第二章,列出了误差场渗透最新理论进展中重要的理论推导,即双流体近似下线性理论、非线性理论,线性动理学理论,并给出双流体近似下线性理论中一些关键细节,作为后继章节工作的基础。
第三章,探讨磁流体近似下误差场渗透的非线性理论。针对磁流体近似下误差场渗透的非线性理论展开了讨论。通过分析得出以前磁流体近似下的非线性理论中,Rutherford机制和Waelbroeck机制间的过渡机制,其一系列参数均没有体现出平滑的过渡趋势,即没有起到很好的过渡作用。在详细分析理论中一些关键细节后,用比较合理的分析(即过渡机制要包含Rutherford机制和Waelbroeck机制间两者的混合性质),修正了以前非线性渗透理论。修改后的机制各个参数基本上都表现出平滑的过渡效果。为了更好地证实该理论分析,通过模拟,从误差场锁定阈值、临界锁定时的磁岛宽度分别与初始速度的定标很好地证实了前面的理论分析。为了更直观地表现其中物理图像,也列出三个机制中达到锁定阈值时的电流分布情况,进一步证实了前面的理论分析。在第三章的最后,针对托卡马克中较受关注的Rutherford机制展开了讨论,分析和模拟讨论得出以前相关模拟文章中的粘性-电阻机制是Rutherford机制。然而从误差场的定标上来说,两者的结论基本一致,因此可以互换使用。通过固定误差场幅值进一步确认了得到的结论。
第四章,讨论误差场渗透理论在托卡马卡中的应用。将以前理论参数定标转化到实验参数定标的两种假设分别进行了讨论。选取比较好的假设,得到的密度定标在非线性的相邻机制之间过渡得比较好。并对自二十世纪九十年代初期以来典型的托卡马克装置中误差场锁模相关实验研究进行了分类及讨论。详细分析了一些装置误差场锁模的实验结果,并得出实验中比较准确的物理机制。通过理论分析,分析了J-TEXT装置参数及最近误差场锁模运行参数,发现目前其锁模实验覆盖了磁流体近似下误差场渗透的全部三种非线性机制。理论分析结果与实验数据拟合吻合。
第五章,通过数值模拟研究反磁剪切位形下的误差场渗透问题。考虑实际托卡马克运行可能包含不同平衡状态,因此在反磁剪切位形下考虑了三种平衡状态,即稳定状态、临界状态及不稳定状态。仔细分析了三种平衡状态下非锁定和锁定情况的主要特征,并讨论了相关机制。模拟结果显示在通常运行双撕裂模稳定情况下,一旦双撕裂模外侧有理面锁定,内侧有理面也会很快锁定,两个有理面上磁岛相互驱动并迅速生长起来,在大范围破坏等离子体约束。这个结果提醒人们要对反磁剪切位形下的误差场锁模有足够的重视。
最后是本论文的结论与展望。
Many investigations indicate that error field will play a significant role in future fusion reactor operations. During the tokamak operation, the error field will still induce the mode locking phenomenon, and further lead to island growth and even major disruption. Meantime, as a remarkable physical phenomenon, error field locked mode receives extensive attention and investigation, and researches are carried out from the points of experiment, theory and simulation. Experimentally, the world's notable tokamakdevices, such as JET, DIII-D, COMPASS, C-Mod etc also took series of investigation. Theoretically, error field locked mode physics also receives extensive studies in the nuclear fusion theoretical cycle. And the simulation was mainly developed in recent years. Nowadays, the simulation are made forward to the real configurations of tokamak plasmas, i.e. from simple study on physical regimes in the slab geometry to coupled three dimensional configuration, and from single fluid to two-fluid and further kinetics. With more than twenty years' studies, error field locked mode physics have become more and more clear. However, revisiting these theories, we still find the necessity of further developments of the existing theories. In this thesis, a comprehensive introduction to error field locked mode is shown at first, and then follows deep analyses to the relevant theory and experiment. On the basis of these, proper answers to these problems are given. The context of this thesis is as follows:
In introduction, the key physics problems in tokamaks in the previous special topic are summarized at first. After then the research history and progress on error field relevant investigation is reviewed. Besides, the significance of error field locked mode in tokamak physics problems is also pointed out.
In chapter2, the newest significant theoretical progress on error field penetration, i.e. linear and nonlinear theories at the two-fluid frame and also linear kinetic theory are present. Some key details in the linear theory under the condition of two-fluid approximation are also shown.
In chapter3, nonlinear error field penetration theories under the condition of magnetohydrodymics (MHD) approximation are reviewed and re-analysed. A discussion on nonlinear error field penetration theory under the condition of MHD approximation is given first. With detailed analysis, the previous transition regime shows little smooth transition characteristic is found. A new transition regime that shows well smooth transition for nearly all parameters is given. To better verify this analysis, a relevant simulation is given. The relation between critical error field amplitude and critical island width, and the detailed scaling results verify our opinion. Besides, we then present the electric current profiles in the three nonlinear regimes at the time of critical error field amplitude. These again verify our theoretical analysis. At the last part of chapter3, extra discussions on the crucial Rutherford regime are shown.
In chapter4, the error field penetration theory is applied in tokamaks. First, a discussion on the two assumptions that are employed when the theoretical scalings transform into experiment parameters is present. On the basis of these, the better assumption is selected, and the more reasonable density scalings are then obtained. Based on these above, an analysis on the error field locked mode relevant experiment investigations is given. After then, follows a comprehensive classification. At the end of chapter4, the theoretical analysis on the very recent error field locked mode experiment results in J-TEXT tokamak is shown. And the present error field locked mode experiments cover all three nonlinear regimes in the frame of MHD. The theoretical result matches well with the experiment data.
In chapter5, error field penetration in reversed magnetic shear configuration is investigated. To give the comprehensive discussion, three states, i.e. stable, marginal and unstable states are considered. The significance is that once error field induces mode locking at the outer rational surface when the double tearing mode is initially stable, the double tearing mode will grow up. This will induce plasma disruption. Hence significant attention should be paid.
At last a summary and prospect ends this thesis.
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