摘要
本论文较为系统地论述了磁化等离子体中的微观不稳定性及湍流理论。我们首先回顾了描述等离子体物理的基本方法和基本方程,其次介绍了等离子体物理中传统的湍流输运理论的物理模型以及研究方法。在此基础上,我们提出了一种新的输运模型:拉格朗日系统的输运理论。利用这种输运理论可以很容易地理解一些新的困扰等离子体物理学界的实验现象,诸如托卡马克等离子体中的非局域输运、粒子流或热流箍缩以及反磁剪切中的稳态中空温度(电流)剖面等等。
论文的第三部分详细介绍了作者在攻读博士期间在等离子体微观不稳定性及湍流理论研究方面完成的一些具体工作。首先是磁曲率对等离子体电阻性不稳定性的影响。这部分研究表明磁曲率的极向分量使得电阻性交换模的色散关系发生变化,它不仅改变不稳定性增长率而且还改变模式的结构。同时我们还发现托卡马克等离子体的坏磁场区域增大了。其次是托卡马克中捕获电子动力学的拉格朗日不变性研究。这部分研究表明托卡马克中的捕获电子流体是一个典型的拉格朗日系统,我们解析地求得了表征系统弛豫态的拉格朗日不变量并与部分实验结果作了定性的比较,发现它们之间具有一致性。再次是平行动力学方程的重整化研究。这部分研究作为位置空间中的非线性相互作用的重整化群处理的推广,发展了一种处理速度空间中的线性和非线性相互作用的重整化方法,得到了碰撞等离子体平行动力学方程的重整化系数。这为等离子体湍流理论甚至其他领域提供了一条新的数学处理途径。最后部分是离子温度梯度模驱动的环带流生长研究。这部分研究采用四波相互作用模型研究了离子温度梯度模驱动的环带流,得到了环带流的增长率与泵浦波的关系。我们发现漂移波确实能够驱动大尺度的环带流
The theory about micro-instability and turbulence in magnetized plasmas is dissertated in some detailed. First, the basic methods and equations describing plasma physics are reviewed. And then, the conventional physical models and studying method of plasma turbulence transport theory are introduced and discussed. A new transport model, which is called as Lagrange transport theory, is suggested. Some new and bewildering phenomena founding in tokamak plasma experiments such as non-local transport, particle flux or heat flux pinch and steady hollow temperature (current) profile in reversed magnetic shear plasmas may be easily explained applying the new model.
In the third section, we give some detail works on plasma micro-instability and turbulence during our doctoral period. The first is that the effects of the magnetic curvature on the resistive interchange mode in tokamak plasmas. It is shown that the poloidal component of the magnetic curvature makes the dispersion relation of the mode change. Both the growth rate of the instability and the mode structure are changed in presence of the poloidal component of the magnetic curvature. Meanwhile, the bad magnetic field region is enlarged. The second is that the Lagrangian invariant of trapped electron dynamics in tokamaks. It is shown that the trapped electron fluid is a typical Lagrange system. Lagrangian invariant marking relaxed state of the system is obtained analytically. Compared with some experimental results, agreement is found qualitatively. The third is that the renormalization study of parallel dynamic
equation. As an extension of the renormalization group theory treating nonlinear interaction in spatial space, a renormalization theory dealing with linear and nonlinear interaction in velocity space is developed. The renormalized coefficients of parallel dynamic equation for collision plasmas are derived. It is suggested as a mathematical approach in plasma turbulence theory and other field. And the final is that the study on zonal flow driven by ion-temperature-gradient mode. Employed four-wave-interaction model, the relations between the growth rate of zonal flow and pumping drift wave are obtained. It is found that the zonal flow with large-scale may be driven by ion-temperature-gradient mode. Some problems and suggestions for next step are discussed in the fourth section.
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