共振磁扰动作用下电阻撕裂模及响应的理论计算研究

发布时间：2018-10-05 17:22

【摘要】：本文从理论分析和数值模拟相结合的角度分别讨论了共振磁扰动(Resonant Magnetic Perturbation.即RMP)对撕裂模不稳定条件下的转动等离子体及撕裂模稳定条件下的静态等离子体的作用。首先,我们从理论上证明了共振磁扰动诱导的锁模现象和磁岛压制现象都可以由误差场模型描述。我们将锁模态看作扰动场对撕裂模不稳定的转动等离子体作用所达到的一个定态并得到了该定态所对应的解析解。解析解表征在不同等离子体区域中锁模磁岛的宽度和相位与RMP幅度的关系。新的解析解有至少两个分支,其中锁模的磁岛宽度小于其自然饱和宽度的分支总是不稳定的。此外,由于扰动场对转动磁岛的调频效应,等离子体也可以有稳态的,随时间振荡的磁岛压制解。总的来说,当扰动场的幅度小于一定阈值时,磁岛在时间平均意义上被扰动场稳定的压制；当扰动场幅度大于该阈值时,磁岛的压制是暂态行为,最终转动的撕裂模将会演化至锁模态。其次,本文从理论分析和数值模拟的角度讨论了锁模阈值和解锁阈值之间间隔的物理机制并运用自主发展的程序去得到锁模阈值和解锁阈值。我们从解析上得到了一个新的解锁阈值定标率并推广了相位跳变不稳定性的判据。给定等离子体区域中,在RMP幅度大于解锁阈值时,RMP幅度被划分成了两个不同的区域。在第一个区域中,演化的磁岛是否会被RMP锁住取决于其初始条件;在第二个区域中,任意初始条件的磁岛都会被RMP锁住。第二个区域的最小RMP幅度被称为锁模阈值。这两个区域不同的性质揭示了锁模阈值和解锁阈值之间间隔以及广泛存在的回滞现象的物理机制。最后,基于我们之前得到的定态解,本文给出了等离子体对外加扰动场的稳态非线性响应理论。该理论预言磁岛宽度和扰动场强度呈正相关,因此非线性效应只有在大扰动场幅度区域中才是重要的。随后我们运用NIMROD程序进行了初步的等离子体响应模拟,非线性的模拟结果从定性上验证了上述推论。此外,单流体框架下的线性模拟结果显示在静态等离子体中即使幅度很小的扰动场也会激发出种子磁岛并达到稳态。
[Abstract]:In this paper, the resonance magnetic disturbance (Resonant Magnetic Perturbation.) is discussed from the point of view of theoretical analysis and numerical simulation. That is, the effect of RMP on the rotational plasma under the condition of tearing mode instability and the static plasma under the stable condition of the tearing mode. Firstly, we prove theoretically that both the mode locking phenomenon induced by the resonance magnetic disturbance and the magnetic island pressing phenomenon can be described by the error field model. The locked mode is regarded as a stationary state of the disturbed field acting on the unstable rotational plasma of the tearing mode and the corresponding analytical solution is obtained. The analytical solution characterizes the relationship between the width and phase of the mode-locked magnetic island and the amplitude of RMP in different plasma regions. The new analytical solution has at least two branches in which the magnetic island width of the mode-locked mode is less than its natural saturation width and the branch is always unstable. In addition, due to the frequency modulation effect of the disturbance field on the rotational magnetic island, the plasma can also have a steady state, oscillating magnetic island suppression solution. In general, when the amplitude of the disturbance field is less than a certain threshold, the magnetic island is suppressed by the disturbance field stably in the sense of time average, and when the amplitude of the disturbance field is larger than the threshold, the suppression of the magnetic island is transient behavior. The tearing mode that eventually rotates will evolve to the locking mode. Secondly, the physical mechanism of the interval between the mode-locking threshold and the unlocking threshold is discussed from the point of view of theoretical analysis and numerical simulation, and the mode-locking threshold and the unlocking threshold are obtained by using self-developed programs. We analytically obtain a new unlocking threshold calibration rate and extend the criterion of phase jump instability. In a given plasma region, when the RMP amplitude is greater than the unlocking threshold, the RMP amplitude is divided into two different regions. In the first region, whether the evolving magnetic island will be locked by RMP depends on its initial condition, and in the second region, the magnetic island with any initial condition is locked by RMP. The minimum RMP amplitude of the second region is called mode-locking threshold. The different properties of these two regions reveal the physical mechanism of the interval between mode-locking threshold and unlocking threshold and the widespread hysteresis phenomenon. Finally, based on the steady-state solution we obtained previously, the theory of the steady nonlinear response of the plasma to the external perturbation field is given in this paper. The theory predicts that the width of the magnetic island is positively correlated with the intensity of the disturbance field, so the nonlinear effect is important only in the amplitude region of the large disturbance field. Then we use the NIMROD program to simulate the plasma response, and the nonlinear simulation results qualitatively verify the above inferences. In addition, the linear simulation results in a single fluid frame show that even a small perturbation field in a static plasma can excite the seed magnetic island and reach a steady state.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O53

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