磁化等离子体双等离子体衰变过程的数值模拟和理论研究

发布时间：2018-08-16 14:17

【摘要】：双等离子体衰变在非磁化激光等离子体中已被广泛研究,但是在托卡马克磁化等离子体中,由于射频波的功率相对较低,目前有关磁化等离子体双等离子体衰变的理论和实验的研究都非常少。然而TEXTOR托卡马克的实验研究发现,当200～600kW的电子回旋波加热和电流驱动穿越磁岛时,实验观测到了强背散波以及离子加热、加速的现象。电子回旋波的双等离子体衰变能解释这些现象,但当前的线性理论表明该衰变过程因其高阈值功率而不可能发生,因此研究低阈值功率的磁化等离子体双等离子体衰变产生机制是有必要的。本文在流体框架下,采用数值模拟和理论解析相结合的方法对磁化等离子体双等离子体衰变过程展开研究。一方面,在二维平板模型下利用等离子体波的双流体方程组,开发了在全时间和空间上研究双等离子体衰变的并行程序。另一方面,采用弱模耦合近似的方法,解析地得到了磁化双等离子体衰变过程的增长率和阈值功率的表达式。最后根据TEXTOR托卡马克电子回旋波加热的实际参数,通过并行程序结合解析结果计算了电子回旋波的双等离子体衰变过程。在并行程序中,首次实现双流体方程的完全匹配层(PML)数值边界条件。讨论了PML方法在双流系统中的可行性和适定性,详细推导了PML控制方程。线性系统的稳定性分析和非线性方程的数值结果都表明,PML边界是完全匹配的。数值结果同时显示：PML的吸收效果与PML厚度和吸收系数直接相关；PML不影响计算区域内部的物理过程；PML的吸收效果不受入射波功率强度和电子温度的影响；PML的极大反射误差小于1%。在理论解析工作中,着重考察了高混杂子波波数、等离子体密度和磁场对双等离子体衰变绝对不稳定性和对流放大的影响。结果表明：磁场对绝对不稳定性的影响依赖于子波垂直和平行于泵波传播方向的波数ky和kx；磁场强弱和波数匆的大小对绝对不稳定性增长率和对流放大的影响完全不同；磁场和密度在kx较小时对放大因子有显著影响；线性阻尼和密度空间非均匀性对对流放大有抑制作用；相对于磁场,密度的非均匀性对对流放大的影响更大。并行程序和闽值的解析结果计算均表明,在线性密度剖面下,TEXTOR托卡马克电子回旋波发生双等离子体衰变的阈值功率为十兆瓦左右。并行程序在非单调密度剖面下的计算结果显示,阈值功率可以降低1个量级,但仍无法解释实验。若采用非单调密度剖面并考虑动理学的修正效应,并行程序计算结果发现,双等离子体衰变阈值功率(约200kW)可以降低2个量级左右,能解释实验现象。结合线性色散关系所示的子波俘获效应,本文的研究结果从理论角度证明,非单调的密度剖面和子波的俘获效应可以显著降低磁化双等离子体衰变的阈值功率,为更进一步开展射频波与磁化等离子体非线性相互作用提供参考。
[Abstract]:Double plasma decay has been widely studied in unmagnetized laser plasma, but in tokamak magnetized plasma, the power of RF wave is relatively low. At present, there are few theoretical and experimental studies on the double plasma decay of magnetized plasma. However, the experimental study of TEXTOR Tokamak shows that when the electron cyclotron wave of 200~600kW is heated and the current is driven across the magnetic island, the phenomenon of strong backscatter wave and ion heating and acceleration is observed experimentally. The double plasma decay of the electron cyclotron wave can explain these phenomena, but the current linear theory shows that the decay process is impossible because of its high threshold power. Therefore, it is necessary to study the mechanism of double plasma decay in magnetized plasma with low threshold power. In this paper, the process of double plasma decay in magnetized plasma is studied by means of numerical simulation and theoretical analysis under the framework of fluid. On the one hand, a parallel program for the study of double plasma decay in full time and space is developed by using the two-fluid equations of plasma waves in a two-dimensional plate model. On the other hand, the expressions of the growth rate and threshold power of magnetized double plasma decay process are obtained analytically by using the weak mode coupling approximation method. Finally, according to the actual parameters of TEXTOR tokamak electron cyclotron wave heating, the double plasma decay process of electron cyclotron wave is calculated by parallel program and analytical results. In the parallel program, the perfectly matched layer (PML) boundary condition for the two-fluid equation is realized for the first time. The feasibility and suitability of PML method in two-flow system are discussed, and the PML control equation is deduced in detail. The stability analysis of linear systems and the numerical results of nonlinear equations show that the PML boundary is perfectly matched. The numerical results also show that the absorption effect of PML is directly related to the thickness and absorption coefficient of PML. The absorption effect of PML is not affected by the power intensity of incident wave and the electron temperature. The maximum reflection error of PML is less than 1. In the theoretical analysis, the effects of high hybrid wavelet number, plasma density and magnetic field on the absolute instability and convection amplification of double plasma decay are investigated. The results show that the effect of magnetic field on absolute instability depends on the wave number Ky and KX which are perpendicular to and parallel to the direction of pump wave propagation, and the effect of the magnitude of magnetic field intensity and wave number on absolute instability growth rate and convection amplification is completely different. The magnetic field and density have a significant effect on the amplification factor when KX is small; the linear damping and density spatial inhomogeneity can inhibit the convection amplification; compared with the magnetic field, the density inhomogeneity has a greater effect on the convection amplification. The parallel program and the analytical results of the threshold values show that the threshold power of the double plasma decay of the electron gyrotron wave of TEXTOR tokamak under the linear density profile is about ten megawatts. The results of the parallel program under the non-monotone density profile show that the threshold power can be reduced by one order of magnitude, but the experiment can not be explained. If the nonmonotone density profile is adopted and the modified effect of kinetic theory is taken into account, the parallel program results show that the threshold power of double plasma decay (about 200kW) can be reduced by about two orders of magnitude, which can explain the experimental phenomenon. Combined with the wavelet trapping effect shown by linear dispersion relation, the theoretical results show that the nonmonotone density profile and wavelet capture effect can significantly reduce the threshold power of magnetized double plasma decay. It provides a reference for the further development of nonlinear interaction between RF waves and magnetized plasmas.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TL612

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