静电等离子体非线性现象中相混和非朗道解研究

Recently, there are still discussions about mechanisms of Landau damping, which is related to many phenomena in plasmas, especially its nonlinear behavior. In this project we shall continue our research on novel phenomena associated with phase mixing in nonlinear Landau damping. We shall use kinetic theory together with the electrostatic kinetic code which we have developed earlier. Firstly, the physics and properties of phase mixing in nonlinear Landau damping, especially the existence of non-Landau effects and their existence conditions, shall be carefully investigated. Secondly, by carefully analyzing the evolution of the electron velocity distribution function, we hope to improve the present understanding of the physics of phase mixing, especially the role played by non-Landau effects on the excitation and nonlinear development of electrostatic instabilities in plasmas. Finally, a BGK collision operator will be included in our simulation code in order to investigate the effect of collisions on nonlinear Landau damping as well as electrostatic instabilities. The results of the proposed research should lay the foundation for further extending our code to include other relevant features, such as magnetic-field and higher-dimensional effects, as well as development of a Berk-Breizman model code for studying problems associated with energetic particle in tokamaks.

等离子体中和许多现象相关的朗道阻尼，尤其是其非线性行为，许多机制目前仍有争论。本项目计划利用等离子体动理学理论和我们之前开发的一维静电等离子体动理学程序，对发现的相混问题的新结果深入研究下去。首先，研究非线性朗道阻尼的相关性质和物理机制，对相混现象，尤其是是否存在非朗道解的问题进行细致研究，力争研究清楚非线性朗道阻尼中相混现象的物理机制和影响因素，解决非朗道解的存在性问题和存在条件。接着，深入研究等离子体静电不稳定性的相关性质和物理机制，细致分析其相空间分布函数演化，以及相混现象，力争研究清楚相混现象和非朗道解在静电不稳定性中的作用和机制。最后，在程序中加入BGK碰撞项，研究碰撞对非线性朗道阻尼和静电不稳定的影响，同时也为下一步扩展程序研究等离子体动理学性质（例如考虑磁场和多维效应，或者开发Berk-Breizman模型程序研究托卡马克中高能粒子相关问题），打下良好基础。

本项目采用动理学理论和数值模拟相结合的方法，对静电等离子体中朗道阻尼、束流不稳定性等现象，尤其是其非线性行为，以及碰撞对这些现象的影响效应进行深入研究。主要发现有：（1）非线性朗道阻尼的长时间演化中，共振电子和低速电子分布在相空间首先由于相混变得混沌，然后发生自组织到很明显的规则结构。（2）噪声激发的双流不稳定性，其增长阶段并不是传统认为的线性增长，而是非线性的。此现象是由不同谐波的相互作用引起的,谐波的波长是由系统的尺寸和数值噪声决定的。（3）多束流不稳定性演化过程中，奇数束流波能量线性增长阶段有明显的震荡行为，偶数束流不存在明显的震荡行为。不同的谐波分别在“线性”增长阶段和非线性饱和阶段，主导不稳定的演化状态。（4）BGK碰撞能够增大朗道阻尼的阻尼率，同时会抑制双流不稳定性的发展，如果碰撞频率较大，不稳定性将很难激发。（5）对于托卡马克高能粒子研究的Berk-Breizman模型中，高能粒子引起的不稳定性和系统本身的阻尼的相互竞争，使得电场随时间演化出现阻尼、周期、混沌、chirping等现象。上述结果，一方面加深了对于静电等离子体非线性现象物理机制和Vlasov-Poisson系统性质的理解，另一方面为后续等离子体动理学研究，尤其是托卡马克高能粒子波粒相互作用研究奠定良好的基础。