关于双束流Weibel不稳定性的研究

【作者】 李纪伟；

【导师】 裴文兵；

【作者基本信息】 中国工程物理研究院 ， 等离子体物理， 2005， 硕士

【摘要】 在空间和实验室等离子体中,粒子速度空间不均匀是一种普遍存在的现象,这种不均匀性能驱动不稳定性。Weibel不稳定性就是由于电子各向温度或者动量异性而导致的一种电磁不稳定性。伴随着该不稳定性,等离子体能激发准静态的磁场。 这些年来,Weibel不稳定性已经引起人们很大的关注,不仅因为其本身的物理机制,还在于它产生的磁场。天体等离子中,Weibel不稳定性常用来作为一种产生磁场的机制;实验室等离子体中,Weibel不稳定性对快点火中超热电子能量的传输有重要的作用。快点火中,对于圆偏振激光,在超热电子传播方向上存在一个轴向磁场,本文的目的就是研究该磁场对Weibel不稳定性的影响。 本文我们先讨论了双束流Weibel不稳定性。这部分首先归纳了电子—离子等离子体的线性色散关系;接着对双束流Weibel不稳定性进行PIC粒子模拟,给出不稳定性的一些特征,并比较了对称流和不对称流的差异;然后从流体方程出发,考虑冷双束流,得到描述非线性发展阶段的方程,在弱非线性近似下,求解该方程,解释了Weibel不稳定性的一些物理图像。 我们重点讨论了导向磁场对Weibel不稳定性的影响。考虑冷的双电子束流,从线性色散关系得出增长率和导向场的关系。理论分析给出,导向场会有效地减少不稳定性的增长率。PIC粒子模拟也得出了这样的结果,并给出在导向场的影响下,非线性阶段的一些复杂的物理现象,自生磁场的饱和水平大于无外场情况等等。在所产生的偶极场和静电场的作用下,一束电子被捕捉在自生磁场的两个峰值之间(梯度为正),另一束被分散到两个峰值之外的区域(梯度为负)。导向磁场的存在使得电子的汇聚更加集中。从饱和之后的电流和磁场分析,饱和之后,电子温度并没有达到各向同性,而是保持一定的异性。有了导向场之后,另一个明显的特征就是导向磁场会被调制为具有k=2的特征(我们初始所加扰动对应k=1),电子的大部分动能相应也会偏转到Weibel场所在的方向。更多还原

【Abstract】 The Weibel instability is a transverse electromagnetic instability driven by temperature or electron’s moment anisotropy (Weibel) or two counter streams (Fried). Apart from its basic theoretical interest, the Weibel instability has attracted much attention in the recent years in the plasma community, due to its capability of generating a (dipolar) magnetic field from essentially any kind of initial, infinitesimal, random noise. The resulting magnetic field could be then the seed for more robust mechanisms, such as the magnetic dynamo, able to produce the large scale fields observed in many celestial bodies. It also plays a crucial role in the transport of fast electrons’ energies to the target in fast ignitor scenarios.Weibel’s work has stimulated a series of further investigation of the transverse electromagnetic instability in unmagnetized plasma. These papers dealt with the linear, quasilinear and fully nonlinear theories as well as the computer simulation experiments of the instability. At the same time several other authors investigated the electromagnetic instabilities in magnetized plasma for a wide different orientations of the propagation vector. Most recently, Califano et al. have carried out further investigations of Weibel-type instability, where the role of temperature anisotropy is taken by two counterstreaming electron populations. All of previous analyses, including that of Weibel, have been based on the Vlasov-Maxwell formalism. As we know, If a circularly polarized super-intense laser is used to generate relativistic electron beam in the fast ignition, there exists a guiding magnetic field along the beam propagation direction due to the electrons circumgyrating with laser electric field. The motivation of our work is to investigate the effect of the guiding magnetic field on the Weibel instability. We focus our interest on one-dimensional non-relativistic case for simplicity. The main conclusion is easily suitable for the relativistic case.First, we study some work on the magnetic-free electron-ion plasmas. Linear dispersion relation is obtained on the basement of Vlasov-Maxwell formalism for both non-relativistic and relativistic cases. Then PIC simulation results show some physicalphenomena in the linear and in the non-linear regimes. Comparison between two symmetry streams and two non-symmetry ones is also done. In order to interpret the simulation results, we give some fluid description of Weibel instability. Considering two cold electron streams, we derive the equation describing the Weibel instability in the non-linear regime. On the weakly nonlinear regime approximation, we solve the equation and obtain its solution.Next, we pay our interests to the effect of a guiding magnetic field along beam propagation direction on the Weibel instability. Linear dispersion relation is obtained in the presence of such an external magnetic field, which shows the field can suppress or even stabilize the Weibel instability. Comparisons of our PIC simulation results with the analytical ones show very good agreement. The growth rate of Weibel instability decreases draftly as the guiding magnetic field increases and then comes to zero, which means the Weibel instability can’t grow. Also observed in the simulation are the suppression of the electrostatic field, a higher level of self-generated magnetic field than that in the absence of guiding magnetic field, mode competition. As we know, on the action of self-generated magnetic field and the guiding magnetic field, one population of electrons will concentrated between two peaks of the field and be trapped there, while other population will diverge besides two peaks and also be trapped there. Then the self-generated magnetic field comes to saturation with a constant value and space configuration. Most of the electrons’ kinetic energies will be deviated to the direction of Weibel magnetic field , and the guiding magnetic field will be devised by a self-generated field which has a characteristic of k=2. What’s more, the guiding magnetic field also makes each electron population bunch further.更多还原