The Weibel instability in relativistic plasmas. I. Linear theory
The Weibel instability in relativistic plasmas. I. Linear theory
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相对论等离子体中的韦贝尔不稳定性。
DOI：
10.1051/0004-6361:20065365
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发表时间：
2007
影响因子：
6.5
通讯作者：
J. Wiersma
中科院分区：
文献类型：
--
作者：
A. Achterberg;J. Wiersma
目标。讨论了超相对论光束驱动的相对论等离子体中的韦伯不稳定性的线性理论，描述了与伽玛射线暴（GRB）相关的超相对论激波中磁场产生的物理过程。我们进行了详细的分析的线性色散关系的非线性计算的好处，我们在配套文件中讨论。方法.我们使用一个协变的方法，其中的线性响应的束等离子体系统是从偏振张量。这个张量将电磁场的四维电流密度与四维势联系起来。显示两种方法，一个基于流体模型和一个动力学的描述，使用一个水袋分布的相空间密度的光束粒子，产生基本上相同的结果，我们比较我们的结果，通过其他方法得到的。我们主要考虑对称的情况下，两个逆流（但在其他方面相同）的光束。结果我们表明，在束密度的不对称性的影响是小的典型参数，并简要讨论了环境磁场的影响。由超相对论光束驱动的韦伯不稳定性的色散关系是相当不敏感的模型来描述等离子体。不稳定性的性质，如增长率和不稳定波长的范围，仅由两个参数决定：束和热背景等离子体的等离子体频率平方的比率，以及“马赫数”，其本质上是束动量和与束等离子体中的热速度（声速）相关联的动量的比率。我们还表明，至少对于与伽玛暴中的超相对论冲击相关的参数，磁场的影响是小的，并且可以使用未磁化等离子体的结果。结论.
Aims. We discuss the linear theory of the Weibel instability in a relativistic plasma driven by ultra-relativistic beams, describing the physics of the generation of magnetic fields in the ultra-relativistic shocks associated with Gamma Ray Bursts (GRBs). We perform a detailed analysis of the linear dispersion relation for the benefit of non-linear calculations that we discuss in the companion paper. Methods. We use a covariant approach, where the linear response of the beam-plasma system is determined from the polarization tensor. This tensor relates the four-current density to the four-potential of the electromagnetic field. Showing that two approaches, one based on a fluid model and one on a kinetic description that uses a waterbag distribution for the phase-space density of the beam particles, yield essentially the same result, we compare our results to those obtained by other approaches. We mainly consider the symmetric case of two counterstreaming (but otherwise identical) beams. Results. We show that the effect of an asymmetry in the beam densities is small for typical parameters, and briefly discuss the effect of an ambient magnetic field. The dispersion relation of the Weibel instability driven by ultra-relativistic beams is rather insensitive to the model used to describe the plasma. The properties of the instability, such as the growth rate and the range of unstable wavelengths, are governed by only two parameters: the ratio of the plasma frequency squared of the beam and hot background plasma, and a “Mach number”, which is essentially the ratio of the beam momentum and the momentum associated with thermal velocity (∼sound speed) in the beam plasma. We also show that, at least for the parameters associated with the ultra-relativistic shocks in GRBs, the influence of the magnetic field is small, and the results for an unmagnetized plasma can be used. Conclusions.