We focus our attention on some relevant aspects of the beam–plasma instability in order to refine some features of the linear and nonlinear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the background plasma in the form of a linear dielectric, we study the non-perturbative properties of the linear dispersion relation, showing the necessity for a better characterization of the mode growth rate in those flat regions of the distribution function where the Landau formula is no longer predictive. We then upgrade the original $N$ -body approach in O'Neil et al. (Phys. Fluids, vol. 14, 1971, pp. 1204–1212), in order to include a return current in the background plasma. This correction term is responsible for smaller saturation levels and growth rates of the Langmuir modes, as result of the energy density transferred to the plasma via the return current. Finally, we include friction effects, as those due to the collective influence of all the plasma charges on the motion of the beam particles. The resulting force induces a progressive resonance detuning, because particles are losing energy and decreasing their velocity. This friction phenomenon gives rise to a deformation of the distribution function, associated with a significant growth of the less energetic particle population. The merit of this work is to show how a fine analysis of the beam–plasma instability outlines a number of subtleties about the linear, intermediate and late dynamics which can be of relevance when such a system is addressed as a paradigm to describe relevant nonlinear wave–particle phenomena (Chen & Zonca, Rev. Mod. Phys., vol. 88, 2016, 015008).

中文翻译：

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对光束-等离子体相互作用的线性和非线性理论的贡献

我们将注意力集中在光束-等离子体不稳定性的一些相关方面，以改进线性和非线性动力学的一些特征。在重新分析泊松方程和处理线性电介质形式的背景等离子体的假设后，我们研究了线性色散关系的非微扰特性，表明有必要更好地表征模式增长在朗道公式不再具有预测性的分布函数的平坦区域中的比率。然后我们升级原版 $N$ -奥尼尔的身体方法等。(物理。流体, 卷。14, 1971, pp. 1204–1212)，以便在背景等离子体中包含返回电流。由于能量密度通过返回电流转移到等离子体，因此该校正项导致 Langmuir 模式的饱和水平和增长率较小。最后，我们包括摩擦效应，因为所有等离子体电荷对束粒子运动的集体影响。所产生的力会引起渐进的共振失谐，因为粒子正在失去能量并降低它们的速度。这种摩擦现象引起了分布函数的变形，与低能粒子群的显着增长有关。这项工作的优点是展示了对束等离子体不稳定性的精细分析如何勾勒出关于线性的许多微妙之处，牧师国防部。物理。, 卷。88, 2016, 015008)。