The solution of the linear dispersion relation of electromagnetic oblique instabilities, for two counterstreaming electron beams, is investigated by using an extended fluid approach that includes the full dynamics of the pressure tensor. Numerical solutions of the simplified polynomial formulation so obtained are analyzed and compared to full kinetic solutions. They correspond to two classes of eigenmodes: low- and high-frequency oblique modes of resonant character. Coexistence of several oblique modes in neighboring regions of the wave vector plane, having close growth-rates, leads to the possibility of a transition starting from a low wave number mode to an oblique mode of high values in wave numbers. For such counterstreaming plasmas, the oblique instability may strengthen and amplify the filamentation process of the distribution function in velocity space, a property of the Vlasov equation. In addition to its simplicity, useful for solving the dispersion relation in the linear regime and for identifying kinetic solutions difficult to calculate otherwise, this extended fluid model is helpful in gaining insight into the fundamental properties of Vlasov theory, which are possibly relevant to kinetic heating processes.

中文翻译：

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倾斜丝状模式的低频和高频特性。一、线性理论

通过使用包括压力张量的完整动力学的扩展流体方法，研究了两个逆流电子束的电磁斜不稳定性的线性色散关系的解。对如此获得的简化多项式公式的数值解进行分析并与完整动力学解进行比较。它们对应于两类本征模式：共振特性的低频和高频斜模。在波矢量平面的相邻区域中，几种斜模式的共存，具有接近的增长率，导致从低波数模式开始过渡到高波数值的斜模式的可能性。对于这种逆流等离子体，倾斜不稳定性可能会加强和放大速度空间中分布函数的丝状过程，这是 Vlasov 方程的一个性质。除了它的简单性、可用于解决线性区域中的色散关系以及识别难以计算的动力学解之外，这种扩展的流体模型还有助于深入了解 Vlasov 理论的基本性质，这些性质可能与动能加热有关过程。