Abstract: The dispersion relations of superluminal waves for the longitudinal collective modes in unmagnetized, collisionless and homogeneous relativistic electron-positron plasmas are derived. Using the standard technique of successive approximations, an analytic study of longitudinal dispersion equations in two limiting cases is presented. The full dispersion equations are transformed so that they are well suited for numerical evaluation in the temperature range where a fully relativistic treatment is needed. Using the numerical simulation method, we obtain the full dispersion curve which can’t get from the analytic method.

Key words: Moving plasma, Lorentz transformation, Wave equation, Dispersion relation

摘要： 根据狭义相对性原理，应用Lorentz变换法则，从相对运动媒质静止参考系中的有关结论，获取了实验室参考系中所需结果。通过证明平面波相位是Lorentz不变量，指出实验室参考系中平面波解的存在性。由Lorentz变换导出了实验室参考系中平面波色散关系表示式，据此给出运动媒质的波动方程。由Lorentz变换导出运动媒质中平面波Maxwell方程。基于这些结果，应用Lorentz变换获得了平面波从自由空间垂直入射到各向同性运动等离子体半空间时反射波与透射波的有关特性。

关键词: 运动等离子体, Lorentz变换, 波动方程, 色散关系