中文摘要：

在相对论性情况下，从等离子体纵介电常数出发，推导出无磁化、无碰撞、各向同性的快电子分布等离子体纵振荡的色散方程．对纵振荡的色散方程进行解析分析，得到长波支和短波支的色散关系．由于解析色散曲线的不连续性，直接对无量纲化的纵振荡色散方程进行数值计算，得到相对论性快电子分布等离子体纵振荡完整的色散曲线．对数值结果进行拟合，得到简单的色散函数表述以便于应用．并在极端相对论条件下，将这种分布与经典Maxwell分布的色散关系进行比较，得出两种分布情况下纵振荡的色散关系在一定的波数范围内有类似的性质．

英文摘要：

In the case of relativistic regime, the dispersion equation of longitudinal oscillation for fast electron distribution is derived from the longitudinal permittivity in unmagnetized, collisionless and isotropie plasmas. The equation is analytically solved, then the long-wavelength and short-wavelength dispersion relations are obtained. Because the analytical dispersion curves are discontinuous, the dimensionless dispersion equation is nu- merically calculated and a full dispersion curve is obtained. Furthermore, by fitting the numerical solutions, a simple function expression of the dispersion curve is given. This is easier to use. Finally, in the case of ultra-relativistic regime, the dispersion relation of fast electron distribution is compared with that of the Maxwell distribution. It is shown that these two dispersion relations share a similar property in a certain range of wave number.