高速旋转电子等离子体的平衡态及其静电波的色散关系

Equilibria and dispersion relation of rotating electron plasmas with high angular velocity

构建了一个角向速度接近光速的圆柱状电子等离子体的模型,推导出该等离子体的径向力平衡方程,发现该等离子体存在两种旋转平衡态:快旋平衡态和慢旋平衡态.通过数值计算径向力平衡方程,得出在快旋平衡态下,电子距离中轴越远,其角速度越小;在慢旋平衡态下,角速度不随电子与中轴距离的变化而改变.进一步推导出了该等离子体中静电波的色散关系,发现静电波频率随角向波矢的增大而快速增大。

model of cylindrical rotating electron plasma with relativistic angular velocity is constructed,the equilibrium equation for the radial forces of the system is derived,and two rotational equilibrium states(a fast one and a slow one) arefound.Applying computational numerical method to the equilibrium equation for the radial forces,we find that,for the fast rotational equilibrium,the further an electron in the plasma is away from the axis,the slower the angular velocity of the electron is.We also find that,for the slow rotational equilibrium,the angular velocity is independent of the distance between electrons and the axis.We further derive the dispersion relation of the electrostatic wave deduced by the plasma and discover that the frequency of the electrostatic wave increases rapidly as the angular wave vector increases.