Study On Dispersion Relations Of Transverse And Longitudinal Modes In The Hot Plasma

The relationship of angular frequencyωand wave vector k can determine the dispersion relations of plasma. The radiation of wave must accord a condition. The condition is that the modes of wave which satisfies the dispersion laws attain energy. In other words, waves of satisfying the dispersion relations are a kind of source excitation and can be the greatest contribution to the energy. Hence it is very important of studying the dispersion relations of plasma.The paper investigates the problem consists of two parts: one part is the numerical study of dispersion relations in non-relativistic electron-ion plasma with Maxwell distribution, another part is the analytical and numerical studies of dispersion relations in ultra-relativistic electron-positron plasma with Fermi distribution.The study of dispersion relations in non-relativistic electron-ion plasma is derived from the dynamics of plasma. The dispersion equations of longitudinal wave and transverse wave are numerically evaluated. The results showed that: using the numerical method, the theoretical results can make up for inadequate, the dispersion curves in different conditions are obtained. According to the fitting expressions of separate parts of the different curve, the fitting dispersion relations are obtained.With the emergence of strong power laser, the production of electron-positron plasma have inevitably involves the relativistic effect. The study of ultra-relativistic degenerated pair plasma is derived from the dynamics of plasma. The analytical results of longitudinal dispersion relation are obtained. But the dispersion curves of analytic theory have the discontinuity due to approximate restrictions. Using the numerical method, the full dispersion curves are obtains.