Study On Dispersion Relations For Degenerate Plasma

Since the dispersion relations are useful in studying instabilities, plasma diagnostics, non-linear phenomena and the spread and dissipation of waves in plasma or ICF, to make them more complete and more effective is necessary. This paper is devoted to research on the dispersion relations further detailed, modify some subsection dispersion relations, and analyze the effects of parameters on dispersion properties.First, based on the Maxwell equations, the dispersion relations for non-relativistic degenerate plasmas are analyzed with the help of modern computer. Around the partial distinctions between degenerate plasmas and classical plasmas, the paper makes some work as follows:1. The more perfect physical model is established and the dispersion equations including items related ions are derived for stressing the effects of ions in dispersion relations.2. The dispersion equations for zero-temperature plasmas, completely degenerate plasmas and semi-degenerate plasmas are derived respectively.3. The dispersion relations of longitudinal waves for zero-temperature plasmas are obtained by analytical method and numerical method. The numerical results are not only in good agreement with the Alexandrov's results, but also filling the blank zone of Alexandrov theory.4. The effects of electron temperature, of temperature-ratios between electron and ion and of plasma densities on the dispersion curves for completely degenerate plasmas and semi-degenerate plasmas are numerically analyzed in detail. The connections and distinctions between the two are compared.In addition, this paper studied the linear modes in the relativistic electron-positron plasmas which are weakly magnetized. Based on relativistic Lorentz equation, the perturbed current in weakly magnetized electron-positron plasmas is derived with perturbation theory. Substituting the current expression into Maxwell equations, two general dispersion relations, which are describing the transverse waves and longitudinal waves in weakly magnetized electron-positron plasmas, are obtained. In non-relativistic case, the two general dispersion relations are in accord with Zank's results.