Dispersion Relation For Relativistic Electron-positron Plasma With Q-distribution

The American made the "Project Sherwood" of developing the controlled thermonuclear reactor and then more and more people were interested in plasmas.Maiman.an American created the first laser-the Ruby laser in1960. Later, the laser fusion was emerged as the times required.Since the pulse of laser became shorter and shorter, the power higher and higher,the relativistic effect of the plasmas produced in laser fusion must be considered inevitability. It’s really significant to do some work one rlativistie plasmas, while the research on the dispersion relation of relativistic plasmas in this paper is the most fundamental and the most important in laser fusion.First, the dispersion relation of longitudinal oscillation in the unmagnetized, collisionless, isotropic and relativistic electron-positron plasma is discussed in the context of q-distribution. The dispersion equations in connection with q-parameter are derived. And then the analytical dispersion laws for ultra-relativistic electron-positron plasma are obtained under the long-wavelength approximation, the short-wavelength and the near light wave approximation. The dispersion equations are numerically simulated with the purpose of getting the full dispersion curve, and the numerical solution are coinciding with the analytical result in the case of long-wavelength, short-wavelength and the near light wave approximation for ultra-relativistic electron-positron plasma. It is shown that the dispersion relation in the context of nonextensive distribution is related to q-parameter and temperature, in the limiting case(qâ†'1), the classical dispersion relation based on the Maxwellian distribution is recovered.Second, we consider the dispersion relation of transverse oscillation in the plasma of q-distribution. The transverse dispersion equations in connection with q-parameter are derived, and then the analytical dispersion laws for ultra-relativistic plasma are obtained under the long-wavelength approximation and the short-wavelength approximation. The dispersion equations are numerically simulated with the purpose of getting the full dispersion curve, and the numerical solution are coinciding with the analytical result in the case of long-wavelength and short-wavelength for ultra-relativistic plasma. It is shown that the dispersion relation in the context of nonextensive distribution is related to q-parameter and temperature, in the limiting case(qâ†'1), the classical dispersion relation based on the Maxwellian distribution is recovered.