New results from exact solution of the dispersion relation for nonextensive electron-ion plasma in the framework of collisionless kinetic theory

Abstract

The electrostatic (ES) oscillations, spatio-temporal Landau damping and growth in an electron-ion (EI) plasma is investigated by taking into account the effect of ion (electron) dynamics on the electron (ion) oscillations in the context of nonextensive particle distributions. The dispersion relation is exactly solved without employing approximations on the phase velocity, in contrast to the procedure developed by Landau where some approximations are applied on the phase velocity. This enables us to obtain some results which are not shown previously duo to approximate numerical and analytical studies. It is remarked that four kinds of ES modes; a high frequency mode (well-known Langmuir wave), two low and high intermediate frequency (LIF and HIF) modes and a very low frequency mode (well-known IA wave) may propagate in desired plasma system. In particular, these ES modes represent very different behavior when moving to left and right directions, from the point of view of spatio-temporal damping and growth. In addition, it is shown that exact solution of the dispersion relation gives rise to some interesting phenomena; such as the existence of non-acoustic electron and ion modes, the frequency and wavelength cutoffs and the existence of backward waves.