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.
Highlights
The most important feature of the plasma is its collective behavior
In the line developed by Landau to solve the dispersion relation, some approximations are employed on the phase velocity
We have investigated the linear electrostatic (ES) waves in the nonextensive statistics framework using general and exact dispersion relation by taking into account the effect of ion dynamics
Summary
The most important feature of the plasma is its collective behavior. The motion of electrons and ions and the presence of electrical and magnetic fields coupled with electron and ion particles in plasma can cover a wide variety of wave modes. Depending on the frequency range, a wide variety of wave modes can exist in the plasma medium. The nonextensive distribution is of importance due to the description of a plasma system in a nonequilibrium stationary state with inhomogeneous temperature and due to its ability to obtain exact dispersion relation without employing any approximation on the phase velocity. Both of the analytical and numerical analyses are straightforward in the context of nonextensive statistics compared to the Boltzmann-Gibbs statistics.. Layout of this paper is as follows: In Sec. II, the linear kinetic theory is considered to derive a dispersion relation for the ES waves in electron-ion (EI) plasma in which both of the electrons and ions follow the q-nonextensive velocity distribution.
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