On the spectrum of plasma modes in a field-free pair plasma: Dispersion and Landau damping in Tsallis statistics

Abstract

The full spectrum of possible plasma modes and their Landau damping in a field-free pair plasma are examined analytically in the context of Tsallis statistics. This study is based on the solving the linearized Vlasov equation and Maxwell’s equations by employing the general method of characteristics, i.e., integrating along unperturbed orbits. Three types of plasma modes are confirmed: two of them are electrostatic waves with Landau damping, i.e., ion plasma waves (IPWs) and ion-acoustic waves (IAWs); and one mode is the transverse electromagnetic waves (light waves) without Landau damping. Our analysis shows that the Landau damping time for IAWs is negligible for most of wave lengths, and so these modes are heavily damped. Furthermore, Landau damping time for IPWs are considerable and these modes are of a great importance. Comparison of Landau damping in the case of a supra-thermal background distribution (confirmed by considering q<1 for spectral index) with the ones for a Maxwellian plasma in thermal equilibrium (confirmed by considering the asymptotic limit q→1) shows that the supra-thermal background makes the Landau damping more effective and prominent and also shifts the normal modes to the regions with less wave numbers. Basically, the damping rate in a supra-thermal plasma is stronger than a Maxwellian plasma. Moreover, the electromagnetic modes are comparatively less sensitive to the background distribution.