Ion-acoustic wave instability driven by drifting electrons in a generalized Lorentzian distribution

A generalized Lorentzian (kappa) particle distribution function is useful for modelling plasma distributions with a high-energy tail that typically occur in space. The modified plasma dispersion function is employed to study the instability of ion-acoustic waves driven by electron drift in a hot isotropic unmagnetized plasma modelled by a kappa distribution. The real and imaginary parts of the wave frequency ω₀ + ιγ are obtained as functions of the normalized wavenumber kλ_D, where λ_D is the electron Debye length. Marginal stability conditions for instability are obtained for different ion-to-electron temperature ratios. The results for a kappa distribution are compared with the classical results for a Maxwellian. In all cases studied the ion-acoustic waves are strongly damped at short wavelengths, kλ_D 1, but they can be destabilized at long wavelengths. The instability for both the kappa and Maxwellian distributions can be quenched by increasing the ion-electron temperature ratio T_i/T_e. However, both the marginally unstable electron drift velocities and the growth rates of unstable waves can differ significantly between a generalized Lorentzian and a Maxwellian plasma; these differences are also influenced by the value of T_i/T_e.