Electrostatic waves in astrophysical Druyvesteyn plasmas: I. Langmuir waves

Plasmas in various astrophysical systems are in non-equilibrium states as evidenced by direct in-situ measurements in the solar wind, solar corona and planetary environments as well as by indirect observations of nonthermal sources of waves and emissions. Specific to observed non-equilibrium plasmas are non-Maxwellian velocity distributions with suprathermal tails, most often described by Kappa (power-law) distributions. In this paper, we introduce an alternative modeling for linear waves in plasmas described by the generalized Druyvesteyn distribution model. This model can reproduce not only high-energy tails, but also low-energy flat-tops of velocity distributions, like those of electrons in interplanetary shocks and the solar transition region. The wave dispersion relation of longitudinal waves is derived in terms of the newly introduced Druyvesteyn dispersion function. The dispersion curves as well as damping rates of high-frequency Langmuir waves are numerically computed for the isotropic case, and their analytical approximations are provided in the limit of weak damping. We thus offer a new tool for modeling longitudinal waves, and in particular Langmuir waves under the specific conditions of Druyvesteyn distributions.