Kinetic models of partially ionized complex plasmas in the low frequency regime

Abstract

The results from three kinetic models of complex plasmas taking into account collisions with neutrals are compared in the low-frequency regime: The "full" model which considers the absorption of plasma fluxes on dust particles and dust charge fluctuations, the "multi-component" model where both these effects are neglected, and the "standard" model which takes into account the dust charge perturbations but not the absorption of fluxes. We derive and numerically evaluate expressions of the low frequency responses of these models, also taking into account the modification of the capture cross-sections due to the effect of neutrals. The role of plasma sources and collisions with neutrals is assessed by computing the plasma permittivities and static permittivities for all the three models.

Low-frequency electrostatic modes in partially ionized complex plasmas: a kinetic approach

“…In the framework of the linear fluctuation theory [25,26], the starting point is the Klimontovich equations of all species [27], which are decomposed in ensemble averaged and fluctuating parts to yield: the Boltzmann kinetic equations that contain the modified collision integrals and also the permittivity ( k,ω ) of the system as a function of the low-frequency responses. For the full kinetic model the low-frequency responses have been derived in [24] in a form ready for numerical evaluation with the additional assumption of Maxwellian distributions and taking into account the effect of neutrals on the ion capture cross-sections. In this work the dispersion equation k,ω = 0 is solved numerically and the ω r (k), ω i (k) relations for the low-frequency longitudinal modes are obtained.…”

“…For the capture cross-sections of plasma particles on dust: in the weakly collisional regime [3,33], the electrons are considered to be collisionless and their capture cross-sections are given by the orbit motion limited (OML) model, σ e (q, v) = πa 2 (1 + 2qe am e v 2 ) [3], while for the ions, considering the effect of charge transfer collisions inside the perturbed radius R 0 , the cross-sections can be approximated by [24,34]…”

“…The permittivity derived from the kinetic model of partially ionized complex plasmas, described in [22,24], has the following form:…”

“…, were originally derived in [24] under the assumptions listed in section 2.1 and for the cross-sections given in section 2.2, in a form ready for numerical calculations. For completeness we provide their explicit forms in the appendix.…”

“…The model considers the absorption of plasma fluxes on dust particles and the dust charge fluctuations self-consistently while taking into account collisions with neutrals via the Bhatnagar-Gross-Krook (BGK) approximation [23] and using a fluctuating plasma source to sustain the plasma. The total permittivity of the system is evaluated using the low-frequency responses that were derived in [24], encompassing the effect of neutrals on grain charging and with the assumption of Maxwellian distributions. 3 Numerical solutions of the kinetic dispersion equation are presented for typical laboratory plasma parameters.…”