Effect of the shape of the electron energy distribution function on the dust grain charge and its screening in glow discharge plasmas

Abstract

The dust grain charge in the plasma of a glow discharge in noble gases and nitrogen is calculated in the orbit motion limited model for reduced fields in the range of E/N = 1–20 Td. The calculations were performed using the electron energy distribution functions (EEDFs) obtained by solving the Boltzmann equation numerically with allowance for elastic and inelastic electron scattering and analytically with allowance for only elastic scattering and (for nitrogen) excitation of rotational levels, as well as using a Maxwellian EEDF. In the latter case, either the characteristic electron energy or mean electron energy multiplied by two thirds was used as the electron temperature. It is shown that the calculations with the use of a Maxwellian EEDF yield larger values of the grain charge as compared to those calculated with EEDFs obtained by solving the Boltzmann equation. The range of E/N values is determined in which analytical expressions for the EEDF obtained with allowance for elastic scattering and excitation of rotational levels are applicable to calculating the grain charge. The effect of the EEDF shape on the screening of the dust grain charge in plasma is investigated. The Debye screening length in case of a Maxwellian EEDF is shown to be shorter than that obtained with EEDFs calculated by numerically solving the Boltzmann equation.