Electron energy distribution in a dusty plasma: Analytical approach

Analytical expressions describing the electron energy distribution function (EEDF) in a dusty plasma are obtained from the homogeneous Boltzmann equation for electrons. The expressions are derived neglecting electron-electron collisions, as well as transformation of high-energy electrons into low-energy electrons at inelastic electron-atom collisions. At large electron energies, the quasiclassical approach for calculation of the EEDF is applied. For the moderate energies, we account for inelastic electron-atom collisions in the dust-free case and both inelastic electron-atom and electron-dust collisions in the dusty plasma case. Using these analytical expressions and the balance equation for dust charging, the electron energy distribution function, the effective electron temperature, the dust charge, and the dust surface potential are obtained for different dust radii and densities, as well as for different electron densities and radio-frequency (rf) field amplitudes and frequencies. The dusty plasma parameters are compared with those calculated numerically by a finite-difference method taking into account electron-electron collisions and the transformation of high-energy electrons at inelastic electron-neutral collisions. It is shown that the analytical expressions can be used for calculation of the EEDF and dusty plasma parameters at typical experimental conditions, in particular, in the positive column of a direct-current glow discharge and in the case of an rf plasma maintained by an electric field with frequency f = 13.56 MHz.