INFLUENCE OF POLARIZATION PHENOMENA ON THE DUST GRAIN CHARGE IN PLASMAS

Abstract

It is believed in the classical treatment of dust particle charging that the material of the dust is a perfect absorber, i.e. all the plasma particles that reach the grain surface are inevitably absorbed. This typically leads to that the grain charge is determined by the buffer plasma parameters and is not material dependent. On the other hand it is known that a charged double-layer exists near the surface of solids, and whenever an attempt is undertaken to pull out an electron from a solid, the polarization phenomena come to play an essential role to cause an attraction. This results in that to extract an electron from the bulk of the solid it is necessary to perform some work, which is called the work function. The main idea of this paper is to account for the polarization effects, which should ultimately lead to a microscopic theory for the charge of the dust particle in a plasma. To do so the interaction potentials of electrons and ions of the buffer plasma with the dust particles are chosen to treat the polarization effects. For the sake of simplicity it is assumed that the material of the dust particle is a conductor, and the polarization phenomenon is simply the electrostatic induction. The latter effect is empowered within the electrostatic image method, so that the polarization is responsi- ble for an additional effective mechanism of attraction. The aforesaid interaction potential energy between the plasma particles and the dust consists of two parts. The first part is determined by the particle charge and the distribution of the plasma around it, i.e. the sheath formation. It is that way the charging of dust particles was interpreted in the literature until recently. The second part of the potential energy is governed by the interaction with surface charges of the dust matter stemming from the polarization effects. Consideration of the charging process is carried out within the orbital motion limited approximation, in which the trajectories of plasma particles, i.e. electrons and ions, are con- sidered ballistic such that the interparticle collisions are completely ignored. To justify such an ap- proach the mean free paths of plasma particles should be much greater than both the size of the dust and the so-called Debye screening radius. When the polarization effects are neglected, application of the conservation laws of energy and angular momentum is sufficient to determine the absorption cross sections of electrons and ions by the dust particle. If the dust grain is assumed polarizable, further consideration turns much more complicated because of the nature of the interaction, which leads to the attraction of both electrons and ions at rather small distances from the dust surface. Although, the angular momentum with respect to the field center is still conserved, subsequent calculations turn much more difficult because the dependence of the effective potential energy on the distance proves to be non-monotonic. This necessitates a numerical solution of an equation for the position of the maximum of the effective potential energy. Nevertheless, it is possible to find an approximate solu- tion since the respective extremum is located very close to the particle surface. This allows one to calculate the electron and ion absorption cross sections, evaluate the corresponding fluxes and then to determine the dust charge as a function of the so-called coupling parameter.

Keywords: coupling parameter, orbit motion limited (OML) theory, absorption cross sections, polarization phenomena, image charge approximation.