A study of dust grain screening in a weakly ionized plasma based on the numerical solution of the Vlasov-Bhatnagar-Gross-Krook kinetic equations

Screening of a dust grain in a weakly ionized plasma is studied for a wide range of collisional regimes. The problem is considered on the basis of the Vlasov-Bhatnagar-Gross-Krook equations for plasma particles. The equations are solved numerically on parallel processors by means of a high-order finite-volume method. The computations are carried out for different pressures of plasma background and different grain sizes. The values of the total grain charge, distributions of the electric potential, and basic macroscopic parameters of plasma particles (concentration, temperature, and velocity) are obtained. For two limiting cases of the collisionless and strongly collisional background, the obtained results are found to be in good agreement with those computed using the commonly known models (nonlinear collisionless models of Bystrenko et al.[Phys. Lett. A 299, 383 (2002)] and Ratynskaia et al.[Phys. Plasmas 13, 104508 (2006)] and drift-diffusion approach). For the transitional collisional regime, it is shown that the electric potential also has the Coulomb-type asymptotical behavior related to the presence of charging currents and existence of some residual (unscreened) grain charge. Both total and residual grain charges are found to increase as the collisional regime tends to the continuum limit. In addition, the influence of collisions on the ion distribution function near the grain surface is demonstrated.