Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma

Abstract

A new approximate expression for the potential distribution around an absorbing particle in isotropic collisionless plasma is proposed. The approximate expression is given by the sum of the Debye-Huckel potential with an effective screening length and the far-field asymptote obtained from the solution of the linearized Poisson equation. In contrast to analogous models, the effective screening length is not fixed but depends on the distance from the particle. This allows us to obtain a more accurate approximation for the potential distribution in the entire range of distances. The dependence of the screening length on the distance is predicted from the analysis of the charge density distribution function. This dependence contains two adjustable parameters, which are calculated by applying the procedure based on charge balance considerations. Using the obtained results, simple expressions for the parameters of the model are proposed. In addition, a simple expression for the characteristic screening length, which can be used to approximate the potential distribution near the particle, is obtained. The developed model potential is shown to be in excellent agreement with the solution of the nonlinear Poisson equation for typical conditions used in experiments with complex plasmas.