Interaction between two conducting spheres in weakly ionized collisional plasma

Abstract

Charging of two conducting spheres in a weakly ionized collisional plasma flow is considered. The spheres are arranged along the flow, and the plasma is assumed to consist of two ion species with the charges equal in magnitude but opposite in sign. The problem is analyzed with allowance for the external electric field, charging of the spheres due to the sedimentation of plasma ions on them, the fields of the sphere charges, the space charge field, and the processes of recombination and molecular diffusion. The interaction between the spheres and plasma is studied by numerically solving a time-dependent problem in a bispherical coordinate system by the finite difference method. The steady-state values of the sphere charges and the distributions of the space charge and ion densities in the ambient plasma are found as functions of the plasma parameters and the distance between the spheres. The electrostatic forces acting on the spheres are determined, and the effects of the external field, the space charge fields, and the fields of the sphere charges are comparatively analyzed. It is shown that, for the considered plasma parameters, the main electrostatic effect in the interaction between two spheres is their mutual approach in the external field due to the difference in their charges (one sphere catches up with the other). Due to the friction force with the neutral gas, this mutual approach is much slower than all other processes in the system. For widely spaced spheres, the results coincide with the solution obtained previously for a solitary sphere.