Ergodic Distribution of Trapped Charged Particles in Coulomb Field

Spatially limited motion of electrons after instantaneous appearance of an external positive point-like charge is considered. The trapped particle distribution function averaged over periods of the motion is determined. Contribution of the electrons to the total perturbation of plasma density is calculated. It is shown that the trapped particle contribution dominates at small distances from the charge, whereas it is negligible at large distances. The developed approach and expressions for the trapped particle number density are applicable to studies of nonlinear screening of charged bodies in collisionless plasmas.