Fundamental difference between the mechanisms of electrostatic field screening in dense and thoroughly collisionless plasmas

Abstract

When an external electric field appears in a homogeneous plasma, ions move into regions where their electrostatic energy is lower. Simultaneously, forces arise that counteract this effect, causing the plasma to reach equilibrium when the field disappears completely. In collisional plasma, the resulting charge inhomogeneities decrease both Coulomb energy and entropy. Randomly induced diffusion flows tend to hinder their growth, minimizing free energy at any point. Accordingly, in the Debye–Hückel theory, the external field strength decreases exponentially with distance within the plasma. In a collisionless plasma, an antiscreening mechanism operates differently. Each ion moves in a self-consistent field along distinct trajectories, following classical dynamics laws. An external field bends these trajectories, bringing ions into regions where their Coulomb energy is lower. The antiscreening mechanism occurs when ions accelerate into potential wells, increasing the distances between them along their trajectories and decreasing their number densities along these paths. The law of energy conservation for any single ion governs this principally nonlocal process, and the dependence of field strength on distance is not necessarily exponential. This paper demonstrates that the Debye–Hückel theory should not be used to describe the charge density distribution within an unrestricted stream of collisionless plasma, such as the solar wind. It also analyzes non-exponential solutions of the Poisson equation for plasma sheaths above flat surfaces, from which such a flow takes off and on which it falls, obtained in quadratures.