Nonlinear shielding of planar test charge in one-dimensional Vlasov-Poisson plasma

Abstract

The shielding of a one-dimensional, planar, permeable test charge has been studied theoretically. General expressions are derived and evaluated which show how the screening of a test charge, represented by the floating potential $\psi$, surface charge density q and screening length L, depends on various plasma parameters such as the temperature of electron and ions and particle streaming velocities. Particular attention has been given to analyzing the influence of particle trapping (reflection) in the charging and screening problem. No charging model can adequately describe the screening mechanism unless proper care is taken in choosing suitable distribution functions for both plasma species. In this paper, such a theory has been developed that provides the general idea about the charging of a grid in plasmas under different environments and conditions. As the main outcome we have found that the shielding of a non-propagating test charge is stronger, the larger the trapped ion population and the higher the temperature ratio T_e/T_i are. Flux equality in the case of a propagating test charge restricts the solubility of the shielding problem to non-Boltzmann electrons and to a weak $\psi$ and q only. In the cold ion limit a lower bound for the ion streaming velocity is found than that predicted by Bohm's criterion.