The fluid approach has been widely used to study plasma sheath dynamics. For a sheath containing hot ions whose temperature is greater than the electron's, how to truncate the fluid hierarchy chain equations while retaining to the fullest extent of the kinetic effects is always a difficult problem. In this paper, a one-dimensional, collisionless sheath containing hot ions is studied via particle-in-cell simulations. By analyzing the ion energy equation and taking the kinetic effects into account, we have shown that the ion polytropic coefficient in the vicinity of the sheath edge is approximately constant so that the state equation with the modified polytropic coefficient can be used to close the hierarchy chain of the ion fluid equations. The value of the polytropic coefficient strongly depends on the hot ion temperature and its concentration in the plasma. The semi-analytical model is given to interpret the simulation results. As an application, the kinetic effects on the ion saturation current density in the probe theory are discussed.
The formation of a sheath in front of a carbon or tungsten material plane immersed in a plasma containing non-Maxwellian energetic electrons and secondary emission electrons is studied using a 1D model. In the model, energetic electrons are described by the electron energy distribution function (EEDF) and secondary electron emission (SEE) is produced by the electrons impinging on the wall. It is found that SEE coefficient depends on not only the sheath potential but also the EEDF profile of energetic electrons when a non-Maxwellian energetic electron component is present. The energetic electrons and associated secondary emission electrons can strongly modify ion velocity at sheath edge, floating potential and I-V probe characteristic. Due to the interdependence between SEE coefficient originating from the impact of non-Maxwellian energetic electrons on the wall and the sheath potential, with the increase in the energy of energetic electrons, a sudden jump phenomenon can be found in the profiles of SEE coefficient and other quantities such as floating potential and ion velocity at the sheath edge for tungsten wall, while for carbon wall they are the continuous variation. To begin with, the energetic electron component does not dominate the sheath, and I-V probe characteristic depends on both the EEDF profile of energetic electrons and material properties. Once the energetic electron component dominates the sheath, the analysis of I-V probe characteristic will yield the energy of energetic electrons.
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