Abstract
It has been shown recently by Kos et al. [Phys. Plasmas 25, 043509 (2018)] that the common plasma-sheath boundary is characterized by three well defined characteristic points, namely the plasma edge (PE), the sheath edge (SE) and the sonic point. Moreover, it has been shown that the sheath profiles, when properly normalized at the SE, as well as the potential drop in the plasma–sheath transition region (PST), (region between between PE and SE) in collision-free (CF) discharges are rather independent of discharge parameters, such as the plasma source profile, ion temperature and plasma density, providing that the sheath thickness is kept well bellow the plasma length. While these findings were obtained by theoretical means under idealized discharge conditions, the question arises whether and to which extent they are relevant under more complex physical scenarios. As a first step toward answering this question the CF discharge with warm ions is examined in this work via kinetic simulation method in which some of the model assumptions, such as independence of time and the Boltzmann distribution of electrons can hardly be ensured. Special attention is payed to effects of ion creation inside the sheath. It is found that only with considerably increased sheath thickness the sonic point always shifts from SE towards the wall. Whether the absolute value of ion directional velocity at the sonic point will increase or decrease depends on the ion temperature and the source strength inside the sheath. In addition preliminary comparison of results obtained under CF assumption with the representative ones obtained with strongly enhanced Coulomb collisions (CC), indicate the relevancy of hypothesis that the VDF of B&J can be considered as a universal one in future reliable kinetic modeling and solving the plasma boundary and sheath problem in both collisional and collision-free plasmas.
Highlights
Ion velocity distribution functions (VDFs), which are characterized by well defined moments and have second moment comparable to the thermal pressure of electrons or even considerably larger, are of a particular interest in laboratory, fusion and space plasmas
It should be emphasized that the lines obtained from theoretical model on one hand and from particle in cell (PIC) simulation on the other can hardly be distinguished in spite of the fact that theoretical and simulation curves have been obtained with different source profiles ( β = 1 and β = 0, respectively)
According to our experience solving the collision-free discharge numerically with a high accuracy is an extremely stiff and CPU expensive task. As it can be seen from Ref. 20 that even when done very carefully, the differentiated profiles obtained on discrete grids are far from being perfect
Summary
Ion velocity distribution functions (VDFs), which are characterized by well defined moments and have second moment comparable to the thermal pressure of electrons or even considerably larger, are of a particular interest in laboratory, fusion and space plasmas. The original B&J model implies intrinsic employment of mathematical two-scale approach[24] constrained to only one free/external parameter of the problem, i.e., to the ion-source temperature T n, with the Debye length disregarded (λD = 0) and, numerical solution has been obtained for a few temperatures only, with the particular ion source profile si proportional to electron (Boltzmann distributed) density ne (si ∼ ne) In this context it should be noted at least that the vanishing Debye length implies infinite electric field at the plasma edge, i.e., infinitely thin charged sheath (separating the neutral plasma from charged terminating planar surfaces) and, even worse, infinitely high plasma density - apparently contradicts the basic assumption of the model, i.e., about negligible cross sections for particle-particle interactions in a collision-free plasma.
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