In this paper the general problem of linking fluid and kinetic plasma parameters, with special attention devoted to the plasma boundaries where, due to strong deviations from thermodynamic equilibrium, there are intrinsic difficulties regarding the closure of the hydrodynamic equations, is considered. This problem is demonstrated by means of two examples for which the solutions of the kinetic equations are known. These examples are the collision-free Tonks-Langmuir model [Phys. Rev. 34, 876 (1929)] and Riemann’s presheath model [Phys. Fluids 24, 2163 (1981)] dominated by charge-exchange collisions. It is found that in the vicinity of the sheath edge the “polytropic” coefficient γ(x) shows an unexpected behavior that contradicts the commonly used hydrodynamic approaches assuming γ=const. In spite of all differences, the two models investigated exhibit quite similar behavior of the hydrodynamic quantities and of the polytropic coefficient in the presheath and sheath regions. This rises to hopes that the results presented in this paper can be generalized to models characterizing other physical scenarios of plasma production and confinement. In particular, the basic findings presented here will, in suitably adopted form, be of importance, e.g., in properly formulating boundary conditions for fluid codes simulating bounded plasmas.

Formation of the potential in a two-electron-temperature plasma region facing a floating collector was studied theoretically with a kinetic plasma-sheath model and by electrostatic particle simulation. The electrons were described by truncated full Maxwellian velocity distribution functions and the ions by an accelerated half-Maxwellian velocity distribution function. The collector potential and the plasma source sheath or presheath potential drop were evaluated as functions of the hot to cool electron temperature ratio and the hot electron density ratio using Vlasov and Poison equations. The results showed that the presheath potential drop varied continuously with electron composition ratio for lower values of the electron temperature ratio, while for higher values in a narrow composition ratio range, triple values of the potential were found. Of the two physically acceptable values, the lower was characterized by the cool electrons and the higher by the hot electrons. It is anticipated that a current-free double layer structure is formed in the plasma system between these two potential regions. The collector floating potential, as a function of electron composition ratio, is mainly dominated by the hot electrons, since already a small value of hot electron current is sufficient to compensate the ion saturation current. In order to complete the theoretical investigation we also study the hydrogen plasma system with the XPDPl particle-in-cell simulation code composed at Berkeley. At certain plasma parameter values formation of a double layer structure was observed. The potential Values on the upper and lower side of the double layer, as well as that of the collector floating potential, corresponded very well to the calculated values. On the upper side the plasma was composed of ions, accelerated through the source sheath potential drop, and electrons consisting of cool full Maxwellian and hot truncated full Maxwellian populations. On the lower side only hot electrons and ions additionally accelerated through the double layer were found.

In a recent paper by Kuhn et al. [Phys. Plasmas 13, 013503 (2006)], it has been demonstrated that in a plasma, the polytropic coefficient γ is a spatially varying quantity rather than a global constant as usually assumed in fluid theory. Assuming cold ion sources and using the asymptotic two-scale approximation (in which the ratio of the Debye length over the characteristic presheath length, ε, is set to zero), it was found that the γ profile exhibits a sharp peak (with values roughly between 6 and 8) at the plasma-sheath boundary. In the present paper, it is shown that in a finite ε approach, this sharp peak is smoothed to a regular maximum, which for increasing ε (e.g., decreasing plasma density) decreases and finally disappears. In any case, assumptions like γ=1 and/or γ=3, which are customarily encountered in the context of fluid approaches, are disproved. Although the present results were obtained for collisionless plasmas, it is reasonable to assume that the behavior uncovered holds qualitatively for any plasma with cold ion sources. In addition to calculating time-independent theoretical solutions by means of an analytic-numerical approach, we primarily employ particle-in-cell (PIC) computer simulations, which intrinsically represent a time-dependent approach. It is confirmed that, although extreme care is required to separate physical from numerical effects, the PIC simulation method is a highly suitable tool also for future investigations of more demanding physical scenarios assuming, e.g., warm ion sources and other more complex aspects that cannot be treated realistically by analytic-numerical means alone. In addition, the extension from time-independent analytic-numerical calculation to time-dependent simulation permits us also to investigate the effect of collective plasma oscillations on the ion velocity distribution function (VDF). Although the ion VDFs obtained in our PIC simulations visibly differ in some details from the time-independent theoretical ones, the related ion-temperature and γ profiles turn out to fit their theoretical counterparts very well over significant parameter ranges. Hence, the two methods may to some extent be applied as alternative ones in future investigations on the plasma-sheath transition.

The properties of a plane collisionless plasma are investigated by using the Tonks-Langmuir model with the assumption of an electron beam in addition to Maxwellian bulk electrons. The case of very energetic beam electrons, as well as the case when the beam electrons acquire the greatest part of their energy in the sheath and the presheath regions, are considered under the condition that the discharge is terminated by a floating wall. In the case of a very energetic beam the plasma can be terminated by a double layer appearing close to the wall or, provided the beam density is high enough with respect to the bulk electron density, by a quasineutral double layer like structure. In the case of a beam of a small initial energy, however, the double layer and double layer like structures appear far from the wall even for very small beam densities. The last result opens a question about the relevance of the initial assumptions made on the electron velocity distribution in non-energetic and very energetic beams. The plasma flow to the boundary was calculated for the cases when the initial assumptions may be regarded as quite regular, and the results were compared with those ones obtained under the assumption of monoenergetic ions at the plasma-sheath boundary.

Plasma presheath and saturation current collection by a planar Langmuir probe in a strong magnetic field perpendicular to the probe surface ares described with the diffusion model. The model takes into consideration the geometry of the probe, that is its size and shape, and dependence of the cross-field charged particles' transport into the effective collection region of the probe on the parallel-field transport to the probe. Experimental study of planar Langmiur probe I -V characteristics in D.C. discharge argon plasma in strong magnetic fields confirms the possibility of deriving the cross-field diffusion coefficient, DY, from the measured electron satuation current. Additional dependence of the electron saturation current on the parallel-field diffusion coeficient, Dt, and the ion temperature, T, derived in the approximate Stangeby's study using the diffusion model of current collection by a planar surface (STANCEBY, P. C., J. Phys. D: Appl. Phys. 15 (1982) 1007) can be eliminated with more rigorous calculation. Series of measurements on two neutral prcssurcs and various magnetic fields gave reproducible values of Df, approximately given by relation Df x ( S n / ( n ) ) k,T,/(eB).