Fluid and kinetic parameters near the plasma-sheath boundary for finite Debye lengths

Abstract

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.