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.

Potential Formation in Front of an Electrode Close to the Plasma Potential Studied by PIC Simulation

“…Since the code BIT1 has the ability to maintain the prescribed electron temperature and the Maxwellian shape of the electron velocity distribution function, it is very suitable for this purpose. It has been shown that the results of this code are in very good agreement with the analytical solutions [11] of the TonksLangmuir model for the ions born at rest. The code could very probably also be used for the study of sheath formation in more fusion relevant conditions with warm ions [19][20][21] and magnetic field [22][23][24] present.…”

Existence of subsonic plasma sheaths

“…The electron kinetic effects have a strong impact on the ion velocity, and the sheath-edge definition needs to be refined according to Eq. (7). This new definition of the sheath edge is coherent with the breaking of neutrality and other sheath-edge quantities and is valid for all η se > 0.…”

“…The condition of ambipolar flow i = e can be found by solving V i,se = V e,se , expressed by Eqs. (4) and (7). This defines the floating potential, which is found to be at η se ≈ for the hydrogen mass ratio (μ = 1836, 2.8) or higher.…”

“…Sheaths have been studied since the pioneering work of Langmuir in 1929 [1], followed by an enormous research effort [2][3][4], which persists still (see, e.g., Refs. [5][6][7][8][9]). Only recently has their detailed experimental investigation become possible [10][11][12].…”

Cutoff effects of electron velocity distribution to the properties of plasma parameters near the plasma-sheath boundary

“…which validity has been further examined by Riemann 12 under particular discharge scenarios and further elaborated by Jelic et al 13 and Kuhn et al 14 Anyway, here we will remain within the framework of kinetic model. In Sec.…”