This paper is concerned with the initial-boundary value problem on the isentropic Euler-Poisson equations arising in plasma physics in the half space for the spatial dimension
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. By ...assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of boundary layer (i.e., stationary solution) in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained.
The numerical solution of a warm ion sheath for an electrode/wall in contact with a low‐density isotropic plasma is analysed for sonic and supersonic flow of ions at the sheath entrance. For this, we ...consider half Maxwellian electron and water bag ion velocity distribution functions at the sheath edge. The generalized kinetic Bohm criterion is used to calculate the average ion velocity at the sheath edge. A relation between electrode/wall floating potential, sheath edge potential, and ion temperature is derived from the floating electrode/wall condition. The numerical solution of potential profiles for sonic and supersonic ions is calculated with varying ion temperature at different values of sheath edge potential. The results show that for sonic ions, the sheath solution merges smoothly into presehath solution, but for supersonic ions, we have density gradients, which increase with increasing ion temperature.
Advanced divertors gain larger plasma wetted area by poloidal or total flux expansion. Qualitative characteristics of supersonic plasma flows which are generated by the magnetic nozzle effect are ...studied by using a plasma fluid model incorporating anisotropic ion pressure (AIP model). The AIP model can self-consistently simulate supersonic plasma flows because, unlike the widely-used plasma fluid model (the Braginskii equations), the equation of parallel plasma momentum in it is described as a hyperbolic-type and the plasma flow velocity is solved without using explicit boundary conditions at the sheath entrance in front of divertor plates. In comparisons of plasma profiles between the AIP model and the Braginskii equations, it is observed that the plasma flow velocity in the Braginskii equations is forced to the sound speed at the sheath entrance in conditions of decelerating supersonic plasma flows leading to qualitative deviations with the AIP model. In an application of the AIP model to a scrape-off layer/divertor region incorporating super-X divertors with various flux-expansion ratios, supersonic plasma flows in divertor regions and highly anisotropic ion temperatures are successfully simulated. It is also demonstrated that it becomes easier with the AIP model to explain the mechanisms of generations of supersonic plasma flows and acceleration/deceleration of them (including stationary shock waves) in flux-expanding divertors from the mirror effect point of view.
We construct a stationary gyrokinetic variational model for sheaths close to the metallic wall of a magnetized plasma, following a physical extremalization principle for the natural energy. By ...considering a reduced set of parameters we show that our model has a unique minimal solution, and that the resulting electric potential has an infinite number of oscillations as it propagates towards the core of the plasma. We prove this result for the non linear problem and also provide a simpler analysis for a linearized problem, based on the construction of exact solutions. Some numerical illustrations show the well-posedness of the model after numerical discretization. They also exhibit the oscillating behavior.
The purpose of this paper is to mathematically investigate the formation of a plasma sheath near the surface of walls immersed in a plasma, and to analyze qualitative information of such a sheath ...layer. In the case of planar wall, Bohm proposed a criterion on the velocity of the positive ion for the formation of sheath, and several works gave its mathematical validation. It is of more interest to analyze the criterion for the nonplanar wall. In this paper, we study the existence and asymptotic stability of stationary solutions for the Euler–Poisson equations in a domain of which boundary is drawn by a graph. The existence and stability theorems are shown by assuming that the velocity of the positive ion satisfies the Bohm criterion at infinite distance. What most interests us in these theorems is that the criterion together with a suitable necessary condition guarantees the formation of sheaths as long as the shape of walls is drawn by a graph.
In this paper, a plasma sheath containing primary electrons, cold positive ions, and secondary electrons is studied using a one‐dimensional fluid model in which the primary electrons are described by ...q‐non‐extensive distribution according to the Tsallis statistics. Based on the Sagdeev potential method and the current balance relation, a modified sheath criterion, and floating potential are established theoretically. The effect of secondary electron emission on q‐non‐extensive plasma sheath characteristics have been numerically examined. A significant change is observed in the quantities characterizing the non‐extensive plasma sheath with the presence of the secondary electrons. It is found that the sheath properties with super‐extensive distribution (q<1) and sub‐extensive distribution (q>1) are different compared with plasma sheath with Maxwell distribution (q=1).
The structure of a plasma sheath has been investigated in front of a caesium‐coated metallic plate, using a simple theoretical model. Along with the electrons, the plasma is composed of multi‐species ...of positive ions, and surface and volume produced negative ions. While the volume produced negative ions are common in many plasma processing chambers, the surface produced negative ions are of critical importance, especially to the Neutral Beam Injection (NBI) systems. The surface negative ions are produced via the coated metallic plate. With a single species of positive ion, the Bohm criterion, which determines the sheath edge potential, is multi‐valued for a specific range of electronegativity (α0$$ {\alpha}_0 $$). The width of the multi‐valued region has been reported to increase with the surface production yield (δ$$ \delta $$). Calculations are done for hydrogen plasma with a slight admixture of a second gas such as argon. Besides discussing the differences brought in by the mere presence of a second ion, the paper highlights the importance of the positive ion current density in determining the Bohm criterion. In addition, the effect of three species of positive ions in the surface production process has been discussed.
The generalized Bohm criterion is revisited in the context of incorporating kinetic effects of the electron and ion distribution functions into the theory. The underlying assumptions and results of ...two different approaches are compared: the conventional 'kinetic Bohm criterion' and a fluid-moment hierarchy approach. The former is based on the asymptotic limit of an infinitely thin sheath (λD/l = 0), whereas the latter is based on a perturbative expansion of a sheath that is thin compared to the plasma (λD/l < 1). Here λD is the Debye length, which characterizes the sheath length scale, and l is a measure of the plasma or presheath length scale. The consequences of these assumptions are discussed in terms of how they restrict the class of distribution functions to which the resulting criteria can be applied. Two examples are considered to provide concrete comparisons between the two approaches. The first is a Tonks-Langmuir model including a warm ion source (Robertson 2009 Phys. Plasmas 16 103503). This highlights a substantial difference between the conventional kinetic theory, which predicts slow ions dominate at the sheath edge, and the fluid moment approach, which predicts slow ions have little influence. The second example considers planar electrostatic probes biased near the plasma potential using model equations and particle-in-cell simulations. This demonstrates a situation where electron kinetic effects alter the Bohm criterion, leading to a subsonic ion flow at the sheath edge.
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