Sheath formation and its characteristics are studied in collisional magnetized plasma consisting of nonextensive electrons and thermal ions. Using two-fluid model, the Bohm criterion for ion velocity ...is deduced as a function of plasma parameters and shown that ion-neutral collisions impose an upper limit for the Bohm criterion. It is also found that deviation from the standard Maxwellian distribution significantly affects the sheath characteristics. Sheath potential and ion density are considered under the effects of magnetic field, ion temperature, nonextensivity and ion-neutral collision frequency. The results indicate that by applying an external magnetic field, it is possible to control the sheath thickness.
A novel concept of the mass ratio of negative to positive ions has been introduced to explore its effect on the sheath structure in three electronegative cold plasmas, namely, CF 4 , O 2 , and C 60 ...plasmas, for spherical geometry with different probe radii. The magnitudes of velocity of positive ions and potential at the sheath edge are found to modify with the mass ratio, electronegativity, and probe radius. The modification in positive ions' velocity is designated as modified Bohm criterion. Expression is obtained for the sheath thickness, which is found to increase with the higher mass ratios, whereas it reduces with the enhancement in electronegativity and probe radius. No oscillatory structure is observed for the potential profile when the negative ions are described by their fluid equations (as that of the positive ions), instead of their Boltzmann distribution assumed by the other workers. Positive ions' density as a function of distance from the probe for the different mass ratios is also examined.
The purpose of this paper is to mathematically investigate the formation of a plasma sheath, and to analyze the Bohm criteria which are required for the formation. Bohm originally derived the ...(hydrodynamic) Bohm criterion from the Euler–Poisson system. Boyd and Thompson proposed the (kinetic) Bohm criterion from a kinetic point of view, and then Riemann derived it from the Vlasov–Poisson system. In this paper, we prove the solvability of boundary value problems of the Vlasov–Poisson system. In the process, we see that the kinetic Bohm criterion is a necessary condition for the solvability. The argument gives a simpler derivation of the criterion. Furthermore, the hydrodynamic criterion can be derived from the kinetic criterion. It is of great interest to find the relation between the solutions of the Vlasov–Poisson and Euler–Poisson systems. To clarify the relation, we also study the delta mass limit of solutions of the Vlasov–Poisson system.
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
n
=
1
,
2
,
3
. 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.
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 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.
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