The characteristics of sheath in a plasma system containing
q
-nonextensive electrons, cold fluid ions, and Boltzmann-distributed negative ions are investigated. A modified Bohm sheath criterion is ...derived by using the Sagdeev pseudopotential technique. It is found that the proposed Bohm velocity depends on the degree of nonextensivity (
q
), negative ion temperature to nonextensive electron temperature ratio (σ), and negative ion density (
B
). Using the modified Bohm sheath criterion, the sheath characteristics, such as the spatial distribution of the potential, positive ion velocity, and density profile, have been numerically investigated, which clearly shows the effect of negative ions, as well as the nonextensive distribution of electrons. It is found that, as the nonextensivity parameter and the electronegativity increases, the electrostatic sheath potential increases sharply and the sheath width decreases.
We propose a hydrodynamic model to study the equilibrium properties of planar plasma sheaths in two-component quasi-neutral magnetized plasmas. It includes weak but finite electron-inertia ...incorporated via a regular perturbation of the electronic fluid dynamics only relative to a new smallness parameter,
δ
, assessing the weak inertial-to-electromagnetic strengths. The zeroth-order perturbation around
δ
leads to the usual Boltzmann distribution law, which describes inertialess thermalized electrons. The forthwith next higher-order yields the modified Boltzmann law describing the putative lowest-order electron-inertial correction, which is applied meticulously to derive the local
Bohm criterion
for sheath formation. It is found to be influenced jointly by electron-inertial corrective effects, magnetic field and field orientation relative to the bulk plasma flow. We establish that the mutualistic action of electron-inertia amid gyro-kinetic effects slightly enhances the ion-flow Mach threshold value (typically,
M
i
0
⩾ 1.140), against the normal value of unity, confrontationally towards the sheath entrance. A numerical illustrative scheme is methodically constructed to see the parametric dependence of the new sheath properties on diverse problem arguments. The merits and demerits are highlighted in the light of the existing results conjointly with clear indication to future ameliorations.
Graphical abstract
For a weakly collisional two-ion species plasma, it is shown that the minimum phase velocity of ion acoustic waves (IAWs) at the sheath-presheath boundary is equal to twice the phase velocity in the ...bulk plasma. This condition provides a theoretical basis for the experimental results that each ion species leaves the plasma with a drift velocity equal to the IAW phase velocity in the bulk plasma D. Lee et al., Appl. Phys. Lett. 91, 041505 (2007)10.1063/1.2760149. It is shown that this result is a consequence of the generalized Bohm criterion and fluid expressions for the IAW phase velocities.
The self-consistent problem of the structure of a perturbed wall sheath in a dc gas-discharge plasma near a flat surface under negative potential relative to the plasma has been solved for an ...arbitrary relation between the Debye radius and the ion mean free path. The solution has been obtained without artificial separation of this layer into the quasi-neutral “presheath” and the wall sheath in which quasi-neutrality is violated substantially. The actual ion distribution function in the unperturbed plasma, the dependence of the charge-exchange cross section on the ion energy, and the nonzero electric field in the unperturbed plasma have been considered. It is shown that when the average electron energy is conserved the structure of the perturbed wall sheath weakly depends on the form of the electron distribution function. It has been established that the mean energy of ions in the unperturbed plasma substantially affects the structure of the quasi-neutral presheath as well as the structure of a part of the wall sheath in which quasi-neutrality is not observed even under the assumption that the mean electron energy is much higher than the mean energy of ions. The calculations of ion flow parameters and the structure of the perturbed wall sheath are in conformity with experimental data obtained by other authors, which could not be adequately interpreted earlier.
This work shows that there is no such thing as a formulation of the Bohm criterion for the case of a collisional plasma. It examines critically the work of several authors who have sought to promote ...their own version of what has come to be called a collisionally modified Bohm criterion.
We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group ...throughout the last years. The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. We introduce the concept of a “relational causality” which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. Combined with the application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a “superclassical” theory. Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie–Bohm theory. By proving the absence of third order interferences in three-path systems it is shown that Born’s rule is a natural consequence of our theory. Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin’s first order sum rule, just as the validity of all higher order sum rules. Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool.
•Calculating the interference patterns and particle trajectories of a double-, three- and N-slit system.•Deriving a new formulation of the guiding equation equivalent to the de Broglie–Bohm one.•Proving the absence of third order interferences and thus explaining Born’s rule.•Explaining the violation of Sorkin’s order sum rules.•Classical simulation of Talbot patterns and exact reproduction of Talbot distance for N slits.
The main concern of the present paper is to analyze the behavior of a boundary layer, called a sheath, which appears over a material in contact with a plasma. The well-known Bohm criterion claims the ...velocity of positive ions should be faster than a certain constant for the formation of a sheath. The behavior of positive ions is governed by the Euler-Poisson equations. Mathematically, the sheath is understood as a monotone stationary solution, whose existence and asymptotic stability in one-dimensional space were proved in Suzuki's previous work. However the stability was proved under the assumption stronger than the Bohm criterion. In the present paper, we refine these results by proving the stability theorem exactly under the Bohm criterion in the spatial dimension up to three. We also deal with the degenerate case in which the Bohm criterion is marginally fulfilled.
The concepts of ‘plasma edge’ and ‘collisionally modified Bohm criterion’ have occupied attention for many years since the publication of work by Bohm that gave rise to the Bohm criterion. He ...acknowledged that his description of the plasma-sheath transition was incomplete. We summarize work that shows that neither concept has precision, at the same time giving a critique.
Between a plasma and a solid target lies a positively charged sheath of several Debye lengths \(\lambda_{\rm D}\) in width, typically much smaller than the characteristic length scale \(L\) of the ...main plasma. This scale separation implies that the asymptotic limit \(\epsilon = \lambda_{\rm D} / L \rightarrow 0\) is useful to solve for the plasma-sheath system. In this limit, the Bohm criterion must be satisfied at the sheath entrance. A new derivation of the kinetic criterion, admitting a general ion velocity distribution, is presented. It is proven that for \(\epsilon \rightarrow 0\) the distribution of the velocity component normal to the target, \(v_x\), and its first derivative must vanish for \(|v_x| \rightarrow 0\) at the sheath entrance. These two conditions can be subsumed into a third integral one after it is integrated by parts twice. A subsequent interchange of the limits \(\epsilon \rightarrow 0\) and \(|v_x| \rightarrow 0\) is invalid, leading to a divergence which underlies the misconception that the criterion gives undue importance to slow ions.
PDF
