Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success ...of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.
Sheath region of an electronegative magnetized plasma consisting of q-nonextensive electrons, Boltzmann distributed negative ions and positive ions with finite temperature is investigated by using a ...steady state fluid model. Considering Sagdeev's pseudo potential method, a modified Bohm criterion is derived. Taking into account the new formation criterion, the fluid model is then solved numerically and the density distribution of charged particles in the sheath region is studied for different values of the initial positive ion velocity at the sheath edge.
This paper introduces how to determine concentrations of ion species in a mixed gas plasma that are not linearly proportional to their neutral partial pressures. A particle balance model was ...developed to predict the relative ion concentrations in multiple-ion-species plasmas, considering their ionization rates and loss fluxes to the wall. Analysis is carried out especially with Ar/Xe and Ar/He multi-dipole plasmas in which the neutral gases are directly ionized by the mono-energetic primary electrons. The experimental data of ion concentrations were obtained using the ion acoustic wave measurement method of the concentration of two ion species. The comparison reveals that the ion concentration ratio is linearly proportional to the ratio of the ionization cross sections and the ion loss velocity between two gas species. Especially, the model prediction is improved with using the two-ion-species sheath model (recently reported by Baalrud and Hegna) for obtaining the ion loss velocity at the sheath boundary.
The speed at which ions enter a sheath is a fundamental property of a plasma that also provides a useful boundary condition in modeling. A recent theory proposed that this can be significantly ...influenced by an instability-enhanced friction force arising from two-stream instabilities in the presheath when multiple ion species are present. Although experiments appeared to confirm this theory, recent particle simulations have brought it into question. We reconcile this controversy using direct numerical solutions of the dispersion relation, which show that there is a dependence on the electron-ion temperature ratio that was not considered previously. In addition, particle-in-cell simulations are used to show that ion-ion two-stream instabilities can arise near the sheath edge and generate an enhanced ion-ion friction force. Only by accounting for the instability-enhanced friction force can theory predict the simulated ion speeds at the sheath edge.
The plasma–sheath transition in stationary low temperature plasmas is investigated for arbitrary levels of collisionality. The model under study contains the equations of continuity and motion for a ...single ion species, Boltzmann's equilibrium for the electrons and Poisson's equation for the field. Assuming that the electron Debye length λ
D
is small compared with the ion gradient length
l
=
n
i
/(∂
n
i
/∂
x
), a first order differential equation is established for the ion density
n
i
as a function of the transformed spatial coordinate
q
= ∫
n
i
d
x
. A characteristic feature of this novel sheath equation is an internal singularity of the saddle point type which separates the depletion-field dominated sheath part of the solution from the ambipolar diffusion-controlled plasma. The properties of this singularity allow us to define, in a nonarbitrary way, a collisionally modified Bohm criterion which recovers Bohm's original expression in the collisionless limit but also remains meaningful when collisions are included.
A comparison is made with the collisionally modified Bohm criteria proposed by Godyak (1982
Phys. Lett.
A
89
80), Valentini (1996
Phys. Plasmas
3
1459) and Chen (1997
Phys. Plasmas
5
804) as well as with the approaches of Riemann (
1991
J. Phys. D: Appl. Phys.
24
493
) and Franklin (
2003
J. Phys. D: Appl. Phys.
36
2821
), who argued that the definition of a collisionally defined Bohm criterion is not possible.
A generalized Lenard-Balescu theory that accounts for instability-enhanced collective responses is used to calculate the collisional friction between ion species in the plasma-boundary transition ...region (presheath). Ion-ion streaming instabilities are shown to cause such a strong frictional force that the relative flow speed between ion species cannot significantly exceed the critical threshold value (DeltaV(c)) at which instability onset occurs. When combined with the Bohm criterion, this condition uniquely determines the flow speed of each ion species at the plasma-sheath boundary. For cold ions, DeltaV(c) --> 0 and each ion species leaves the plasma at a common system sound speed c(s).
A one-dimensional two-fluid model is presented and used for numerical analysis of the asymptotic two-scale limit of the plasma-wall transition. Numerical results confirm that when the problem is ...treated on the pre-sheath scale, the sheath edge is determined by the electric field singularity. When the problem is approached on the sheath scale, electric field at the sheath edge must be larger than zero in order to obtain any solutions of the model equations. In this case the Bohm criterion is determined by two parameters: the electric field and the ion velocity at the sheath edge.
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