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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Critical role of electron heat flux on Bohm criterion

Bohm criterion, originally derived for an isothermal-electron and cold-ion plasma, is often used as a rule of thumb for more general plasmas. Here, we establish a more precise determination of the Bohm criterion that are quantitatively useful for understanding and modeling collisional plasmas that still have collisional mean-free-path much greater than plasma Debye length. Specifically, it is shown that electron heat flux, rather than the isothermal electron assumption, is what sets the Bohm speed to be $\sqrt{k_B(T_e||+3T_i||)/m_i}$ with T e,i∥ the electron and ion parallel temperature at the sheath entrance and m i the ion mass.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Bohm Criterion of Plasma Sheaths away from Asymptotic Limits

The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasineutral plasma modeling. In this work, the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed has explicit dependence on local plasma heat flux, temperature isotropization, and thermal force. Comparison with kinetic simulations demonstrates its accuracy over the plasma-sheath transition region in which quasineutrality is weakly perturbed and the Bohm criterion applies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Effects of fast monoenergetic electrons on the generalized Bohm criterion for electronegative dusty plasma

In this work, we have generalized the computation of Bohm criterion for electronegative complex plasma in the presence of fast monoenergetic electrons coming from a plane electrode. For this, we have established a 1D, collisionless, stationary, and unmagnetized electronegative plasma sheath model. The electrons and negative ions are considered in thermodynamic equilibrium; however, the positive ions, the dust grains, and the fast monoenergetic electrons are described by cold fluid equations. The generalized Bohm criterion has been calculated by using Sagdeev's pseudo potential method and the dust grain charge equation. The self-consistent relation between the dust grain surface potential at the edge and dust grains density is also derived. The numerical results reveal that the presence of the fast monoenergetic electrons increases the positive ion Mach number. On the other hand, the raise of electronegativity decreases this positive Mach number. The evolution of dust grain surface potential at the sheath edge is also illustrated and discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindrical probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

The limits of the Bohm criterion in collisional plasmas

The sheath formation within a low-pressure collisional plasma is analysed by means of a two-fluid model. The Bohm criterion takes into account the effects of the electric field and the inertia of the ions. Numerical results yield that these effects contribute to the space charge formation, only, if the collisionality is lower than a relatively small threshold. It follows that a lower and an upper limit of the drift speed of the ions exist where the effects treated by Bohm can form a sheath. This interval becomes narrower as the collisionality increases and vanishes at the mentioned threshold. Above the threshold, the sheath is mainly created by collisions and the ionisation. Under these conditions, the sheath formation cannot be described by means of Bohm like criteria. In a few references, a so-called upper limit of the Bohm criterion is stated for collisional plasmas where the momentum equation of the ions is taken into account, only. However, the present paper shows that this limit results in an unrealistically steep increase of the space charge density towards the wall, and, therefore, it yields no useful limit of the Bohm velocity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Unified Bohm criterion

Recent decades have seen research into the conditions necessary for the formation of the monotonic potential shape in the sheath, appearing at the plasma boundaries like walls, in fluid, and kinetic approximations separately. Although either of these approaches yields a formulation commonly known as the much-acclaimed Bohm criterion (BC), the respective results involve essentially different physical quantities that describe the ion gas behavior. In the fluid approach, such a quantity is clearly identified as the ion directional velocity. In the kinetic approach, the ion behavior is formulated via a quantity (the squared inverse velocity averaged by the ion distribution function) without any clear physical significance, which is, moreover, impractical. In the present paper, we try to explain this difference by deriving a condition called here the Unified Bohm Criterion, which combines an advanced fluid model with an upgraded explicit kinetic formula in a new form of the BC. By introducing a generalized polytropic coefficient function, the unified BC can be interpreted in a form that holds, irrespective of whether the ions are described kinetically or in the fluid approximation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Bohm criterion in a dusty plasma with nonextensive electrons and cold ions

The Bohm criterion in a dusty plasma containing nonextensively distributed electrons and cold ions is investigated within the framework of probe model including the effects of dust charge fluctuation. It is shown that the critical Mach number upshifts with the decrease of electron nonextensive parameter (q{sub e}) and the increase of the ion-to-electron number density ratio (R{sub n}) when the effects of dust charge fluctuation are out of consideration. Once the effects of dust charge fluctuation are included, with the increase of R{sub n}, the critical Mach number increases first, then decreases. The slop of the critical Mach number curves in the region R{sub n} Much-Greater-Than 1 for q{sub e}>1 becomes more gradual than that for q{sub e}<1. When critical Mach number is defined with respect to modified ion acoustic wave speed, it should be larger than unity in the case free of dust charge fluctuation. Whereas when R{sub n} Much-Greater-Than 1, it may be smaller than unity due to the effect of dust charge fluctuation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Generalized Bohm Criterion for Electronegative Complex Plasma

In this work, we have generalized the computation of Bohm criterion for electronegative complex plasma. For this, we have established a one-dimensional, unmagnetized and stationary theoretical model where the positive ions and dust particles are modeled by fluid equations. The electrons and negative ions are considered in thermodynamic equilibrium; therefore they obey to Boltzmann's statistic. In this case, the numerical results show that the generalized Bohm velocity is small compared to the classical value. For electronegative dusty plasma, the corrections are less important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Singularity and Bohm criterion in hot positive ion species in the electronegative ion sources

The structure of the discharge for a magnetized electronegative ion source with two species of positive ions is investigated. The thermal motion of hot positive ions and the singularities involved with it are taken into account. By analytical solution of the neutral region, the location of the singular point and also the values of the plasma parameter such as electric potential and ion density at the singular point are obtained. A generalized Bohm criterion is recovered and discussed. In addition, for the non-neutral solution, the numerical method is used. In contrast with cold ion plasma, qualitative changes are observed. The parameter space region within which oscillations in the density and potential can be observed has been scanned and discussed. The space charge behavior in the vicinity of edge of the ion sources has also been discussed in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Physics of the intermediate layer between a plasma and a collisionless sheath and mathematical meaning of the Bohm criterion

A transformation of the ion momentum equation simplifies a mathematical description of the transition layer between a quasi-neutral plasma and a collisionless sheath and clearly reveals the physics involved. Balance of forces acting on the ion fluid is delicate in the vicinity of the sonic point and weak effects come into play. For this reason, the passage of the ion fluid through the sonic point, which occurs in the transition layer, is governed not only by inertia and electrostatic force but also by space charge and ion-atom collisions and/or ionization. Occurrence of different scenarios of asymptotic matching in the plasma-sheath transition is analyzed by means of simple mathematical examples, asymptotic estimates, and numerical calculations. In the case of a collisionless sheath, the ion speed distribution plotted on the logarithmic scale reveals a plateau in the intermediate region between the sheath and the presheath. The value corresponding to this plateau has the meaning of speed with which ions leave the presheath and enter the sheath; the Bohm speed. The plateau is pronounced reasonably well provided that the ratio of the Debye length to the ion mean free path is of the order of 10{sup -3} or smaller. There is no such plateau if the sheath is collisional and hence no sense in talking of a speed with which ions enter the sheath.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

The plasma–sheath transition and Bohm criterion in a high recycling divertor

The high recycling regime of a divertor is characterized by high plasma particle fluxes and low temperature at the target, where a strong hydrogen recirculation loop exists. Atomic processes in the high recycling regime, such as ion–neutral friction and radiation, can affect the plasma momentum and energy transport in the sheath transition region. Here, in this work, the plasma–sheath transition near a high recycling wall is investigated. The Bohm speed, which constraints the ion exit flow speed, is evaluated from a transport model that accounts for the effect of the anisotropic transport and atomic collisions in the transition layer. A first principles kinetic code vector particle-in-cell with the atomic collision package is used to investigate a 1D self-consistent slab plasma with a high recycling boundary for the tungsten and carbon divertors. The results demonstrate the accuracy of the Bohm speed model in predicting the ion exit flow speed in the transition region, as well as the reduction of the Bohm speed due to the ion–neutral friction. The effect of different wall materials, tungsten, and carbon, on the Bohm speed and near-wall plasma profile is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

An analytic expression for the sheath criterion in magnetized plasmas with multi-charged ion species

The generalized Bohm criterion in magnetized multi-component plasmas consisting of multi-charged positive and negative ion species and electrons is analytically investigated by using the hydrodynamic model. It is assumed that the electrons and negative ion density distributions are the Boltzmann distribution with different temperatures and the positive ions enter into the sheath region obliquely. Our results show that the positive and negative ion temperatures, the orientation of the applied magnetic field and the charge number of positive and negative ions strongly affect the Bohm criterion in these multi-component plasmas. To determine the validity of our derived generalized Bohm criterion, it reduced to some familiar physical condition and it is shown that monotonically reduction of the positive ion density distribution leading to the sheath formation occurs only when entrance velocity of ion into the sheath satisfies the obtained Bohm criterion. Also, as a practical application of the obtained Bohm criterion, effects of the ionic temperature and concentration as well as magnetic field on the behavior of the charged particle density distributions and so the sheath thickness of a magnetized plasma consisting of electrons and singly charged positive and negative ion species are studied numerically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Nonextensive statistics and the sheath criterion in collisional plasmas

The Bohm criterion in an electropositive plasma containing nonextensively distributed electrons and warm ions is investigated by using a steady state two-fluid model. Taking into account the ion-neutral collisions and finite temperature of ions, a modified Bohm criterion is derived which limits both maximum and minimum allowable velocity of ions at the sheath edge (u{sub 0i}). It is found that the degree of nonextensivity of electrons (q) and temperature of positive ions (T{sub i}) affect only the lower limit of the entrance velocity of ions into the sheath while the degree of ion collisionality (α) influences both lower and upper limits of the ion velocities at the sheath edge. In addition, depending on the value of q, it is shown that the minimum velocity of positive ions at the sheath edge can be greater or smaller than its Maxwellian counterpart. Moreover, it is shown that, depending on the values of α and T{sub i}, the positive ions with subsonic velocity may enter the sheath for either q > 1 or −1 < q < 1. Finally, as a practical application, the density distribution of charged particles in the sheath region is studied for different values of u{sub 0i}, and it is shown that monotonical reduction of the positive ion density distribution occurs only when the velocity of positive ions at the sheath edge lies between two above mentioned limits.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

On the upper bound in the Bohm sheath criterion

The question is discussed about the existence of an upper bound in the Bohm sheath criterion, according to which the Debye sheath at the interface between plasma and a negatively charged electrode is stable only if the ion flow velocity in plasma exceeds the ion sound velocity. It is stated that, with an exception of some artificial ionization models, the Bohm sheath criterion is satisfied as an equality at the lower bound and the ion flow velocity is equal to the speed of sound. In the one-dimensional theory, a supersonic flow appears in an unrealistic model of a localized ion source the size of which is less than the Debye length; however, supersonic flows seem to be possible in the two- and three-dimensional cases. In the available numerical codes used to simulate charged particle sources with a plasma emitter, the presence of the upper bound in the Bohm sheath criterion is not supposed; however, the correspondence with experimental data is usually achieved if the ion flow velocity in plasma is close to the ion sound velocity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Bohm's criterion in a collisional magnetized plasma with thermal ions

Using the hydrodynamic model and considering a planar geometry, the modified Bohm's sheath criterion is investigated in a magnetized, collisional plasma consisting of electron and positive ions with finite temperature. It is assumed that the singly charged positive ions enter into the sheath region obliquely, i.e., their velocity at the sheath edge is not normal to the wall, and the electron densities obey Boltzmann relations. It is shown that there are both upper and lower limit for the Bohm entrance velocity of ions in this case and both of these limits depend on the magnitude and direction of the applied magnetic field. To determine the accuracy of our derived generalized Bohm's criterion, it reduced to some familiar physical condition. Also, using this generalized Bohm's criterion, the behavior of the electron and positive ion density distributions are studied in the sheath region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗