Bohm Criterion Research Articles

Plasma sheath in a magnetic field

The structure of the plasma sheath in an oblique magnetic field was investigated with the fluid method. In various different magnitude and directions of the ma g netic field, the electron and ion density distribution, ion flow velocity, elect ron potential and Bohm's criterion have been calculated. It is shown that the magnetic field has obvious effect on the plasma sheath. Under the action of electrostatic and Lorentz forces, the ion flow makes a helical movement, and the ion densi ty distribution fluctuates.

The Bohm criterion for the dusty plasma sheath

The hydrodynamic-fluid model and the self-consistent dust charging model are used to investigate the Bohm criterion for the dusty plasma sheath. The variation of the ion critical Mach number and the dust Mach number with dust density are presented, and the relation between the dust surface potential and the dust density at the sheath edge is discussed. It is shown that the ion velocity entering the sheath would exceed the ion sound velocity due to the existence of dust particles. The ion critical Mach number began declining after a maximum with the incessant increase of the dust density. The numerical results satisfy the qualitative analysis of the Sagdeev potential.

A note on the Bohm criterion for electronegative gases

The Bohm criterion for electronegative gases is known to yield a multi-valued solution for certain plasma parameters. The prescription for the determination of the correct solution, in the original paper by Braithwaite and Allen (1988 J. Phys. D: Appl. Phys. 21 1733), was to choose the smaller value of the two possible potential drops in the quasi-neutral plasma. Several authors have recently questioned this procedure, but this paper affirms the correctness of the original method. It is a fact, however, that this application of the Bohm criterion becomes less useful than is normally the case, since it relates to only one part of the discharge plasma; it will not itself suffice to calculate the flux of positive ions leaving the entire system.

There is no such thing as a collisionally modified Bohm criterion

The conventional equations describing plasma and sheath are examined over a full range of collisionality to determine the influence of collisionality on the ion equation of motion—that is, when the ion motion is essentially inertial and when it is collisional. When it is inertial in the sheath the Bohm criterion has been satisfied, while when the sheath is collisional the ions remain in equilibrium with the field all the way to the wall.

Kinetic analysis of the collisional plasma–sheath transition

The subdivision of the plasma boundary layer into a quasi-neutral presheath and a collision-free sheath is strictly valid only in the asymptotic limit λD/λ → 0, where λD is the electron Debye length and λ the ion mean free path. This trivial fact requires one to discuss the applicability and correct interpretation of the plasma–sheath concept for finite ratios λD/λ. In a former fluid analysis (Riemann K-U 1997 Phys. Plasmas 4 4158) based on the charge exchange model the plasma–sheath transition was investigated on an intermediate scale. The analysis showed that there is no need and no justification for a modification of the Bohm criterion for finite λD. The former results and conclusions are confirmed and improved by a new kinetic analysis. The kinetic analysis of the plasma–sheath transition can be generalized to other presheath mechanisms.

Analytical fit of the I–V characteristic for cylindrical and spherical Langmuir probes

A unified radial model of the collisionless sheath for both cylindrical and spherical Langmuir probes is developed. The I–V characteristics are obtained and analytically fitted, taking into account both the probe radius and the probe biasing potential as parameters of the model. This parameterization allowed us to obtain an analytical approach for the potential profile, the floating potential and the sheath edge according to the Nachmann and Tahn criterion [M. Nachmann and P. C. Tahn, IEEE Trans. Plasma Sci. 19, 423 (1991)]. An alternative criterion for the sheath edge is established. This is referred to as the curvature criterion and it matches the Bohm criterion in the limiting case of planar Langmuir probes. The case of a planar sheath is obtained as a limiting case of the model when the probe radius is large enough.

Sheath Structure of an Electronegative Plasma

We investigate the sheath structure of an electronegative plasma atsteady state with the assumptions of cold positive ions and hot negativeions. The modified Bohm criterion is obtained with the Sagdeev potentialby introducing a modified ion sound velocity. At the same time theelectric potential, net space charge and particles densities in thesheath are analysed in several cases of different temperature ratios ofelectrons to negative ions and different density ratios of negative ionsto positive ions.

The Bohm criterion for the dusty plasma sheath

The Bohm criterion for the dusty plasma sheath is investigated with a fluid model. It is shown that the presence of dust particles near the interface between the bulk plasma and the sheath should have effects upon the ion Mach number. The dust particles charging and density variation are taken into account, and therefore the self-consistent relation between the dust surface potential and ion Mach number at the sheath edge is derived. The numerical results reveal that both the ion critical Mach number and the dust critical Mach number with variation of density ratio of dust-to-electron begin to decline after a maximum.

On asymptotic matching and the sheath edge

The position of the sheath edge and the value of the electric field at the sheath edge are found using asymptotic matching techniques for collisionless plasma-wall systems. It is demonstrated that specifying the position of the sheath edge by the Bohm criterion or by Riemann's weak electric field is inconsistent with the asymptotic matching theory and contradicts the commonly accepted definition of the sheath as a region where ionization can be neglected. It is shown that the sheath found using the asymptotic matching theory is the ion sheath, characterized by negligible electron density, and that the value of the electric field at the sheath edge practically coincides with the value of Godyak's electric field. In addition, analytical expressions are given for the position of the wall, the sheath width, and sheath characteristics for arbitrary potentials at the wall.

Particle-in-cell Monte Carlo (PIC-MC) simulations of plasma–wall interactions in low-pressure AR plasma

The 1d3v (1D in displacement and 3D in velocity space) PIC-MC model is used in this work in order to study the sheath formation and the ambipolar diffusion in low-pressure, small-diameter Ar discharge. The departure from plasma neutrality and its consequences are investigated. The Bohm criterion for a sheath formation is not fulfilled in the low range of Ar concentrations.

Experimental studies of the Bohm criterion in a two-ion-species plasma using laser-induced fluorescence.

The Bohm criterion is studied experimentally in the case of a two ion species plasma. Measurements are carried out in Ar and Ar+He plasmas (PA(r I) approximately 0.1 mtorr, 0< or =P(He)/P(Ar)< or =25, and 0< or =n(+)(He)/n(e)< or =0.5, T(e)< or =2 eV) created in an unmagnetized dc hot filament discharge confined by surface multidipole magnetic fields. Laser-induced fluorescence (LIF) measurements of Ar II ion velocity distribution functions (ivdfs) within the presheath up to the sheath edge show that the ions reach the sheath edge traveling faster than their individual Bohm speed by more than 75%, approaching a speed equal to the ion sound speed of the system.

Investigation of sheath properties in Ar/SF6 dc discharge plasma

Properties of plasma sheath boundary in multicomponent plasma with negative ions have been investigated experimentally. The modified Bohm sheath criterion derived for thermal electron–thermal negative ion–cold positive ion model predicts the decrease of positive ion drift speed toward the sheath when the negative ion concentration is gradually increased. This modified Bohm criterion has been discussed in this experimental investigation. The experimental parameters (e.g. discharge voltage, discharge current) set for argon plasma production are kept floating during the addition of SF6 gas. Two important effects caused by the presence of negative ions, e.g. decrease in Bohm speed of positive ions toward the sheath and reduction in plasma density have been observed. The reduction in the ion flux toward the sheath therefore causes the expansion of the sheath. The numerical solution of Poisson's equation, which includes the contribution of negative ions, is compared with the experimental findings.

A method of kinetic description of the near-wall plasma and non-local effects

As is known, ion kinetics play an essential part in the formation of a near-wall plasma layer. The scatter processes with ions involved (ionization, recombination, charge exchange, etc.) influence both the value of the near-wall potential jump (and, accordingly, the value of the electric field on the surface) and the unipolar arc formation. The applicability of the Bohm criterion which is widely used in many works, also depends on the processes of ion scattering. In this paper a new method of the ion kinetics in a magnetic field is proposed which can been applied to the problems mentioned above.

The influence of particle beams on the criterion of Bohm sheath

A twofluid model has been used to study the influence of the existence of the directive ions and directive electrons on the Bohm criterion of sheath. The main collisions included in this study consist of the charge exchange collision, ionization collision and total energy loss collision. The operated gas is argon with a gas pressure 101325 Pa. Numerical calculation results are obtained, which show that the minimal speed at which drift ions enter into the sheath for directive ions is decreased. This is also valid for the charge exchange collision. The directive electrons make this speed increase, but the ionization collision related to directive electrons makes the speed decrease obviously.

Joining active plasma and sheath when the plasma contains two species of positive ions

The complete plasma–sheath is examined in the situation where there is an active plasma generated by electron impact ionization in a mixture of gases, with a view to determining the structure. It is already well known that at low pressures and for a collisionless sheath, a composite Bohm criterion applies. The way in which this relationship breaks down at higher pressures is examined. However, specifically for the situation with two positive ions, we find no evidence of structure in the plasma, but rather that the two ion species behave similarly in the outer regions adjacent to the wall.

How to patch active plasma and collisionless sheath: A practical guide

Most plasmas have a very thin sheath compared with the plasma dimension. This necessitates separate calculations of the plasma and sheath. The Bohm criterion provides the boundary condition for calculation of plasma profiles. To calculate sheath properties a value of the electric field at the plasma–sheath interface has to be specified in addition to the Bohm criterion. The value of the boundary electric field and a robust procedure to approximately patch plasma and collisionless sheath with a very good accuracy are reported.

Transition region between a nonequilibrium plasma and a negative electrode

A model is developed that describes the transition region between a quasineutral plasma and a planar negative electrode and in which the electron velocity distribution is represented as the sum of two Maxwellian distributions with different temperatures or as the sum of a Maxwellian distribution and distribution corresponding to an electron beam directed toward the electrode. Criteria for the formation of a sheath of positive space charge and a secondary plasma in the transition region are derived. An analysis is made of the dependence of the structure of the transition region on the parameters of the electron distribution, the space charge density distribution in the sheath, and the density of the ion current to the electrode. The criteria obtained are compared with the Bohm criterion.

What significance does the Bohm criterion have in an active collisional plasma–sheath?

The known solutions joining plasma and sheath for the situation where both plasma and sheath are collisional (Blank 1968 Phys. Fluids 11 1688–98, Benilov and Franklin 2002 J. Plasma Phys. 65 163–73) are examined in the context which produces the Bohm criterion as a necessary condition for collisionless sheath formation. The conditions under which even in a collisional situation the ions might exceed the ion sound speed before reaching the wall are examined for both the constant ion collision frequency model and the constant ion mean free path model. It is concluded that under such conditions the ions remain in collisional equilibrium with the electric field and that there is no such thing as a collisionally modified Bohm criterion.

Bohm criterion failure in nonstationary plasmas

The Bohm criterion, generally used as a boundary condition at the plasma-sheath edge, is not compatible with the time evolution of the voltage fall across the collisionless cathode sheath in a pulsed hollow-cathode discharge. Similarly this criterion is not valid for the interpretation of probe measurements of the plasma in this discharge. The discrepancy disappears only when the discharge reaches its steady state. The duration of this invalidity is much longer than the time needed to fill the device with plasma and than the time needed for the formation of the plasma sheath. The sheath evolution in nonstationary plasmas is described quantitatively by assuming at the sheath edge a temporary growth of the ion speed from an initial low value up to the ion sound velocity, i.e., up to the Bohm criterion requirement.

Dynamic model and electrical characteristics for rf-biased electronegative plasma sheath

The dynamic model for the sheath of an RF-biased electronegative plasma is developed. The low-pressure high-density plasma conditions are assumed and considered as an electric-field-free boundary. The Bohm criterion for collisionless sheath is assumed to be valid and the presheath region is separately considered in calculating the sheath properties. The electron density n/sub e/ and the electronegativity /spl alpha/ /spl equiv/ n/sub -//n/sub e/ are taken to be determined independently of the sheath dynamics. The time-resolved wave forms of the sheath potential and thickness are obtained. The characteristics for the RF power dissipation mechanisms are also investigated. The RF bias power is assumed to be dissipated through two power loss channels - the first is due to ion acceleration in the sheath and the second is due to the electron heating at the plasma-sheath boundary. From the power loss point of view, the equivalent circuit model is developed and the sheath impedance is calculated. The electronegativity, as well as the current and RF bias frequency, is found to be an important factor in determining the electrical characteristics for the RF-biased electronegative plasma sheath.