Two‐Fluid Theory of Presheath and Space Charge Sheath in Low Pressure Plasmas

Valentini, H.-B.

doi:10.1002/ctpp.2150310206

Cited by 23 publications

(51 citation statements)

References 38 publications

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“…as suggested by VALENTINI [13]. Fig.14a shows the radial dependences of the electron, ion, and neutral atom densities.…”

Section: Resultsmentioning

confidence: 57%

“…Thus, FRIEDMAN and LEVI [10], INGOLD [11], VALENTINI [12,13], and METZE, ERNIE and OSKAM [14] abandoned the assumption of quasi-neutrality and developed a two-fluid model, in which no derivative shows a singularity at the Bohm velocity. However, two new singularities arise at the isothermal ion and electron sonic velocities (2) While the electrons do not reach the sonic velocity within the plasma, the ion velocity of sound is reached within the positive column.…”

Section: Introductionmentioning

confidence: 99%

“…However, two new singularities arise at the isothermal ion and electron sonic velocities (2) While the electrons do not reach the sonic velocity within the plasma, the ion velocity of sound is reached within the positive column. Since the approximate quasi-neutral solution provides continuous curves for density and drift velocity at those points, FRIEDMAN and LEVI [10], INGOLD [11], FRANKLIN [15] and VALENTINI [12,13] postulated that the singularity in the two-fluid model must be removable. FRIEDMAN and LEVI [10] therefore assumed that the ratio of ion and electron densities on the axis cannot be chosen arbitrarily but is fixed by an internal condition at the ion sonic point.…”

Section: Introductionmentioning

confidence: 99%

“…~ 0). The radial variation of the electron temperature was calculated by VALENTINI [13] by means of a two-fluid model including the energy balance of the electrons but assuming constant ion temperature.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Modeling of the Non‐Isothermal Positive Column of an Ar⁺‐Laser

Zech

Ertl

Herold

et al. 1992

Contrib. Plasma Phys.

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A hydrodynamic description of the positive column is used to study the radial variation of particle densities, drift velocities, temperatures and heat fluxes of electrons, singly-charged ions and neutral atoms and the radial electric field. Elastic collisions between the plasma particles and neutrals as well as Coulomb collisions between ions and electrons are taken into account. The relevant equations to solve are the balance equations of particle densities, momentum, energy and the equations for the heat fluxes for each of the three studied particle types; the Poisson equation has to be added for closure. They form a system of 13 nonlinear differential equations with critical points. One singularity occurs when the ions reach the ion sound velocity which is the case inside the positive column. Therefore, a numerical method for multipoint boundary value problems was used which can also successfully handle removable singular points. The applied relaxation method is an iterative method which demands some preliminary knowledge of the solution looked for. The necessary knowledge can be retrieved from the quasineutral model and from a simplified two-fluid model.

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“…as suggested by VALENTINI [13]. Fig.14a shows the radial dependences of the electron, ion, and neutral atom densities.…”

Section: Resultsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar⁺‐Laser

Zech

Ertl

Herold

et al. 1992

Contrib. Plasma Phys.

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“…The monotonic state is well known. A slightly positive plasma core is surrounded by a positive boundary sheath in front of an insulating wall [5][6][7][8][9][10]. In the non-monotonic state, a zone with a very slightly negative space-charge density exists between the slightly positive core and the positive boundary sheath [4].…”

Section: Introductionmentioning

confidence: 99%

Effect of Microparticles on Acousto-Optic Diffraction in Water

Izumida¹,

Hayashi²,

Saito³

1997

Jpn. J. Appl. Phys.

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Using a two-fluid model it is shown that bounded collisional plasmas can exist in two different states if the plasma generation is localized within a small region and volume recombination processes occur in addition to the recombination at the wall. First, there is the well-known diffuse state involving a positive boundary sheath. Second, in the so-called breeze state a slightly positive plasma core is surrounded by a broad zone with very slightly negative space-charge density. In this case, the drift velocities of the ions and the electrons pass through a maximum and, then, tend to very small values if the distance from the plasma source becomes large. The half width of the density profile of the charged particles is smaller in the breeze state than it is in the diffuse state. The transition between the two states occurs within a small interval of the relevant parameters. The variations in the ion drift velocity, the electric field and the space-charge density caused by the transition are more characteristic than is the variation in the density profile of the electrons. The occurrence of the breeze state is assisted by outwards decreasing temperatures of the electrons and the ions. The results hint that the contracted positive column represents the breeze state of a plasma.

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Sheath formation in the presence of non‐extensive electron distribution

Moulick¹,

Garg

Kumar

2021

Contributions to Plasma Physics

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The main aim of this article is to recognize the sheath formation in the presence of non-extensive electron distribution. The role of ion-neutral collision parameter K and the non-extensive parameter "q" has been discussed. Existing literature suggests that the presence of non-extensive electrons potentially modifies the plasma sheath behaviour. However, numerical calculations over the full plasma range, jointly addressing the sheath and presheath, are rare. Sheath formation, being a very fundamental phenomenon, deserves enough investigation in the region of non-extensive distribution of particles. This study attempts to bridge the gap in understanding the formation of the sheath in collisional plasma in the light of both Boltzmann and q-distributed non-extensive electrons.

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Two‐Fluid Theory of Presheath and Space Charge Sheath in Low Pressure Plasmas

Abstract: In low pressure plasmas the transition between the prlsheirth and the sheath is investigated taking into account solutions o f a two-fluid model in the whole plasma.The kinetic theory is reviewed only shortly. The hydrodynamic theory is described in detail.

Cited by 23 publications

References 38 publications

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar⁺‐Laser

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar⁺‐Laser

Effect of Microparticles on Acousto-Optic Diffraction in Water

Sheath formation in the presence of non‐extensive electron distribution

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Two‐Fluid Theory of Presheath and Space Charge Sheath in Low Pressure Plasmas

Abstract: In low pressure plasmas the transition between the prlsheirth and the sheath is investigated taking into account solutions o f a two-fluid model in the whole plasma.The kinetic theory is reviewed only shortly. The hydrodynamic theory is described in detail.

Cited by 23 publications

References 38 publications

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar+‐Laser

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar+‐Laser

Effect of Microparticles on Acousto-Optic Diffraction in Water

Sheath formation in the presence of non‐extensive electron distribution

Contact Info

Product

Resources

About

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar⁺‐Laser

Numerical Modeling of the Non‐Isothermal Positive Column of an Ar⁺‐Laser