Asymptotic matching of plasma and sheath in an active low pressure discharge

Franklin, R N; Ockendon, J. R.

doi:10.1017/s0022377800005067

Cited by 128 publications

(164 citation statements)

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“…According to the works of Franklin and Ockendon [2] and Riemann [1], [3]- [5], intermediate scale matching provides an appropriate estimate of the electric field and space charge density at the sheath edge for the hydrodynamic model. For the case the following electric intensity and charge density guesses are good for the range and satisfactory for [5]:…”

Section: Sheath Thickness and Sheath Edge Position Evaluationmentioning

confidence: 99%

“…Treating this problem as a two-scale problem, Riemann [1], [5] and other early researchers [2]- [4] introduced the intermediate scale matching which has been shown to work well for even more collisional plasmas. In addition, Riemann also showed that the Bohm criterion is the right choice for the sheath boundary only if where is the ion mean free path in presheath region.…”

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confidence: 99%

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Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas

Wang

Wendt

1999

IEEE Trans. Plasma Sci.

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Abstract-The widely used Child-Langmuir law for sheath thickness evaluation in semi-infinite collisionless plasmas makes the assumptions of quasi-neutrality (n e = n i ) and zero electric field intensity E = 0 at the sheath edge, as well as applying the Bohm criterion for ions entering the sheath. However, through a whole region fluid model, Poisson's equation has been solved numerically for the steady-state solution through the sheath and presheath without these assumptions. With the sheath edge defined, as in the Child-Langmuir law, at the place where the ion velocity is equal to the Bohm velocity, the sheath thickness of a bounded collisionless or weakly collisional plasma has been found with this model in some cases to be much larger than that obtained with the Child-Langmuir Law. The sheath thickness discrepancy is significant under conditions found in low pressure high density plasma (HDP) tools for plasma processing. Results presented indicate that the sheath thickness is very sensitive to the electric field and space charge density at the sheath edge. The electric field and space charge density can be successfully estimated by an intermediate scale matching method [1]-[5], and are used to derive a modified expression for the potential in the sheath that can be solved numerically for sheath thickness. With these results, the matching problem, arising when sheath and plasma are modeled separately, can be overcome.

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Section: Sheath Thickness and Sheath Edge Position Evaluationmentioning

confidence: 99%

mentioning

confidence: 99%

Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas

Wang

Wendt

1999

IEEE Trans. Plasma Sci.

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“…Such situations arise in sheath problems (see e.g. [16], [18], [11] ; other references can be found in [8]). In such problems, one has often to deal with a dynamic interface the tracking of which gives rise to a complex numerical problem.…”

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confidence: 99%

Analysis of an Asymptotic Preserving Scheme for the Euler–Poisson System in the Quasineutral Limit

Degond¹,

Liu²,

Vignal³

2008

SIAM J. Numer. Anal.

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Abstract. In a previous work [8], a new numerical discretization of the Euler-Poisson system has been proposed. This scheme is 'Asymptotic Preserving' in the quasineutral limit (i.e. when the Debye length ε tends to zero), which means that it becomes consistent with the limit model when ε → 0. In the present work, we show that the stability domain of the present scheme is independent of ε. This stability analysis is performed on the Fourier transformed (with respect to the space variable) linearized system. We show that the stability property is more robust when a space-decentered scheme is used (which brings in some numerical dissipation) rather than with a space-centered one. The linearization is first performed about a zero mean velocity, and then about a non-zero mean velocity. At the various stages of the analysis, our scheme is compared with more classical schemes and its improved stability property is outlined. The analysis of a fully discrete (in space and time) version of the scheme is also given. Finally, some considerations about a model nonlinear problem, the Burgers-Poisson problem, are also given.

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“…The purpose of this note is to examine critically the patching process and the developments of it, because that process denies the existence of the region that is necessary to join plasma and collisionless sheath smoothly. Such a region was the natural result of the analyses of the probe-plasma situation given by Lam [2], [3], and for the plasma-wall sheath by Franklin and Ockendon [4]. The analyses referred to, involved the use of the method of matched asymptotic approximations which had by then transformed the field of fluid mechanics and gas dynamics [5].…”

Section: Introductionmentioning

confidence: 99%

“…The analyses referred to, involved the use of the method of matched asymptotic approximations which had by then transformed the field of fluid mechanics and gas dynamics [5]. Its use in plasma physics has been less intensive, but the list of references [2]- [4], [6]- [25], [33], [34], shows that it has been applied in a variety of situations with a significant increase in recent years.…”

Section: Introductionmentioning

confidence: 99%

You cannot patch active plasma and collisionless sheath

Franklin¹

2002

IEEE Trans. Plasma Sci.

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Abstract-The fluid equations for the plasma-sheath are examined over the range of collisionality from collisionless to fully collisional. The method of "patching" plasma to sheath is examined critically in comparison with matched asymptotic approximations and solutions computed without approximation. It is concluded that it is necessary to include a transition layer in order to smoothly join plasma and collisionless sheath-and then the Bohm Criterion applies. When the sheath is collisional, the orderings are different and there is no transitional layer but equally there is no collisionally modified Bohm Criterion. Nevertheless, a method is given for calculating the ion flux to the wall under conditions where the sheath is collisional.

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Asymptotic matching of plasma and sheath in an active low pressure discharge

Cited by 128 publications

References 11 publications

Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas

Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas

Analysis of an Asymptotic Preserving Scheme for the Euler–Poisson System in the Quasineutral Limit

You cannot patch active plasma and collisionless sheath

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