2001
DOI: 10.1063/1.1413953
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Unipolar ion sheath

Abstract: In technical applications, the ion sheath in front of a highly negative wall is frequently described by the well known Child-Langmuir law. Due to inaccurate boundary conditions, however, this yields only a rather poor approximation. The collisionless Child-Langmuir law can be substantially improved by accounting for universal initial conditions following from the Bohm criterion. By a simple analytical ansatz the resulting unipolar ion sheath law is generalized to account for ͑charge exchange͒ ion collisions in… Show more

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Cited by 25 publications
(25 citation statements)
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“…³ÎÇAEÖâ ÕÇÓÏËÐÑÎÑÅËË, ÒÓÇAEÎÑÉÇÐÐÑÌ Ä ÔÕÂÕßÇ ²ËÏÂ-Р˸ÇÐAEËР[25], ÃÖAEÇÏ ÅÑÄÑÓËÕß, ÚÕÑ AEÇÃÂÇÄÔÍËÌ ÔÎÑÌ Ð ÒÑÄÇÓØÐÑÔÕË ÒÎÂÊÏÞ ÑÕAEÇÎÈÐ ÑÕ ÍÑÎÎÇÍÕÑÓ ËÑÐÑÄ ÖÐËÒÑÎâÓÐÞÏ ÔÎÑÇÏ, Ä ÍÑÕÑÓÑÏ ÒÑÕÇÐÙËÂÎ ÒÓËÃÎËÉÈÐ-ÐÑ ÒÑAEÚËÐâÇÕÔâ ÊÂÍÑÐÖ ¹ÂÌÎAE ë ÇÐÅÏáÓ [26,27]. £ ÔÖÏÏÇ AEÇÃÂÇÄÔÍËÌ Ë ÖÐËÒÑÎâÓÐÞÌ ÔÎÑË ÑÃÓÂÊÖáÕ ÕÂÍ ÐÂÊÞÄÂÇÏÞÌ ÎÇÐÅÏáÓÑÄÔÍËÌ ÔÎÑÌ [25,28].…”
Section: £äçAeçðëçunclassified
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“…³ÎÇAEÖâ ÕÇÓÏËÐÑÎÑÅËË, ÒÓÇAEÎÑÉÇÐÐÑÌ Ä ÔÕÂÕßÇ ²ËÏÂ-Р˸ÇÐAEËР[25], ÃÖAEÇÏ ÅÑÄÑÓËÕß, ÚÕÑ AEÇÃÂÇÄÔÍËÌ ÔÎÑÌ Ð ÒÑÄÇÓØÐÑÔÕË ÒÎÂÊÏÞ ÑÕAEÇÎÈÐ ÑÕ ÍÑÎÎÇÍÕÑÓ ËÑÐÑÄ ÖÐËÒÑÎâÓÐÞÏ ÔÎÑÇÏ, Ä ÍÑÕÑÓÑÏ ÒÑÕÇÐÙËÂÎ ÒÓËÃÎËÉÈÐ-ÐÑ ÒÑAEÚËÐâÇÕÔâ ÊÂÍÑÐÖ ¹ÂÌÎAE ë ÇÐÅÏáÓ [26,27]. £ ÔÖÏÏÇ AEÇÃÂÇÄÔÍËÌ Ë ÖÐËÒÑÎâÓÐÞÌ ÔÎÑË ÑÃÓÂÊÖáÕ ÕÂÍ ÐÂÊÞÄÂÇÏÞÌ ÎÇÐÅÏáÓÑÄÔÍËÌ ÔÎÑÌ [25,28].…”
Section: £äçAeçðëçunclassified
“…£ ÔÖÏÏÇ AEÇÃÂÇÄÔÍËÌ Ë ÖÐËÒÑÎâÓÐÞÌ ÔÎÑË ÑÃÓÂÊÖáÕ ÕÂÍ ÐÂÊÞÄÂÇÏÞÌ ÎÇÐÅÏáÓÑÄÔÍËÌ ÔÎÑÌ [25,28]. ¡ÐÂÎËÕËÚÇÔÍÂâ ÕÇÑÓËâ ÒÎÂÊÏÇÐÐÑÅÑ àÏËÕÕÇÓ ÑÅÓÂ-ÐËÚËÄÂÇÕÔâ ÑAEÐÑÏÇÓÐÞÏË ÏÑAEÇÎâÏË.°AEÐÑÏÇÓÐÂâ ÕÇÑ-ÓËâ ÒÓËÊÄÂРÒÑÏÑÚß Ô×ÑÓÏÖÎËÓÑÄÂÕß ÅÓÂÐËÚÐÞÇ ÖÔÎÑ-ÄËâ AEÎâ ÚËÔÎÇÐÐÞØ ÍÑAEÑÄ, ÍÑÕÑÓÞÇ ÒÓËÏÇÐâáÕÔâ AEÎâ ÓÂÔÚÈÕ ÓÇÂÎßÐÞØ ËÔÕÑÚÐËÍÑÄ ÊÂÓâÉÇÐÐÞØ ÚÂÔÕËÙ.…”
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“…This phase, the matrix extraction phase, lasts until all ions of the initial matrix have been extracted to the wall. The sheath expansion continues until a steady state is reached that can be approximated by the Child-Langmuir 4 law or by an improved model 5,6 describing the stationary unipolar ion sheath. This late phase, however, is characterized by a low ion current to the wall and is of minor interest for the application in PIII.…”
Section: Introductionmentioning
confidence: 99%
“…Indeed, at the background pressure of about 5 Torr, the mean free path of electron-neutral collisions is n ϳ2ϫ10 Ϫ3 cm, that is much smaller than the probe radius R p ϭ250ϫ10 Ϫ3 cm. Estimation of the sheath thickness 19 yields hϳ0.3ϫ10 Ϫ3 cm. Thus, we should suppose that at Pϳ5 Torr R p ӷ n ӷh.…”
Section: Gas Discharge Mode Of Fps Operationmentioning
confidence: 99%