{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T14:31:59Z","timestamp":1773325919865,"version":"3.50.1"},"reference-count":34,"publisher":"AIP Publishing","issue":"12","funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/FIS\/50010\/2019"],"award-info":[{"award-number":["UID\/FIS\/50010\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013276","name":"Interreg","doi-asserted-by":"publisher","award":["PlasMa-M1420-01-0145-FEDER-000016"],"award-info":[{"award-number":["PlasMa-M1420-01-0145-FEDER-000016"]}],"id":[{"id":"10.13039\/100013276","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2019,12,1]]},"abstract":"<jats:p>New first integral is found in the collision-free Tonks-Langmuir model. The integral has a clear physical interpretation: the weighted mean inverse kinetic energy of ions, evaluated in the quasineutral approximation, equals (kTe\/2)\u22121 at all points in space. This feature is also present in the full (not relying on the assumption of quasineutrality) model: for small values of the Debye length, the weighted mean inverse kinetic energy is with good accuracy equal to (kTe\/2)\u22121 in the entire region of quasineutral plasma, including in the vicinity of the space-charge sheath. These results constitute a mathematical proof of the kinetic Bohm criterion and provide a new look at the problem, which has been discussed for several decades. In particular, these results show that the much-debated problem of divergence for slow ions stems from a misinterpretation. Moreover, these results explain why no unique form of kinetic Bohm criterion, modified with the account of ionization and\/or collisional and\/or geometrical effects in the sheath, has emerged: it cannot be postulated in a nonarbitrary way since there is simply no definite value of the inverse mean kinetic energy with which the ions enter the sheath, if these effects are non-negligible.<\/jats:p>","DOI":"10.1063\/1.5121022","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T15:51:07Z","timestamp":1575388267000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Kinetic Bohm criterion in the Tonks-Langmuir model: Assumption or theorem?"],"prefix":"10.1063","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9059-1948","authenticated-orcid":false,"given":"M. S.","family":"Benilov","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Faculdade de Ci\u00eancias Exatas e da Engenharia, Universidade da Madeira, Largo do Munic\u00edpio , 9000 Funchal, Portugal and , 1049-001 Lisboa, Portugal"},{"name":"Instituto de Plasmas e Fus\u00e3o Nuclear, Instituto Superior T\u00e9cnico, Universidade de Lisboa , 9000 Funchal, Portugal and , 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6499-3609","authenticated-orcid":false,"given":"N. A.","family":"Almeida","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Faculdade de Ci\u00eancias Exatas e da Engenharia, Universidade da Madeira, Largo do Munic\u00edpio , 9000 Funchal, Portugal and , 1049-001 Lisboa, Portugal"},{"name":"Instituto de Plasmas e Fus\u00e3o Nuclear, Instituto Superior T\u00e9cnico, Universidade de Lisboa , 9000 Funchal, Portugal and , 1049-001 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2019,12,3]]},"reference":[{"key":"2023062818440528200_c1","volume-title":"Principles of Plasma Discharges and Material Processing","year":"2005","edition":"2nd ed."},{"key":"2023062818440528200_c2","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1103\/PhysRev.34.876","volume":"34","year":"1929","journal-title":"Phys. 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