Kinetic Bohm criterion in the Tonks-Langmuir model: assumption or theorem?

• Autor(a) principal: Benilov, M. S.
• Data de Publicação: 2019
• Outros Autores: Almeida, N. A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.13/4394
• topic: Tonks-Langmuir model; Kinetic Bohm criterion; .; Faculdade de Ciências Exatas e da Engenharia

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 ðkTe=2Þ 1 at all points in space. This feature is also pre sent 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 ðkTe=2Þ 1 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.