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Kinetic Bohm criterion in the Tonks-Langmuir model: assumption or theorem?
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Abstract(s)
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.
Description
Keywords
Tonks-Langmuir model Kinetic Bohm criterion . Faculdade de Ciências Exatas e da Engenharia
Citation
Benilov, M. S., & Almeida, N. A. (2019). Kinetic Bohm criterion in the Tonks-Langmuir model: assumption or theorem?. Physics of Plasmas, 26(12), 123505. 10.1063/1.5121022
Publisher
American Institute of Physics