Extension of the Bissell-Johnson plasma-sheath model for application to fusion-relevant and general plasmas
- LECAD Laboratory, Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana (Slovenia)
- Association EURATOM-OeAW, Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria)
This article presents an approach to solving a special Fredholm-type integral equation of the first kind with a particular kernel containing a modified Bessel function for applications in plasma physics. From the physical point of view, the problem was defined by Bissell and Johnson (B and J) [Phys. Fluids 30, 779 (1987)] as a task to find the potential profile and the ion velocity distribution function in a plane-parallel discharge with a Maxwellian ion source. The B and J model is a generalization of the well-known Tonks-Langmuir (T and L) [Phys. Rev. 34, 876 (1929)] discharge model characterized by a ''cold'' ion source. Unlike the T and L model, which can be readily solved analytically, attempts to solve the B and J model with a ''warm'' ion source have been done only numerically. However, the validity of numerical solutions up to date remains constrained to a rather limited range of a crucial independent parameter of the B and J integral equation, which mathematically is the width of a Gaussian distribution and physically represents the ion temperature. It was solved only for moderately warm ion sources. This paper presents the exact numerical solution of the B and J model, which is valid without any restriction regarding the above-mentioned parameter. It is shown that the ion temperature is very different from the temperature of the ion source. The new results with high-temperature ion sources are not only of particular importance for understanding and describing the plasma-sheath boundary in fusion plasmas, but are of considerable interest for discharge problems in general. The eigenvalue of the problem, found analytically by Harrison and Thompson [Proc. Phys. Soc. 74, 145 (1959)] for the particular case of a cold ion source, is here extended to arbitrary ion-source temperatures.
- OSTI ID:
- 21282132
- Journal Information:
- Physics of Plasmas, Vol. 16, Issue 9; Other Information: DOI: 10.1063/1.3223556; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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