Affordable Access

Access to the full text

Polytropic Coefficient Function for Tonks-Langmuir-Type Bounded Plasmas with Kappa-Distributed Electrons and Cold Ion Source

Authors
  • Khan, Majid1, 2
  • Hussain, S. S.3
  • Sheng, Z.2
  • Kamran, M.4
  • 1 Quaid-i-Azam University, Department of Physics, Islamabad, Pakistan , Islamabad (Pakistan)
  • 2 Zhejiang University, Department of Physics, Institute of Fusion Theory and Simulations, Hangzhou, 310027, People’s Republic of China , Hangzhou (China)
  • 3 Islamic International University, Department of Physics, FBAS, Islamabad, Pakistan , Islamabad (Pakistan)
  • 4 COMSATS University Islamabad, Department of Physics, Park Road, Chak Shahzad, Islamabad, Pakistan , Islamabad (Pakistan)
Type
Published Article
Journal
Brazilian Journal of Physics
Publisher
Springer US
Publication Date
Apr 08, 2019
Volume
49
Issue
3
Pages
372–378
Identifiers
DOI: 10.1007/s13538-019-00659-4
Source
Springer Nature
Keywords
License
Yellow

Abstract

In the fluid description of the classical Tonks-Langmuir (TL) model [Tonks and Langmuir, Phys Rev., 34: 876, 1929], arises the “closure problem.” The continuity and the momentum equations need, in addition, a closure equation. Usually, this closure equation assumes zero ion pressure (pi = 0), or a constant ion polytropic coefficient (γi). These simplified assumptions are likely to produce incorrect results, because (i) the ions have a non-zero temperature, even if the ion source is assumed to be cold, and (ii) the polytropic coefficient is, in fact, a function of space (or potential), and is far from constant (Kuhn et al., AIP Conference Proceedings, 1306: 216, 2010). Here, the concept of polytropic coefficient function (PCF) is applied to a TL-type discharge with a Kappa-distributed ion source. The ion density and temperature are calculated numerically, for different values of the spectral index κ. The polytropic coefficient function is then calculated using the relation γ = 1 + (n/T) (dT/dn). Striking deviation from results of the classical case are observed. It is shown here that, for Kappa-distributed ion sources, the ion PCF is not a constant, but is a function of the potential. Moreover, the sheath-edge potential differs significantly from the classical case. It is concluded that in order to close the set of fluid equations in an appropriate manner, better approximations to the PCF are needed.

Report this publication

Statistics

Seen <100 times