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Title: The ion polytropic coefficient in a collisionless sheath containing hot ions

Abstract

The fluid approach has been widely used to study plasma sheath dynamics. For a sheath containing hot ions whose temperature is greater than the electron's, how to truncate the fluid hierarchy chain equations while retaining to the fullest extent of the kinetic effects is always a difficult problem. In this paper, a one-dimensional, collisionless sheath containing hot ions is studied via particle-in-cell simulations. By analyzing the ion energy equation and taking the kinetic effects into account, we have shown that the ion polytropic coefficient in the vicinity of the sheath edge is approximately constant so that the state equation with the modified polytropic coefficient can be used to close the hierarchy chain of the ion fluid equations. The value of the polytropic coefficient strongly depends on the hot ion temperature and its concentration in the plasma. The semi-analytical model is given to interpret the simulation results. As an application, the kinetic effects on the ion saturation current density in the probe theory are discussed.

Authors:
; ;  [1];  [2]
  1. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)
  2. (China)
Publication Date:
OSTI Identifier:
22599952
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; CONCENTRATION RATIO; CURRENT DENSITY; ELECTRONS; EQUATIONS; FLUIDS; ION TEMPERATURE; IONS; ONE-DIMENSIONAL CALCULATIONS; PLASMA SHEATH

Citation Formats

Lin, Binbin, Xiang, Nong, E-mail: xiangn@ipp.ac.cn, Ou, Jing, and Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031. The ion polytropic coefficient in a collisionless sheath containing hot ions. United States: N. p., 2016. Web. doi:10.1063/1.4960558.
Lin, Binbin, Xiang, Nong, E-mail: xiangn@ipp.ac.cn, Ou, Jing, & Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031. The ion polytropic coefficient in a collisionless sheath containing hot ions. United States. doi:10.1063/1.4960558.
Lin, Binbin, Xiang, Nong, E-mail: xiangn@ipp.ac.cn, Ou, Jing, and Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031. 2016. "The ion polytropic coefficient in a collisionless sheath containing hot ions". United States. doi:10.1063/1.4960558.
@article{osti_22599952,
title = {The ion polytropic coefficient in a collisionless sheath containing hot ions},
author = {Lin, Binbin and Xiang, Nong, E-mail: xiangn@ipp.ac.cn and Ou, Jing and Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031},
abstractNote = {The fluid approach has been widely used to study plasma sheath dynamics. For a sheath containing hot ions whose temperature is greater than the electron's, how to truncate the fluid hierarchy chain equations while retaining to the fullest extent of the kinetic effects is always a difficult problem. In this paper, a one-dimensional, collisionless sheath containing hot ions is studied via particle-in-cell simulations. By analyzing the ion energy equation and taking the kinetic effects into account, we have shown that the ion polytropic coefficient in the vicinity of the sheath edge is approximately constant so that the state equation with the modified polytropic coefficient can be used to close the hierarchy chain of the ion fluid equations. The value of the polytropic coefficient strongly depends on the hot ion temperature and its concentration in the plasma. The semi-analytical model is given to interpret the simulation results. As an application, the kinetic effects on the ion saturation current density in the probe theory are discussed.},
doi = {10.1063/1.4960558},
journal = {Physics of Plasmas},
number = 8,
volume = 23,
place = {United States},
year = 2016,
month = 8
}
  • The continuity and momentum equations of a fluid plasma component may be viewed as four scalar evolution equations for the four scalar fluid variables n(x-vector,t)(density) and u(x-vector,t)(fluid velocity), which are zeroth- and first order velocity moments of the velocity distribution function (VDF). However, the momentum equation in addition contains the gradient of the pressure p(x-vector,t), which is a second-order velocity moment for which another equation, the 'closure equation', is needed. In the present work, closure by means of the polytropic-coefficient function (PCF) is discussed which, by analogy with the well-known polytropic coefficient (also called the 'polytropic index' or 'polytropic exponent')more » in macroscopic thermodynamic systems, is formally defined by {gamma}(x-vector,t) = (nDp/Dt)(pDn/Dt) = (n/p)(Dp/Dn), with D/Dt = {partial_derivative}/{partial_derivative}t+u-vector{center_dot}{partial_derivative}/{partial_derivative}x-vector, which amounts to the closure equation if {gamma}(x-vector,t) is known. In fluid problems, however, the PCF is usually unknown and hence must be assumed or guessed, but in kinetic problems it can be calculated exactly. These general concepts are first developed and then applied specifically to the basic Tonks-Langmuir (TL) model [L. Tonks and I. Langmuir, Phys. Rev. 34, 876, 1929]. It is shown for the first time that results obtained from the fluid equations closed with the correct PCF coincide with the corresponding results calculated on the basis of the exact kinetic solution [K.-U. Riemann, Phys. Plasmas 13, 063508 (2006)], but differ visibly from those obtained from the approximate fluid equations closed with the zero-pressure approximation [Riemann et al., Plasma Phys. Control. Fusion 47, 1949 (2005)]. Also, it is again confirmed that the correct PCF may be a strongly varying function of position, so that the simple constant values of {gamma} usually assumed [K.-U. Riemann, XXVIII International Conference on Phenomena in Ionized Gases, 479 (2007)] may lead to markedly erroneous results especially near material walls. All of these findings lead us to conclude that better approximations to the PCF are needed for closing fluid equations in an appropriate manner.« less
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  • Sheath energy transmission governs the plasma energy exhaust onto a material surface. The ion channel is dominated by convection, but the electron channel has a significant thermal conduction component, which is dominated by the Knudsen layer effect in the presence of an absorbing wall. First-principle kinetic simulations reveal a robustly supersonic sheath entry flow. The ion sheath energy transmission and the sheath potential are accurately predicted by a sheath model of truncated bi-Maxwellian electron distribution. The electron energy transmission is further enhanced by a parallel heat flux of the perpendicular degrees of freedom.