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Title: Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory

Abstract

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindrical probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.

Authors:
 [1]
  1. Theoretical Physics Division, PINSTECH, P. O. Nilore, 44000 Islamabad (Pakistan)
Publication Date:
OSTI Identifier:
22599950
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; ARGON; BOHM CRITERION; CATIONS; COMPARATIVE EVALUATIONS; CYLINDRICAL CONFIGURATION; PLASMA PRESSURE; PROBES; SPHERICAL CONFIGURATION

Citation Formats

Din, Alif. Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory. United States: N. p., 2016. Web. doi:10.1063/1.4960319.
Din, Alif. Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory. United States. doi:10.1063/1.4960319.
Din, Alif. 2016. "Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory". United States. doi:10.1063/1.4960319.
@article{osti_22599950,
title = {Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory},
author = {Din, Alif},
abstractNote = {The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindrical probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.},
doi = {10.1063/1.4960319},
journal = {Physics of Plasmas},
number = 8,
volume = 23,
place = {United States},
year = 2016,
month = 8
}
  • The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen, Boyd, and Reynolds [Proc. Phys. Soc. 70, 297 (1957)]. For a given value of the ion current, the boundary values of the matched “nonneutral” or “sheath” solution V{sup ~}{sub nn}{sup (m)}(r; r{sub m}) were obtained from the “quasineutral” or “presheath” solution V{sup ~}{sub qn}(r) by choosing the small potential and electric-field values corresponding to some large “matching radius” r{sub m}. Here, a straightforward but efficient numerical method is presented for systematically determining an optimal value of the matching radius at whichmore » the presheath and sheath solutions are joined to yield the “matched” potential profile. Some suitable initial matching radius r{sub m1} is chosen and the related potential and electric-field values of the quasineutral solution are calculated. Using these as boundary conditions, Poisson's equation is integrated to yield the matched nonneutral solution including the corresponding potential at the probe surface. This procedure is repeated for increasing values r{sub m2}, r{sub m3},…. until the resulting potential at the probe surface becomes practically constant. The corresponding value of r{sub m} is taken as the “optimal” matching radius r{sub mo} at which the presheath and sheath solutions are ultimately joined to yield the “optimal” matched potential profile in the entire plasma-probe transition region. It is also shown that the Bohm criterion is inapplicable in the present problem.« less
  • Emmert et al. (Phys. Fluids 23, 803 (1980)) have modeled the flow of a one-dimensional collisionless plasma to a material wall by formulating and solving the warm-ion plasma equation. In contrast to the result of the cold-ion plasma equation it was found that the electric field at the plasma--sheath boundary was finite. It is first shown that Emmert's solution satisfies the generalized Bohm criterion, and is thus a valid solution, before discussing the cause of the difference in the results of the two models in calculating the boundary electric field.
  • For a weakly collisional two-ion species plasma, it is shown that the minimum phase velocity of ion acoustic waves (IAWs) at the sheath-presheath boundary is equal to twice the phase velocity in the bulk plasma. This condition provides a theoretical basis for the experimental results that each ion species leaves the plasma with a drift velocity equal to the IAW phase velocity in the bulk plasma [D. Lee et al., Appl. Phys. Lett. 91, 041505 (2007)]. It is shown that this result is a consequence of the generalized Bohm criterion and fluid expressions for the IAW phase velocities.
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  • The problem of numerically evaluating absorption correction factors for cylindrical samples has been revisited using a treatment that fully takes advantage of the sample symmetry. It is shown that the path lengths for all points within the sample at all possible diffraction angles can be trivially determined once the angle-dependent distance distribution for a single line of points is calculated. This provides advantages both in computational efficiency and in gaining an intuitive understanding of the effects of absorption on the diffraction data. A matrix of absorption coefficients calculated for μRproducts between 0 and 20 for diffraction angles θ Dof 0–90°more » were used to examine the influence of (1) capillary diameter and (2) sample density on the overall scattered intensity as a function of diffraction angle, where μ is the linear absorption coefficient for the sample andRis the capillary radius. On the basis of this analysis, the optimal sample loading for a capillary experiment to maximize diffraction at angles of 0–50° is in general expected to be achieved when the maximum radius capillary compatible with the beam is used and when the sample density is adjusted to be 3/(4μR) of its original density.« less