Talk:Debye sheath

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[edit] Formula

In this formula,

\int_0^\xi \chi' \chi''\,d\xi_1 = \int_0^\xi \left( 1 - \frac{2\chi}{\mathfrak{M}^2} \right)^{-1/2} \chi' \,d\xi_1 - \int_0^\xi e^{-\chi} \chi''\,d\xi_1,

should not the last

χ'' actually be a χ'??

Looks like it to me. I'll change it. Now I'm worried that the following equation

\frac{1}{2}\chi'^2 = \mathfrak{M}^2 \left[ \left( 1 + \frac{2\chi}{\mathfrak{M}^2} \right)^{1/2} - 1 \right] + e^{-\chi} - 1

should actually be

\frac{1}{2}\chi'^2 = \mathfrak{M}^2 \left[ \left( 1 - \frac{2\chi}{\mathfrak{M}^2} \right)^{1/2} - 1 \right] + e^{-\chi} - 1

Am I missing something? --Art Carlson 14:01, 27 November 2006 (UTC)
I decided the problem was not here but in the previous equations. χ is defined to have the opposite sign from φ. Changed accordingly, but would appreciate it if somebody would check up on me. --Art Carlson 14:21, 27 November 2006 (UTC)

[edit] Image

Double sheath (or double layer) characteristics showing the potential (Φ), electric field (E) and space charge distribution (ρ) across the layer
Double sheath (or double layer) characteristics showing the potential (Φ), electric field (E) and space charge distribution (ρ) across the layer

You are right, Ian, that this article could use a sketch, and I appreciate the effort you have made, but this image, while it may represent a double layer, doesn't look much like a Debye sheath. I wish there were a wiki-way to generate sketches, but let me at least make a couple comments:

  1. Toward the surface, the electric field rises monotonically. At the surface it does not vanish but takes on its maximum value.
  2. Toward the plasma, the electric field decreases smoothly, without changing curvature. There is therefore only one region and one sign of space charge.

An approximate analytic form is derived in the article:

\frac{4}{3}\chi(x)^{3/4} = 2^{3/4} \mathfrak{M}^{1/2} x,

or

\phi(x) \propto x^{4/3},

E(x) \propto x^{1/3}, and

\rho(x) \propto x^{-2/3}.

x = 0 is the "entrance" to the Deye sheath from the plasma, and the approximations break down there, but they are good toward the wall.

--Art Carlson 13:01, 16 May 2006 (UTC)

OK, I've tried another. --Iantresman 18:18, 17 May 2006 (UTC)

[edit] Article title

Do you think that "Debye sheath" is the best title for the article? I wonder if "Plasma sheath" or "Electrostatic sheath" is better; the latter seems to outnumber the others dramatically. --Iantresman 18:18, 17 May 2006 (UTC)

In fusion research Debye sheath is the most common term, although I sometimes see and use the name electrostatic sheath as well. Obviously I favor the current name since I started the article, but as long as there is a redirect from Deye sheath, I wouldn't get hot about calling it electrostatic sheath. --Art Carlson 19:09, 17 May 2006 (UTC)
OK. So I've created redirects to Debye sheath, from Electrostatic sheath, Plasma sheath, and Space charge sheath. --Iantresman 21:39, 17 May 2006 (UTC)
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