Talk:Debye sheath

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

$$\chi''$$ actually be a $$\chi'$$??


 * 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)

Image


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: An approximate analytic form is derived in the article:
 * 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.

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

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)

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)

Child vs. Langmuir
Child developed his equation for PLANAR diodes (1911), while Langmuir developed his equation for CYLINDRICAL diodes (1913), but both equations established the 3/2-power relationship between voltage and thermionic current in vacuum tubes, ie: I = G*(V)^(3/2). —Preceding unsigned comment added by 97.112.203.145 (talk) 18:06, 27 December 2008 (UTC)