Talk:Debye length

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Hannes Alfven would role over in his grave if he saw that the solar core had no magnetic field. —Preceding unsigned comment added by 75.157.177.51 (talk) 19:05, 22 February 2008 (UTC)[reply]

Electronegative Plasmas

Maybe the formula for the Debye length should be modified to take into account negative ions? Ga2re2t 17:02, 28 October 2007 (UTC)[reply]

The notion of Debye length is also used in semiconductor physics. Perhaps a section on this should be included as well?MagnusBL (talk) 07:59, 21 November 2007 (UTC)[reply]

Cold ions

The formula for a plasma is given as

\lambda _{D}={\sqrt {\frac {\varepsilon _{0}k/q_{e}^{2}}{n_{e}/T_{e}+\sum _{ij}j^{2}n_{ij}/T_{i}}}}

and then it is stated

The ion term is often dropped, giving

\lambda _{D}={\sqrt {\frac {\varepsilon _{0}kT_{e}}{n_{e}q_{e}^{2}}}}

although this is only valid when the ions are much colder than the electrons.

Mathematically, assuming quasineutrality and reasonable charge states, taking the limit $T_{i}/T_{e}\rightarrow 0$ doesn't make the ion term disappear, it makes it dominate. That makes some sense physically, since cold ions (like any cold charged particles) will cluster more compactly around foreign charges, shielding them before warm charged particles have a chance to notice them. What is wrong with this argument, and how can the article be rephrased to make mathematical and physical sense? --Art Carlson (talk) 09:52, 11 January 2008 (UTC)[reply]

I agree with Carlson, the above simplification doesn't sound right. A simple counter-example: In a neutral deuterium plasma there are only electrons and one kind of ions (charge +1), and their densities are the same ( $n_{i}=n_{e}$ ), so the general equation can be reduced (for this particular case) to:

\lambda _{D}={\sqrt {\frac {\varepsilon _{0}kT_{e}}{n_{e}q_{e}^{2}(1+T_{e}/T_{i})}}}

The mentioned simplification could only be valid if the electrons (not ions) were much colder. CharlieM, 10 May 2008 —Preceding unsigned comment added by 81.61.248.109 (talk) 19:22, 10 May 2008 (UTC)[reply]

CAUTION!

This page about the "Debye length" makes incorrect statements:

To name a few:

1) " ... where, as a mathematical convenience for purposes of illustration, the charge has been arranged to vanish when the potential is zero"

In fact this can never be done and though there is some leeway in choosing the potential (gauge invariance) nothing like that will add a 1 to

http://upload.wikimedia.org/math/0/5/c/05cc7eee4bbdbb80aea1034e82965fb4.png

The "1" is there to represent the opposite charge background and is a physical necessity rather then a mathematical convenience.

Which leads to:

2) "It is assumed that the potential has the correct polarity to raise the energy of the charges screening the potential"

No. The polarity of the field comes out of the equations with no such imposition.

Summary: It was very nice of someone to try and explain the Debye length! They, along with everyone else who would like to correctly understand its derivation (with its limitations, e.g., decoupling the background charges from the field(!)) should at the very least open up J. D. Jackson's 2nd Edition "Classical Electrodynamics" (AKA as "The Bible" among some) to page 495 and enjoy. (and then write back a proper introduction)

Have a good day and keep up adding/correcting wikipedia.