Talk:Debye length

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)

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)

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)

Cold ions
The formula for a plasma is given as
 * $$ \lambda_D = \sqrt{\frac{\varepsilon_0 k/q_e^2}{n_e/T_e+\sum_{ij} j^2n_{ij}/T_i}}$$

and then it is stated
 * The ion term is often dropped, giving
 * $$ \lambda_D = \sqrt{\frac{\varepsilon_0 k T_e}{n_e q_e^2}}$$
 * although this is only valid when the ions are much colder than the electrons.

Mathematically, assuming quasineutrality and reasonable charge states, taking the limit $$T_i/T_e\rightarrow0$$ 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)

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:
 * $$ \lambda_D = \sqrt{\frac{\varepsilon_0 k T_e}{n_e q_e^2 (1 + T_e/T_i)}}$$

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)

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. —Preceding unsigned comment added by 65.26.183.175 (talk) 21:36, 13 August 2009 (UTC)

Can there be more discussion of the physics before getting into the math?
I'm a EE who doesn't really understand the physics of the problem. In other words, if there is an anode, electrons ought to keep moving (by F = qE) until they impact the anode and neutralize its positive charge. Therefore I can't understand why there would be a cloud of electrons hanging around the anode, unless there are other phenomena present (like maybe collisions with neutral atoms) that are keeping the electrons from getting to the anode, and thus causing the electron cloud to be formed instead. This is the kind of discussion on phenomenology that, if it preceded the mathematics, would be very helpful to readers like me who don't really fully understand what's going on here. —Preceding unsigned comment added by 157.127.124.15 (talk) 17:06, 24 March 2010 (UTC)


 * One reason is the collisions of electrons and ions with each other, which preserves the Boltzmann distribution (from statistical mechanics, lower energy states are occupied more preferentially).
 * However, there still should be a Debye length without collisions, as the electrons have thermal velocities which carry them past the low potential energy region around the anode. An accumulation of altered trajectories (electrons passing a little closer to the anode) leads to the shielding.129.2.129.155 (talk) 15:54, 27 May 2011 (UTC)


 * I will try to make this a bit clearer this weekend. To start however, as an EE the most common place where you will see this is in a FET, where the gate (anode) is separated from the charged by an dielectric (SiO2, HfO, etc) barrier.  A13ean (talk) 01:24, 28 May 2011 (UTC)

Debye Length Formula
Are you sure Debye length is $$\lambda_D = \left(\frac{\varepsilon \, k_B T}{\sum_{j = 1}^N n_j^0 \, q_j^2}\right)^{1/2}$$ Instead of $$\lambda_D = \left(\sum_{j = 1}^N \frac{\varepsilon \, k_B T_j}{n_j^0 \, q_j^2}\right)^{1/2}$$ ? Heitorpb (talk) 16:53, 17 October 2015 (UTC)

Ionic strength units
I am not quite knowledgeable about this to make the edit myself, but the article says "I is the ionic strength of the electrolyte, and here the unit should be mole/m3, even though I is commonly found in mol per kg of solvent,", and I am pretty sure it should be mole/L or mole/dm^3. Can anyone confirm? — Preceding unsigned comment added by 24.16.99.132 (talk) 15:56, 3 March 2018 (UTC)


 * Even worse, the formulae given for solutions are inconsistent in their use of gas consant vs. Boltzmann constant. For the last one -
 * $$ \kappa^{-1}(\mathrm{nm}) = \frac{0.304}{\sqrt{I(\mathrm{M})}}$$ where κ−1 is expressed in nanometers (nm) and I is the ionic strength expressed in molar (M or mol/L)
 * - the units do not check out. It is probably meant to be a Zahlenwertgleichung, but it would seem appropriate to make that more clear to the reader. --Lpd-Lbr (talk) 19:53, 9 June 2019 (UTC)

Lpd-Lbr (talk) 19:53, 9 June 2019 (UTC)