# Debye length?

1. May 15, 2005

### Nylex

Can someone explain to me what this is? All we were told in my Physics of Stars module was that for a plasma,

$$L \gg \lambda_{D}$$, where $$\lambda_{D}$$ is the Debye length.

We were also told that it's an "e-folding distance" for a potential, but that doesn't help to understand it.

I'm not even sure what L is either (the length of the plasma?? ) :/.

Thanks.

2. May 15, 2005

### dextercioby

3. May 15, 2005

### marlon

Last edited: May 15, 2005
4. May 15, 2005

### Staff: Mentor

In the context of a plasma, L is probably a characteristic length, as in the mean distance between successive particle collisions, for example.

In nuclear interaction, $L = \frac {1}{\Sigma}$, where $\Sigma$ is the macroscopic cross-section of the particle interaction.

I assume the module is indicating that the distance between successive collisions of particles is much greater than the Debye length.

5. May 5, 2010

### LuisVela

When you apply a potential diference to a plasma, electrons and ions will be attracted by the positive and negative electrodes respectively. The electric potential generated by the electrodes will then we screened out by the charged particles.The screening decays exponentially as you go away from the elctrode.
A debye lenght is the lenght by which the potential has decayed 1/e.-thats what they mean by an e-folding.
Big L in plasma means the characteristic lenght of the ''plasma''. Thats is, is you talk about space plasma, L is in the AU order, in tokamaks L is in the order of meters, in neon lamps L is in he order of centimeters...and so on.
The condition L>>ld is one of the 3 criteria that separates a common ionized gas from a plasma. The other 2 criteria are:
Nd>>1
wt>1
Where Nd is THE plasma parameter (number of charged particles in a spherical volume of radius ld), w is the frequency of typical plasma oscilation, and t is themean time between collisions.

I hope i was clear enough.=D

6. May 5, 2010

### jasonRF

Previous posts are good. Another resource is the free book from Richard Fitzpatrick:

http://farside.ph.utexas.edu/teaching/plasma/380.pdf

see section 1.6. This is a very nice book. HIs derivation uses teh fact that for the vast majority of plasmas ("weakly coupled" - see section 1.7), classical statistics apply, and furthermore $$e \phi << k T$$.

I'm guessing your prof. means that the length scales you care about are much larger than a Debye length. This statement holds for hte vast majority of plasma physics.

jason

7. May 5, 2010

### LuisVela

Thanks for the pdf.
Looks promising =D