Interpretation of the Debye length

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Discussion Overview

The discussion revolves around the concept of Debye length, particularly in the context of plasma physics. Participants explore its definition, derivation, and the implications of screening effects in different temperature regimes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the definition of Debye length, suggesting it relates to the distance at which the potential of a charge falls by 1/e.
  • Another participant confirms this understanding and introduces the concept of a mean field approximation for the screened Coulomb interaction.
  • There is a question regarding the context of screening, specifically whether it pertains to zero temperature in metals or finite temperature in plasmas, with a focus on the latter being expressed by one participant.
  • A later reply emphasizes the use of Poisson's equation to connect potential and density, and mentions Boltzmann's equation as a means to relate density to potential.

Areas of Agreement / Disagreement

Participants generally agree on the basic definition of Debye length and its relation to screening effects, but there is no consensus on the specific methods or contexts for deriving it, particularly regarding temperature conditions.

Contextual Notes

The discussion includes references to different screening conditions (zero temperature vs. finite temperature) and the mathematical relationships involved, but does not resolve the complexities or assumptions inherent in these approaches.

ian2012
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What exactly is the Debye length?

From what I understand, when a charge q>0 is shielded by an electron cloud, then the Debye length is the distance the potential of the charge q falls by 1/e. Is it that simple?
Furthermore, how do you go about deriving the expression:

[tex]\lambda_D=\sqrt{\frac{\epsilon_0 \kappa_B T_e}{n_e e^{2}}}[/tex]
 
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Yes, that's right. The screened coulomb interaction represents some sort of average or mean field approximation to the induced field due to a point charge.

Are you interested in zero temperature screening in a metal or finite temperature screening in a plasma? In either case, the basic method for determing the potential is a self consistent method. The density determines the potential via Poisson's equation and the field determines the density in terms of the compressibility [tex]dn/d\mu[/tex] or the Boltzmann equation for probability, roughly speaking.
 
Physics Monkey said:
Are you interested in zero temperature screening in a metal or finite temperature screening in a plasma?

Thanks for your response and it is screening in a plasma i am interested in.
 
Then you can use Poisson's equation to relate the potential to the density and Boltzmann's equation to relate the density to the potential. Also, dimensional analysis tells you a lot.
 

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