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Interpretation of the Debye length

  1. Mar 13, 2010 #1
    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]
     
  2. jcsd
  3. Mar 13, 2010 #2

    Physics Monkey

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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.
     
  4. Mar 13, 2010 #3
    Thanks for your response and it is screening in a plasma i am interested in.
     
  5. Mar 13, 2010 #4

    Physics Monkey

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    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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