Interpretation of the Debye length

[ian2012]

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:

$$\lambda_D=\sqrt{\frac{\epsilon_0 \kappa_B T_e}{n_e e^{2}}}$$

 

[Physics Monkey]

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 $$dn/d\mu$$ or the Boltzmann equation for probability, roughly speaking.

 

[ian2012]

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.

 

[Physics Monkey]

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.