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Plasmas generally do not contain strong electric fields in their
rest frames. The shielding of an external electric field from the
interior of a plasma can be viewed as a result of high plasma conductivity:
i.e., plasma current generally flows freely enough to short out interior electric fields.
However, it is more useful to consider the shielding as a dielectric
phenomena: i.e., it is the polarization of the plasma medium, and the
associated redistribution of space charge, which prevents penetration by an
external electric field. Not surprisingly, the lengthscale associated with such
shielding is the Debye length.
Let us consider the simplest possible example. Suppose that a quasineutral
plasma is sufficiently close to thermal equilibrium that its particle
densities are distributed according to the MaxwellBoltzmann law,

(11) 
where
is the electrostatic potential, and and
are constant. From
, it is clear that quasineutrality
requires the equilibrium potential to be a constant. Suppose that this
equilibrium potential is perturbed, by an amount ,
by a small, localized charge density
. The total
perturbed charge density is written

(12) 
Thus, Poisson's equation yields

(13) 
which reduces to

(14) 
If the perturbing charge density actually consists of a point charge , located
at the origin, so that
, then
the solution to the above equation is written

(15) 
Clearly, the Coulomb potential of the perturbing point charge is
shielded on distance scales longer than the Debye length by a shielding
cloud of approximate radius consisting of charge of the opposite sign.
Note that the above argument, by treating as a continuous function, implicitly
assumes that there are many particles in the shielding cloud. Actually,
Debye shielding remains statistically significant, and physical, in the
opposite limit in which the cloud is barely populated. In the latter case,
it is the
probability of observing charged particles within a Debye length of the
perturbing charge which is modified.
Next: Plasma Parameter
Up: Introduction
Previous: Plasma Frequency
Richard Fitzpatrick
20110331