Talk:Electric field screening
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Note on the Validity of the Debye Screening Theory
The assumption of a Boltzmann energy distribution (i.e. a barometric height formula) in the Debye-Hückel theory implies a collisionally dominated isothermal situation where the pressure gradient exactly cancels the force due to the electric field. This non-vanishing potential is therefore the consequence of the implicit assumption of collisions in Thermodynamic Equilibrium preventing the purely electrostatic screening which would hold in a collisionless plasma. However, collisions (and the related pressure forces) should only be relevant in a plasma if the collision frequency is higher than the plasma frequency (which determines the timescale for the electrostatic re-arrangement of charges). Unless one is dealing with a very low degree of ionization, this condition is only satisfied for extremely high plasma densities as encountered in solids, fluids or the interior of the sun.
It is clear that in almost all cases of practical interest, a force free steady-state situation can only exist if the electric field is exactly zero within the whole plasma. This is obviously only possible if the test charge is directly neutralized at its surface by charges that have been attracted from the plasma. Charge neutrality within the volume is hereby conserved by the electrons slightly contracting towards the center, which leaves therefore the positive charge excess at the surface of the plasma volume (as one would expect for a conducting medium).
In addition, one should note that for near collisionless plasmas not only will the assumption of TE be invalid (as indicated above), but also the approximation of a Local Thermodynamic Equilibrium (LTE), i.e. the velocity distribution function may become non-Maxwellian due to diffusion effects in the presence of spatial inhomogeneities. This in turn will produce self-consistent electric fields which serve to adjust the electron flux balance as to maintain local charge neutrality. These plasma polarization fields are obviously not being screened by the plasma, as they are themselves the result of the dynamical imbalance between electrons and ions. In general, a consideration of the force balance is therefore not appropriate, but one has to consider the flux balance of particles (this is how one treats for instance the well known problem of spacecraft charging).
For related aspects see my website http://www.plasmaphysics.org.uk