Talk:Electric-field screening
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
- Okay, this is all WAY over my head here, but I want to ask something to help my understanding. Is this screening process the phenomena that caused the merging and and diverging of forces at the Beginning of the universe or is this a different thing? Reading articles like Relativistic Heavy Ion Collider tend to make me believe that is the case. But this still seems irrelevant of two forces becoming one or a force splitting into different forces. I would imagine that the issues in cosmology deal with plasmas that are screened for different forces depending on the time and thus temperature, but perhaps the more specific claims of "this force existed after this time in the history of the Universe" would be due to a different cause. I really don't know, which would it be? Does my question even make sense? theanphibian 07:11, 15 May 2007 (UTC)
I really dont like the mixture of Nabla Operators and Delta as difference indicator, since it also could mean the Laplacian. [bernhard]
Hello,
I don't think the references to the astrophysics are very well written in the introduction part. Especially where it says 'this is a relevant topic for astrophysics'.
I am making some minor changes. Please leave a message if you want to discuss this further.
LudwigBoltzmann (talk) 00:54, 31 October 2008 (UTC)
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Coulomb Force Equation
[edit]Subject: suggested term definition clarifying for this equation.
There is a Coulomb Force Equation symbol clarity issue in Wiki articles. It arises from unit vector symbol formatting. Your article is where I first became aware of the confusion potential (pun intended!). Consider the following format aspects of this equation with respect to q1 - q2 separation distance r.
One common Coulomb equation format uses the vector r divided by the scalar r cubed. The denominator scalar r is cubed, instead of squared (as in the scalar form of the equation), because the numerator r vector is the scalar r with direction. Absolute value brackets are not used.
The article Coulomb equation format uses a unit vector in place of the r vector and squares r in the denominator. The symbol r with ^ is used for the unit vector. I suggest use e ^ instead (al a Feynman) for the unit vector. Also, it would not be remiss to define e ^ (i.e., e^ = e / abs(e). [In appropriate Wiki format of course, which I do not know! My bad.]