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PuZHANG0702@gmail.com
#6
Jan8-08, 05:00 AM
P: n/a
On Jan 4, 2:09 am, Thomas Smid <thomas.s...@gmail.com> wrote:
> On 2 Jan, 10:54, "PuZHANG0...@gmail.com" <PuZHANG0...@gmail.com>
> wrote:
>
>
>
> > Dear all,

>
> > Happy new year!

>
> > I'd like to get a clear concept of Debye potentials.
> > For the sake of this, I searched around the internet and
> > checked several classic textbooks, like Jackson's and
> > Stratton's, but no satisfactory results. Instead I get
> > several papers describing Debye potentials published
> > decades before ("Debye potential representation of
> > vector fields").

>
> > From those papers I find out that:
> > Debye potentials have something to do with the special
> > case of Helmholtz Theorem with divergenceless vector
> > fields. It's proved then this field can be represented by
> > two scalar potentials:
> > F = L=F8 + curl(L=F7),
> > where F is the vector field and L is the standard orbital
> > angular momentum operator. It's said these two scalar
> > potentials are Debye potentials. (Is this obsolete? Why
> > isn't there any like content in today's textbooks)

>
> > Except this I also get various descriptions, but I can't
> > figure out a unified idea. Could anyone suggest some
> > detailed reading?

>
> > BTW, it seems that Debye potentials have close
> > relation with multipole expansion. Is this true and what's
> > that?

>
> > Thanks for any reply!

>
> Hi,
>
> In plasma physics, the Debye potential is the potential arising from
> the screening of a test charge by the free charges in the plasma (seehttp://farside.ph.utexas.edu/teaching/plasma/lectures/node7.html).
>
> Note however that a fundamental assumption in this derivation is the
> existence of a thermodynamic equlibrium i.e. a Boltzmann energy
> distribution. This implies a collisionally dominated isothermal
> situation where the pressure gradient exactly cancels the force due to
> the electric field. The Debye 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.
>
> Thomas


Thanks!

Actually the Debye potential I care is that related to Helmholtz
Theorem.

Now I'm clear what Debye potential is in my sense. Here's a list of
helpful
papers:
1, Debye potential representation of vector fields
2, Multipole expansions of electromagnetic fields using Debye
potentials
3, Debye Potentials by Wilcox