# Re: What are Debye potentials?

*From*: "PuZHANG0702@xxxxxxxxx" <PuZHANG0702@xxxxxxxxx>*Date*: Mon, 7 Jan 2008 13:00:37 +0000 (UTC)

On Jan 4, 2:09 am, Thomas Smid <thomas.s...@xxxxxxxxx> wrote:

On 2 Jan, 10:54, "PuZHANG0...@xxxxxxxxx" <PuZHANG0...@xxxxxxxxx>

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

.

**References**:**What are Debye potentials?***From:*PuZHANG0702@xxxxxxxxx

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