# Re: What are Debye potentials?

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

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

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