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 P: n/a On Jan 4, 2:09 am, Thomas Smid wrote: > On 2 Jan, 10:54, "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