Wave Guides: Understanding Reality

[quasar987]

There's something I don't understand about wave guides.

We assume a perfect conductor guide, so that the atenuation is total and instantaneous and $\vec{E}=0$ inside the guide. But the parallel component of E is continuous at the boundary, so just outside the conductor, $\vec{E}_{\parallel}=0$.

But I'm thiking, this can't be a good representation of reality! Because no conductor is truly a perfect conductor. The attenuation is never total or instantaneous. In truth, $\vec{E}_{\parallel}$ just inside the conductor must have the same value as $\vec{E}_{\parallel}$ just outside of it and such a non zero value is perfectly consistent with theory.

 

[physics girl phd]

The question you are asking really isn't particular to waveguides... what about the fields at a metal surface? There are all kinds of fun way to think about modeling a surface interface.

First -- Do you want to model the bulk via a free electron/jellium manner (the usual way to think of metals)? Do you want to model it like a "fluid" with some olmic damping or other things thrown in (magnetohydrodynamics)? Do you want to represent it as an array of electrons and atoms tied together, and therefore the electrons interact with the fields but are also in some harmonic-like potential well (better for insulators)?

Then -- How do the fields interact with the atoms? Do you want to model that classically, use a simple quantum treatment, use a many body theory like "hartree-fock", use something more complex like "density functional theory"?

Then -- Do you want the bulk to be a simple step interface to vaccum, or a smooth continuous profile? Those are reasonable, but probably still not quite accurate. (as that deals mostly with the perpendicular component of the fields.. and surely roughness affects the parallel components right??)

Eventually it usually comes down to picking a model, picking a profile, integrating the current density or charge density over that surface region(which are sources in Mawell's equations) and then looking at little guassian boxes or the like, as they cross this interface. What are your boundary conditions then?

Fun stuff, right? I think so!

 

[quasar987]

My problem is that even though perfect conductors do not exits, supposing that a given conducting guide has 0 resistivity doesn't produce a result that is even near reality. Because in the perfect conductor case, the boundary conditions are drastically different: E field is 0 inside for the perfect conductor while is drops continuously for the real one, and this does not impose the condition that E be 0 just outside the conductor.

 

[Meir Achuz]

The case for good, but not perfect, conducting walls is treated in most grad EM textbooks. E_parallel just outside the conductor is very small and falls quickly to zero inside the conductor. The small parallel component leads to
some energy loss at the conductor which results in attenuation of the wave.

 

[quasar987]

If the parallel component is small just outside the conductor like you say, then the perfect conductor approximation is good.

But why should it be small? Why couldn't it be just any size?!? I'd still be continuous!

 

[Meir Achuz]

Inside the conductor, E_par << B_par for a good conductor.
Since E_par is continuous, it must be << just outside.