From: Michael Motyka <mmotyka@lsil.com>
Date: Sat, 7 Nov 1998 08:11:27 +0800
To: cypherpunks@EINSTEIN.ssz.com
Subject: Re: Grounding (fwd)
Message-ID: <3643312D.5C2@lsil.com>
MIME-Version: 1.0
Content-Type: text/plain



OMYGAWD!

I can see that I'll have to give up soon.

> The solutions to the wave equation inside the cavity have a real part ~0
> in the exponent.
***
It's not a question of a Schroedingers Wave Equation, it's a question of
Maxwell's Equations. 
***

Yeah I've got my old copy of Jackson. MTW too, for all the good it did
me. Maxwell's equations can be used to form a wave equation too. I only
bring up the Schroedinger equation because the solutions to simple
particle-in-a-box examples are easy to generate and easy to visualize.
Anyone who even began a decent Physics program should have done many of
these. The probability function for the Quantum example *looks like* the
amplitude for the EM example...analogy is a good tool.

> The boundary condition at the inside surface of the
> copper box splices together the solutions in the cavity and inside the
> conductor.

***
What conductor? The shell is equipotential unless you're trying to play
head
games with me so there follows there can be no current flow through it
except radialy to the outside of the sphere.
***
DC, Yes. AC, things are happening.

To solve the diffeq's for an EM wave incident on a conducting surface
you have to make the solutions !inside! the conductor match the
solutions outside the conductor. Only if the conductor is *perfect* does
your assumption of nothing going on inside the conductor make sense.

BTW - the skin depth for Cu at 100MHz is about 0.00026". The skin depth
is proportional to f^(-0.5).

In brief, here's what happens to the wave incident on a copper sheet:
Wave is incident on surface
Most of the wave is reflected
  the better the conductor, the more is reflected
the portion that is not reflected is attenuated in the conductor ( loss
)
any amplitude on the other surface of the sheet radiates energy.

It should be obvious that, if the conductor is good, there will be very
little amplititude inside the conductor, low loss reflection. Further,
that 4 mils of Cu should provide ~80 dB loss in even the tiny amount
that is not reflected at the inner surface. At 100MHz. I haven't solved
this system for many years and I'm not inclined to go back to it now.
Take my word for it : a little RF can get through a copper sheet but
only a *very* little. It's the finite conductivity that alters the
simple scenario.

***
Let's walk through it using your model....

The spark gap generates sparks and that builds up free electrons in the
space inside the sphere (whether it is gas filled or a vacuum is
irrelevant). As that charge builds up it will be all of one type,
electrons.
Now the electrons repel each other and therefor move in a circular
motion
with the spark gap as the center. They strike the surface of the sphere
and
tunnel through to the outside surface where they reside. The amount of
charge at any one point is related to the curvature of the surface at
that
point. Since a sphere is constant curvature the charge will be evenly
distributed. It will continue to build up so long as you supply power to
the
spark gap. In an ideal world it will get bigger and bigger. In the real
world at some point insulation breaks down and normal current flow takes
place.
***
Wild!

Forget all this, this patchwork of pieces doesn't hold together as a
description of the physical problem. If it helps, forget about the spark
gap. Waves waves waves. Start with a wave packet in the box. Don't worry
about how it got there. Worry about keeping it there.

Best regards Jim,
Mike