RE: Mega-Sized Secondaries

[paul-at-xxxxxxxxxxxxxxxxxxx (by way of Terry Fritz <twftesla-at-xxxxxxxxxx>)]

John Couture wrote:

> I understand that you are saying there are other losses.  What are
> these losses and the equations to find them?

I should make clear that I've not introduced any additional source
of dissipative loss, I assume you mean loss of current between
base and top. 

> You mentioned Maxwell's displacement currents. Maxwell said these
> currents can only exist during the "variation" of the electric
> displacement.

Yep,

> I take this to mean that the currents would be negligible because the
> variation time would be almost instantaneous.

No, this is the C dV/dt current through a capacitance that I'm sure
you'll be familiar with. One way or another the entire base current
(in the absence of breakout) ends up as a displacement current in some
capacitance, either the distributed capacitance of the coil, or the
capacitance of the topload. 

> But how would you test a Tesla coil to prove this conclusion?

Measure the base current and the current flowing into the topload and
see the difference. Terry Fritz has demonstrated the necessary
techniques and describes a set of results in

 http://users.better-dot-org/tfritz/site/papers/modact/modact.html

in which he also compares the results with the predictions of a 
lumped equivalent model.
 
> Maxwell compared electric displacement to the displacement of elastic
> bodies in the mechanical world. The force in this case would cover
> much longer periods of time and the work done would not be negligible.

A fair comparison, up to a point. The work done in charge displacement
is equal to the stored energy 0.5 CV^2, (assuming the displacement is
perfectly elastic, ie loss-free) regardless of the time taken to carry
out the displacement.

If the moderator will permit a slight digression...

Maxwell's invention of displacement current was truly a most awesome
leap.  The conductor leading into a capacitor has a magnetic field
wrapped around it (Ampere's law) and so does the outgoing conductor,
but what about the gap in the middle?  In trying to find a unified
mathematical framework for the various empirically derived laws of the
time, Maxwell realised this could only be done if he supposed that the
charge displacement across the gap was equivalent to some sort of
'current' flowing through the gap, to which Ampere's law also applied.
>From this inspired (and controversial) idea, it would probably have
taken just an evening's works for this lone Scottish mathematician to
develop the consequences - the electromagnetic wave.  This was so far
ahead of its time that 25 years elapsed before Hertz was able to
demonstrate its existence.  Some forty years later, a subtle feature of
Maxwell's equations led directly to a certain well known fellow revising
our basic ideas of space and time, and as a result, we now understand
that magnetic fields don't really exist - they're just a consequence of
the electric field being seen through a modified spacetime!

FYI,
http://www.physics.gla.ac.uk/introPhy/Famous/maxwell/maxwell.html
http://www.treasure-troves-dot-com/physics/DisplacementCurrent.html
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter35/chapter35.html

Thanks Daftie, we owe you!

Regards,
--
Paul Nicholson,
Manchester, UK.
--