Re: TC Secondary Currents - was ( Experimental Help - Terry?)

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Richard Wayne Wall wrote:

> Can you give an experimental reference to this mysterious
> magnetic field around this "displacement current"?

There's nothing mythical about displacement current, and it's
trivially easy to prove that it has its own magnetic field.
Simply turn on a radio.  If it receives a distant signal, then you
have proved the case: radio waves require Maxwell's displacement
current [*].

> Does anyone dispute there are longitudinal compression like ES
> forces in capacitors?

The definition of electric field is based on the force between
charges.  Those forces can be transferred to the material that hosts
the charges, and the result can be a very measureable force between
the plates of a cap.

John Couture wrote:
> What I am trying to do is determine how to use the measured
> secondary current to find the TC output of the secondary coil.

Output voltage?  Simply multiply the measured base current by the
equivalent series inductance (Les) of the coil.  Find Les from the
coil geometry using the formula in 
 http://www.abelian.demon.co.uk/tssp/formulae.html

> How should these currents be used to find the TC output energy.

Ah, you'll have to define TC output energy.  Presumably you will 
include arc and streamer energy, but do you consider energy 
dissipated in the surroundings as 'output' or 'loss'.  All depends on
what you're doing, I suppose.

> Overall efficiency = TC output/TC input

The designer of a museum coil will have a different definition of
'TC output' to that used by the designer of an ion motor.

Let's say you want to measure energy dissipated in the streamers 
around the topload.  Then you must capture a scope trace of the
current entering the topload from the coil, and multiply this by
another trace containing the top volts.  Integrate the product to
obtain the total energy dumped overboard by the topload.  If the
topload C where perfectly lossless, the topvolts V(t) would lag 
90 degrees behind the topload current I(t) (at each component
frequency) and the integral of V(t).I(t).dr would be zero over the
bang.

Needless to say, the above direct measurement would be very tricky.
With the impedances involved, any probing of the topload would 
introduce its own source of loss, and you would have to calibrate
away the phase shifts in each of the I and V measurement paths.
And then you'd still have to allow for the loss due to the tan(delta)
of the surroundings, which you would do by repeating the loss
measurement at a voltage level below breakout.

Indirect measurements could be made perhaps, by looking at the Q
factor at different power levels.  For TCs used as HV power supplies,
into a specific load impedance, we can, given a single measurement
of the small-signal unloaded Q, calculate quite accurately the power
transfer efficiency. 

Antonio wrote:
> Phasor analysis is only applicable to steady-state single-frequency
> sinusoidal signals.
> A Tesla coil operates with transients,

Yes. See
 http://www.abelian.demon.co.uk/tssp/pn2511.ps
for a look at the steady state analysis.  For the math behind the
transient response of a TC, see the first part of a work-in-progress,
 http://www.abelian.demon.co.uk/tssp/pn1401.ps
Integral operators appear to lend themselves very nicely to the 
description of the TC.

[*] My personal hero Maxwell.  A mathematician, he had a hard time
convincing folk that his proposed displacement current was a
feature of reality.  But the math involved was just too simple and
beautiful for nature to have missed the opportunity.  It was with
this discovery that the first cracks began to appear in the naive and
constrictive notion of an absolute space and time. IMO modern physics
began with Maxwell's displacement current - it was the time that
physics first started getting weird, and it's carried on getting a
lot weirder in the intervening 130 years! 
--
Paul Nicholson
--