Re: Explanation of K

["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>

Jason Petrou wrote:

> A very high coupling will mean a fast energy transfer,
> but a great potential difference in the secondary. The fast
> rising difference between the top and the bottom of the coil
> causes the racing arcs. The trick is to couple as tightly as
> possible without racing arcs.

Antonio Carlos M. de Queiroz wrote:

> Allow me to disagree with the last two phrases. If you look at
> the waveforms deduced from the lumped model, there is no
> significant difference in rising time, dv/dt, di/dt, etc.,
> anywhere in the system when the coupling is high.
> "Racing sparks" can't be caused by this, at least not directly.

Antonio, don't forget, real coils don't follow the lumped model,
and it is dv/dx not dv/dt that you have to worry about.

Over-couple a Tesla secondary and you start to get significant
amount of higher mode excitation.  (See base current waveform
in http://www.abelian.demon.co.uk/tssp/tmod.html)

This may provide a mechanism for dv/dx to exceed the turn-turn
breakdown at some point on the coil.

Consider the consequences of, say, the 5/4 wave mode having 10%
the amplitude of the fundamental modes.  This puts 10% of the
top volts across 20% of the coil, thus adding up to 50% to the
existing dv/dx of the fundamentals.

For those wondering what higher mode excitation is:  take an object
such as a metal or wooden bar, or guitar string, and strike it.
You don't get a pure note, you get a more or less rich tone 
containing several sound frequencies - the precise mix depends on
the material and its geometry.  Bass guitar players will be well
aware of the difference in tone between plucking the strings
near the bridge, and plucking further along towards the neck.
The former case gives you much more of these 'higher modes'.

Similar occurs when a Tesla secondary is 'struck' into resonance
by an impulsed primary.  For a typical TC, the higher modes are
less than 5% of the fundamental amplitude.  Increasing the 
coupling raises this fraction.  Although it is by no means
proved, there is at least the possibility that this mechanism
can enable localised breakdown of the secondary, even in situations
when the v/turn appears to be within safe limits according to the
lumped model. 

The higher mode frequencies and their amplitudes can be calculated
very accurately (they are not harmonically related) by a careful
and thorough distributed analysis of the secondary,

http://www.abelian.demon.co.uk/tssp/pn2511.html
http://www.abelian.demon.co.uk/tssp/pn1401.html
http://www.abelian.demon.co.uk/tssp/tests.html

(the pn1401 document still a work-in-progress).

For more waveforms - a closer look at the higher modes of Marco's
Thor system, see

  http://www.abelian.demon.co.uk/tssp/md110701/

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