Re: Magnifer vs. Tesla Coil

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk>

 > Many thanks for the figures from mrn6.  Things are beginning to
 > become much clearer with regard to how the lumped and distributed
 > models coincide.   And coincide they must, if they are both correctly
 > implemented (which I think they both are).

Nice simulations. Note that the middle frequency is always the
resonance frequency of the L3-C3 system alone. So, if we consider
this to be "the" resonance frequency of the magnifier, then the
third coil operates in 1/4 wave mode, and the secondary coil
operates in 1/2 wave mode. No relation to the secondary being
a voltage source driving the third coil, as sometimes mentioned
(the voltage there is always zero at the central frequency).

 > I'll just summarise the primary voltage of each mode at t=0:
 >
 >   mode 1: 16 kV
 >   mode 2:  7 kV
 >   mode 3:  6 kV
 >
 > These add up to 29kV which is close to the firing voltage of 30kV.
 > In fact, it should add up exactly to 30kV, and the difference is made
 > up from all the other higher modes which are excited by the firing,
 > modes 4, 5, 6... etc.
 >
 > Similary, note the top voltage at t=0:
 >
 >   mode 1: -200kV
 >   mode 2:  220kV
 >   mode 3:  -30kV
 >
 > which together add to -10kV. Again the precise value is zero and
 > introducing further higher modes makes up the difference.
 >
 > The crucial point is that in any firing, the modes are excited in
 > just the right mix of amplitudes to ensure that Vpri equals the
 > firing voltage; that Vtop equals zero; and also for everywhere else
 > on the resonator - that the initial conditions are matched by the sum
 > of all the modes.  This is a strict enough condition to determine all
 > the mode amplitudes.

In fact, the components of the output are a quite simple function of
the resonance frequencies. See my paper:
http://www.coe.ufrj.br/~acmq/papers/mress01.pdf

 >   http://www.abelian.demon.co.uk/tmp/mag1.anim.gif
 >
 > which accounts for all resonant modes up to around 3Mhz.

A lossless model, I imagine.

 > I wonder if the lumped model predicts similar proportions for the
 > mode energies.  I suspect things would be a little different if the
 > model was tuned properly.

See the paper above. The relation depends on the resonance frequencies.

 > At this stage it would be nice to apply the distributed model to
 > reproduce the behaviour of some particular real magnifier.  It would
 > be great to examine a system which was known to produce good or
 > exceptional spark performance.

There is my magnifier:
http://www.coe.ufrj.br/~acmq/tesla/mag345.html
It didn't work very well due to the lossy C2, but I have the
experimental
waveforms at low power listed and all dimensions.

Antonio Carlos M. de Queiroz