Re: Magnifer vs. Tesla Coil

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

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

Antonio wrote:
 > These "wave modes" make some sense, however, if the voltage profile
 > along the secondary-tertiary system when the output voltage is
 > maximum is considered.

Yes, they arise from considering the electrical length of the
secondary-tertiary-topload path.  Divide by 90 degrees to get the
number of 'quarter waves'.

With the heavily toploaded maggy, the topload itself takes up most of
90 degrees, at all resonant modes. Thus the quarter wave mode shows
almost uniform current along the secondary-tertiary and the 3/4 wave
mode looks more like a half-wave, with the voltage peak appearing
around half way along the secondary-tertiary electrical length.

Just how that electrical length divides up between the physical
lengths of the two coils depends on h/d ratios, heights above ground,
and turn counts, that sort of thing.

 > I would say the first zero (of voltage) of the 3/4 wave mode at
 > the transmission line.

No, the voltage zero of this mode is not far below the topload,
and the voltage peak is about half way.  Ideally, the voltage peak of
the 3/4 wave adds to the 1/4 wave mode giving an instantaneous zero
volts on the transmission line, coincident with peak topvolts.
In this 'perfect tuning' scenario, both 1/4 wave and 3/4 wave modes
peak together in the time domain.  On the transmission line they sum
to zero, but on the topload they sum to a peak (because the 3/4 wave
mode has an extra half-wave of electrical length in between, so is
inverted at the top wrt to the transmission line).

Hope that makes sense!  I think this distributed description is
equivalent to the lumped model tuned for complete energy transfer to
the topload, in terms of the relative phases of the three normal modes
involved:
   a) All three peak simultaneously, and at that instant...
   b) sum to zero on the t-line,
   c) zero on Cpri,
   d) no current anywhere,
   e) and a max volts on the topload.

 > And there is no need of a special relation between the inductances
 > of dimensions of the secondary and tertiary coils (many are possible).

I think the 3/4 wave voltage peak can be positioned on the transmission
line by suitable choice of h/d and turns.
Whether that does any good or not...

Perhaps I should prepare some animations of the voltage/current
distributions along the maggy.  That would make things a lot clearer,
I think, for many of the list members interested in maggy operation.
A picture says a thousand words, or something.  It's really a lot
simpler than it all sounds!!

The top voltage of the maggy, in which the 3/4 wave mode is supported
on the pedestal of the 1/4 wave beat waveform, might turn out to
be beneficial to streamer formation - due to the extra heating
effect of the higher frequency current.  Could it be that the large
1/4 wave voltage provides the main impetus for streamer extension,
and the 3/4 wave ripple into the streamer capacitance (at quite a low
impedance from the topload [*]) serves then to get the channels nicely
heated up?

Some basic questions about maggies that need to be answered:

1/ Is there any point to tuning so that the 3/4 wave voltage peak is
    on the transmission line.
2/ Should the maggy be designed to enhance relative amplitude of the
    3/4 wave mode, ie is this mode beneficial, or is it just something
    to be contained efficiently?
3/ Does the relative phase of 1/4 and 3/4 wave modes actually matter,
    ie do they really need to come together to peak at the same time?
    Perhaps only the relative 3/4 mode *amplitude* is significant, if
    at all?

Some food for thought there.  One day I'll stitch the integral
operators for the three coils together to produce a single matrix
whose eigenvectors are the overall voltage/current distributions [+].
That would tell us precisely what's going on 'in the coils', but it
still brings us up against the usual brick wall of topload-streamer
interaction.

 >> So, the magnifier, if you want a definition, is a means to control
 >> and exploit the 3/4 wave mode which would otherwise be a nuisance
 >> if left to take care of itself - the nuisance being energy wasted
 >> and racing arcs.

 > A nice interpretation.

So do we exploit, or merely contain the 3rd mode?  That's the crux
of the issue with maggies, I think.   Design pivots around this
point - which way does it tip in the real world?  Once again, I think
it comes back to understanding the topload-streamer relation.

One thing for sure, the topology of a maggie is just a perfect
recipe for producing bags of the 3rd mode in a distributed model.
But is that the hidden intent of the real system?

[*] The severely shortened top 1/4 wave of the 3/4 wave mode makes
     the topload quite a low impedance 'source' at that mode.

[+] Fredholm integral operators transform voltage distribution
     'vectors' into current distributions, and vice versa.  The
     eigenvectors of the 'round-trip' operator are the normal modes of
     the resonator.  These operators are parameterised by a complex
     frequency, and the complex frequencies at which the eigenvectors
     occur give us the resonant frequencies and decay rates of each
     mode. A least squares fit allocates mode amplitudes and phases
     to match the initial 'firing' conditions of the resonator. The
     subsequent time domain evolution is then trivial to compute.
-
Paul Nicholson
Manchester, UK
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