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Re: Magnifier system
Hello Jeff,
You ask....
> From what I have read, I thought the secondary coil could be
> electrically modelled as a series RLC circuit in some sense because
> of the way it behaves when driven at different frequencies.
Adding a large topload is lumping capacitance at one end so the
system does tend to a series RLC. It wouldn't be pure RLC series
unless all secondary Cself was eliminated (impossible). Also, since
the primary couples mostly into the bottom end of the resonator,
waves propagate up and down the structure.
> And to
> get maximum output voltage at the terminal, we should drive it at
> the 1/4 wavelength frequency to produce a voltage maximum at the
> terminal, but you pointed out that this is the electrical length of
> the wire (not physical) when we wind up the coil. So how exactly is
> electrical length mathematically determined?
As a matter of convenience I use the quantities that appear to us as
inductance and capacitance to predict the fundamental vibrational mode
of the coil. They work well in practice. However, as the Corum's
have shown, these things can be shown even more convincingly by
examining the structure as a waveguide. I have serious doubts whether
their predicted voltages for cap discharge systems are correct though.
After all the discussion on conservation of energy recently I don't
think you can ignore the fact that there is real measurable
capacitance in the system and there is a fundamental limit on the
voltage that can be obtained with a given amount of energy. Here's
an interesting one to consider: We can measure the coil inductance
with a fair degree of accuracy as a lump, and lo and behold, when we
apply Medhurst's Cself formula, we find that the lumped L and Cself
tell us with a good degree of accuracy what the fundamental resonant
frequency will be. BUT, the inductance is not all effective in
practice for a resonator with no topload. Consider: current in the top
turns is all but zero, so not all the L is effectively there. What is
the actual Cself then that makes the coil resonate as though our
calculations suggest it is? I think this is where the Corum's view of
things departs from the recipe approach and more accurately describes
resonator action (more said below).
You mention: > > >Mutual inductance
> >between turns gives uo a multiplier and the huge drop in physical
> >length of the coil (winding height) over the longwire considerably
> >reduces the capacitance of the structure, so much so in fact that
> >the increase in inductance is insufficient to compensate for the drop
> >in capacitance for the actual wirelength to resonate as though it were
> >an isolated longwire.
>
> How is uo multiplied?
By mutual inductance between turns. No significant equivalent coupling
exists for a longwire between portions of its length.
> And isn't the capacitance due to the effect of the
> wire or loops of the wire above ground?
Experiments I and others have done suggest the coil self-C is that of
a (not-so-well) isolated cylinder - i.e. inter-turn capacitance
doesn't count. What I read in the Colorado Springs Notes suggests
Tesla didn't understand this, at least initially. He thought of
various schemes to reduce Cself which, had interturn capacitance been
the culprit should have worked. If you look up the coil, each turn is
shielded from all but its immediate neighbors above and below so you
have a stack of tiny capacitances in series. The bottom turn appears
to have quite significant coupling with ground as it has no effective
shielding below it.
> And for the magnifier system, how exactly does this system multiply
> the base fed input voltage to produce a higher output voltage?
NOTE TO ALL: What I'm about to say here is my opinion, is not fixed
in concrete (yet), and is open to any other opinion that explains
things better. It's a bit wordy since I use such opportunites to get
get my own thoughts in order and also submit these to peer review for
critical examination. I am not afraid of being found incorrect so all
views welcomed.
It is important first to note that what is presented to the base
of the resonator is not just voltage but current as well.
Both the resonator used as a TC secondary and magnifier are the
same and accumulate whatever energy is imparted by the
primary/oscillator by wave action.
The bottom turn in each has the highest current of all turns
since it subjected to the greatest capacitive loading of all turns.
As you travel up the winding, the loading becomes progressively less
and if you have no terminal, the top turns pass virtually no current
at all (under no spark conditions). Each turn is inducing a current in
its neighbours and hence voltage across its neighbours. IMO the
volts/turn should be rather high at the base and virtually nil at the
top, but the sum of the voltages is great, and there is a volt/turn
gradient that tapers off as one reaches the top of the winding i.e.
the top turn barely contributes. I should note here that an analysis
by Greg Leyh suggests that mutual inductance between the turns does
not greatly contribute though and I'd be very interested to hear what
he has to say about this.
It is my opinion that the magnifier and standard two coil system
should show equal outputs *if* they can be coupled to their driving
systems by the same degree. The reason for that contention is that
in each system with the same bang energy and gap losses (all other
losses being minimized), gap losses are reduced for tight coupling by
virtue of the fact that it takes fewer cycles for the energy to be
transferred to the resonator. I also assume that we are talking equal
capacitance in the resonator systems. A smaller resonator is going to
have a smaller Cself than a large one so should develop higher
voltages for a given lump of transferred energy. This could be part of
the reason for MAG #11- E's amazing performance.
I suspect that there are also considerable differences in
resonator behaviour in the two systems. The classic 2-coil system
exhibits all the characteristics of any double-tuned circuit system,
namely side frequency generation and the upper frequency can excite
the resonator to a voltage maximum part way down. I think it possible
that choosing k carefully may minimize the chance of this happening
because some resonator vibrational modes are favoured over others, the
determining factor being reflections from the top end. This something
that begs a serious investigation.
However, an end-fed resonator should not produce this frequency
split since it is not e.m. coupled so winding flashovers should be
less of a problem for a given rate of energy transfer. Another one to
check out with the scope.
In practice, mag drivers can use very tight coupling because
the driver prim/sec is fundamentally a transformer and built to
withstand the strain of a high volt/turn gradient over the whole
winding whereas the close turns in the resonator won't permit this
without seriously bolstered insulation. K's of 0.65 have been reached
in specially built accelerator coils however so it can be done.
It is also important to remember that in the magnifier system,
the base of the resonator is already at a very high voltage so less
of a voltage across the resonator itself needs to be developed for
the same total output voltage.
Spark output from any system is not dependent on voltage alone.
Channel heating (current) and duty cycle (average power throughput)
also play an important role in generating long sparks.
I must try the following too (IMO it should work): charging a
capacitor with one end connected to ground and discharging the other
end through a gap to the bottom of the resonator should do similar
things to a transformer driver circuit (don't try this with a
normal Tesla power supply - there is *NO* isolation between the
resonator and the 60 Hz circuitry).
Finally, I welcome comments on this analogy. Imagine
the resonator as being like a beach. As one moves from bottom to top
(deep to shallow), wave tops get higher and higher as the energy
moves from the deep to the shallows. Unlike the resonator, the
distance from deep to the shallows is considerably greater than a
wavelength for a beach so the beach behaves more like a transmissive
medium than a resonator (where energy is being bounced between two
ends). It might go some way to showing how wave amplitude builds as
energy travels from bottom to top though.
Jeff, thanks for asking some very interesting questions.
Leaving the field wide open for comment, criticism and experimental
evidence,
Malcolm
PS - I will be measuring spectral characteristics of mag systems
before the year is out so hope to answer some of the questions above.