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Corum's Resonator Theory
From: Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: Thursday, October 30, 1997 6:03 PM
To: tesla-at-pupman-dot-com
Subject: Corum's Resonator Theory
Hello All,
After some cogitating and some discussion with Kenneth
Corum, I now understand where they are coming from when comparing
lumped vs distributed theory. Before I launch into this, please note
that (a) I am assuming *no* topload for the resonator, and (b) no
spark is issued from the resonator under any conditions (see
"problems" below). Assuming these two points, here are the basic
ideas:
(1) The claim is made that in the two-coil system while the primary
is coupled to the secondary (spark gap conducting), the resonator
current is uniform (i.e. current is the same at every point along the
resonator). Now I am at a loss to see how that can be given (a) that
the coupling to the primary is vastly lower at the top than the
bottom, and (b), in a resonator without topload, how a current equal
to base current can be present in the top turns. Let's suppose anyway.
Suppose the current is uniform. Then the voltage increase along
the resonator is a linear one i.e. voltage linearly increases from
bottom to top while the current is the same. That voltage gradient is
entirely reasonable if one considers that a current through a portion
of L generates a voltage across that L. In this situation, it is clear
that energy is evenly distributed throughout the resonator (according
to E = 0.5Li^2 where one considers the resonator to be devoid of any
self capacitance. Unfortunately it does have capacitance distributed
along its length. Exactly how that capacitance is distributed is a
matter of contention. However, the Corums are modelling the resonator
as a uniform line so let us suppose that it consists of equal L and C
sections. Now it is clear that energy under conditions of uniform
current must be lumped towards the top end because one can sum Li^2
and CV^2 for each portion and the sums are different if one considers
the bottom vs the top. Hence, one can say that for this model under
coupled conditions, energy is not evenly distributed *even if the
current is uniform*.
It seems to me to be highly important now that the actual current
distribution under coupled conditions is definitively measured for
once and for all to establish the truth of this picture. Ken Corum
tells me that one should disregard the uneven coupling and simply
think about the resonator as being very much shorter than the
wavelength so all portions of the resonator are immersed in the
primary field - hence the uniform current. Anyone here buy that
argument? Anyone here measured current in different portions of the
resonator when it is coupled to the primary?
(2) Now we go from the coupled to non-coupled situation. Here is what
they are saying happens (and why the resonator differs from a lumped
circuit). The spark goes out, and at the instant it does so, the V-I
distribution as outlined above is present. Suddenly the resonator is
no longer gripped by the primary. Now, *supposing* that the current
*was* uniform, what happens next? Well, the idea is that over some
period of time depending on the propagation delay along the length of
the resonator, the current *now* becomes NON-UNIFORM. That is, it now
assumes a maximum at the base and a minimum at the top. If it does so
re-arrange itself, what happens to the voltage distribution? Now if
we look at the Ldi/dt scenario, most of the voltage rise will be in
the bottom turns with virtually none at the top. In other words, the
rise going up from the base is huge and tapers off as one reaches the
top. Energy has now evened itself out over the resonator length, at
least that is the picture I get. Voltage distribution is no longer
linear but is now sinsoidal. But we still have the same total energy
in the resonator.
I would be obliged to the mathematicians among us if they could
quantify how voltage at the top might now be different under these
conditions.
Problems as I see them:
(1) I don't think anyone has actually measured current distribution
under coupled conditions (or have they?). Please let us know if so.
It is crucial to this model to know whether k influences current
in different portions of the resonator or not. It is also crucial
to know whether one really can have as much current in the top turns
*even with what capacitive loading there is*. Mr Corum dismissed the
coupling argument and ignored the second despite being asked twice.
We do *know* that k is an order of magnitude less between the primary
an top turns and the primary and bottom turns in general terms.
(2) No breakout under these conditions is a total piece of fiction
when it comes to practice IMHO. Is MHO wrong? Anyone ever prevented
breakout from a piece of wire at XXX,000 Volts?
(3) The re-arrangement of current (which it is claimed would result
in a voltage rise over the lumped situation) has not been observed by
anyone I know. Personally I have captured waveforms using a
storage scope many, many times and not once have I ever seen a
hint of this, breakout conditions or no. In fact, I will touch on
this problem in point (4) below. Perhaps someone has seen it.
If so, please, please post.
(4) As most will be aware, trying to quench a gap under no breakout
conditions is a notoriously difficult exercise. However, the
implication is that a voltage rise should be observed *any time* the
gap is quenched, no matter how little energy remains as long as it is
not zero. Once again, has anyone ever seen it?
According to Mr Corum, it is this extra rise that is the secret
of a "true" Tesla Coil. I repeatedly queried him on quench issues and
came up against a brick wall in trying to extract an answer. How many
people who have examined coil waveforms in minute detail believe that
you can cut a gap off when all the energy remains bottled up in the
system (e.g. ideal first notch quench without discharge)? If Mr C's
theory is correct and this can be done, then I think we are in for a
treat. If not...... None of my coils have ever done it including the
one with the difficult-to-break-out-of topload I posted on in the
last couple of days. In attempting to do this, I blew a *jet* of
compressed air through the gap. No voltage rise was observed on the
scope from the time the gap was cutoff and to make matters worse, the
gap losses roughly doubled according to both a discharge test and
the scope not to mention the gap flame and noise.
If anyone has observations, measurements, comments etc. I for one
would love to hear them. This post is done as much to advance my own
understanding as it is an attempt to clarify the issues. I would just
like to observe two things - the distributed model fails to predict
the resonant frequency if one uses lumped L and lumped C, and from
the diagrams I have seen in the Corum's papers, they are considering
a *balanced* line as a model. Does that make any difference? (I plead
with those into scalar theory not to make an issue of this). Mr Corum
states that Maxwell and other conventional engineering theory are all
that is needed to predict resonator behaviour.
Thanks for listening,
Malcolm