Hi Ken,
The apparatus is basically a Tesla coil secondary wound on a trumpet-shaped
former instead of the usual cylindrical former. The purpose of the trumpet
shape is to make the radius of the winding change continuously and in a
mathematically controlled way from one end of the secondary to the other.
The important feature is that this is not simply a conical or tapered coil.
The proposed winding uses an exponential taper. If z is the distance along
the axis of the coil, the radius is:
r(z) = r0 * exp(-k*z)
In other words, the logarithm of the radius changes uniformly with distance
along the coil:
d[ln(r)]/dz = -k
In practical shop terms, imagine a smooth trumpet or horn-shaped coil form.
One end has a relatively large diameter and the other has a relatively
small diameter. The diameter should not decrease along a straight line as
it would on a cone. It should follow a calculated exponential curve. The
secondary wire is then wound continuously along that surface.
I have intentionally not specified one mandatory overall length, wire size,
number of turns, or starting diameter. Those dimensions can be selected to
make a practical Tesla resonator compatible with the builder's equipment.
What is important is that the radius as a function of axial position is
accurately controlled and documented, particularly the ratio between the
large and small radii.
Ideally, the former would be machined, 3-D printed, or otherwise fabricated
from a calculated table of axial positions and corresponding diameters.
This would give us an accurately known physical profile rather than an
approximate trumpet shape.
The reason for using this geometry is that an ordinary cylindrical Tesla
secondary has essentially constant radius. The trumpet secondary
deliberately introduces a continuously changing geometrical condition along
the propagation path. The QMU model predicts that the accumulated
geometrical phase depends upon the logarithm of the radius ratio.
The proposed relationship is:
phi_geom = 2 * alpha * ln(r_w / r_n)
where:
phi_geom = predicted geometrical phase
alpha = fine structure constant, approximately 1/137.036
r_w = radius at the wide end
r_n = radius at the narrow end
For example, the geometrical control variable is not simply the difference
between the two radii. It is:
ln(r_w / r_n)
The experiment should therefore not consist merely of building an unusual
Tesla coil and seeing whether it produces impressive sparks. It should be
treated as a precision resonator experiment.
The preferred procedure is to construct the trumpet secondary and
characterize it at low power with a VNA or equivalent phase-sensitive RF
instrumentation. Measure its resonant frequencies, impedance behavior, and
phase response. This allows the resonator to be studied without the
complications of spark discharge and high-power operation.
The conventional electrical behavior of the coil must be accounted for.
That includes distributed inductance, self-capacitance, winding pitch,
propagation delay, lead inductance, top-load capacitance, primary coupling,
and other ordinary transmission-line effects.
After those effects have been modeled or measured, we look for a
reproducible residual phase associated specifically with the changing
radius.
A much stronger experiment would construct several interchangeable trumpet
secondaries having similar electrical construction but different ratios of
wide-end radius to narrow-end radius.
For each coil calculate:
X = ln(r_w / r_n)
Then measure the residual phase:
Y = phi_residual
Finally plot:
phi_residual
against:
ln(r_w / r_n)
The important point is that the theory does not merely predict that
"something unusual" should happen. It predicts a scaling relationship.
The expected relationship is:
phi_residual = 2 * alpha * ln(r_w / r_n)
so the predicted slope is:
2 * alpha
or approximately:
0.0145947
when phase is expressed in radians.
A cylindrical secondary should be measured as a control. For a cylinder:
r_w = r_n
therefore:
ln(r_w / r_n) = ln(1) = 0
and the predicted trumpet-geometry contribution is zero.
Additional control coils would be valuable. For example, a conventional
conical secondary could help determine whether an observed effect is simply
caused by changing diameter or whether it follows the specific logarithmic
relationship predicted for the trumpet geometry.
There is also a second measurement that would be particularly interesting.
In the QMU model, the broad and narrow ends of the trumpet represent
different limiting electrical conditions. The broad end is associated more
strongly with the current/magnetic side of the system, while the narrow end
approaches the potential/electrostatic side.
For that reason, simultaneous measurements of return current at one end and
calibrated top-load charge, capacitance, and voltage at the other could
provide an independent test in addition to the phase measurement.
The associated QMU charge-partition relationship contains the
fine-structure factor:
8 * pi * alpha
This could become a second experiment after the basic geometrical phase
experiment has been characterized.
So, in plain engineering terms, I am asking someone to build a Tesla
secondary whose radius follows a known exponential trumpet curve,
characterize it accurately as an RF resonator, and determine whether
changing the trumpet ratio produces a phase contribution proportional to:
ln(r_w / r_n)
that cannot be accounted for by conventional distributed-circuit effects.
The experiment becomes much stronger if several geometries are tested. One
coil can produce an anomaly. A family of coils can establish a scaling law.
The decisive test is therefore not "Does the trumpet coil behave
differently?"
The decisive test is:
Does the measured residual phase vary linearly with
ln(r_w / r_n), with a slope of approximately 2*alpha?
That gives us a quantitative prediction that can either succeed or fail.
I have built more than 25 experimental Tesla secondaries in the past,
including solenoids, flat spirals, and combinations of the two. The trumpet
experiment grew out of that experimental experience, but I am no longer
physically able to construct the coils myself.
If someone on the list is interested in building the apparatus, I would be
glad to work with the builder on calculating the trumpet profile, selecting
practical dimensions, and developing the measurement and control procedure.
The first step would simply be to agree on the large diameter, small
diameter, and overall winding length. From those three dimensions, the
exponential former profile can be calculated.
David W. Thomson
On Wed, Aug 26, 2026 at 3:20 PM Ken <pupman.com@xxxxxxxxxxxxxxxxxxx> wrote:
> That's a whole lot of circular mumbo jumbo.
>
> Can you describe the apparatus to be constructed and experiment to be run
> in plain English?
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