I would like to invite technically minded builders to look at an experiment
involving a tapered ("trumpet") Tesla coil geometry and a two-channel
measurement method.
The objective is to compare two quantities measured in the same resonant
device:
1.
an electrostatic carrier derived from the topload capacitance and peak
voltage
2.
a magnetic-mode proxy derived from the base current
The experiment compares how these two quantities scale as the drive level
and geometry change.
Important note on geometry:
The "trumpet" coil is a secondary whose radius gradually decreases toward
the top. In other words, the flare points downward toward ground and the
smaller diameter is at the top near the topload. The taper helps distribute
electric field stress and tends to stabilize operation before breakout.
Measurement definitions
Electrostatic channel
q = C_top * V_pk
Magnetic channel
Q = kappa * I_pk
where
C_top = effective topload capacitance
V_pk = peak topload voltage
I_pk = peak base current
kappa = calibration factor obtained from the toroidal magnetic field B_phi
near the base region
In the Quantum Measurement Unit (QMU) framework there is an additional step
because capacitance is inversely related to potential. The measured voltage
and current therefore must be converted through the charge conversion
factor (CCF):
ccf = e_emax^2 / e
The CCF converts between conventional charge-based units and QMU units. In
practice this means the measured potential and current channels are scaled
by the CCF before comparing the electrostatic and magnetic quantities.
After applying the conversion, the experiment tests the relation
Q^2 = q^2 / (8 * pi * alpha)
where alpha is the fine structure constant.
The extracted value
alpha_extracted = q^2 / (8 * pi * Q^2)
can then be examined while varying
-
drive power
-
coupling
-
secondary geometry
If the ratio remains constant across these changes (within measurement
uncertainty), the two channels scale together in a nontrivial way. If the
ratio varies strongly with geometry, the effect reduces to conventional
resonator behavior.
Required measurements
C_top
V_pk
I_pk
C_top can be obtained using low power resonant shift measurements or VNA
fitting.
V_pk can be measured with a calibrated capacitive divider or other HV
measurement method.
I_pk can be measured with a current transformer at the base of the
secondary.
Calibration of kappa can be done using a small magnetic probe to map the
toroidal magnetic field B_phi(r,z) near the base.
Important experimental condition
Runs should be performed in a no-streamer regime. Once streamers appear the
electrostatic channel becomes contaminated and the measurement is no longer
reliable.
The full experimental description is available here:
https://zenodo.org/records/17408713
I would especially appreciate feedback from experienced builders regarding
-
reliable high-voltage measurement methods
-
practical techniques for determining C_top
-
magnetic probe methods for calibrating kappa
-
any pitfalls in the measurement protocol
If anyone on the list is interested in attempting a replication
measurement, I would be glad to collaborate and compare results.
Best regards,
David Thomson
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