I've been searching the web to find info on solenoid transformers and found almost nothing, most info is about air-core,, toroid, and commonly used E-cores or square core transformers that are constructed to close the magnetic circuit.
I find it both mysterious and interesting that a conventional spark coil has the secondary on the outside of the outside of the can, and also found that ignition coil cores were laminated steel rather than ferrite.
I also notice that the primary of the original potted coil was made by potting a rod ferrite core inserted into the multi-layer HV secondary center's plastic form. The primary seemed to be wound on a circular core floating in epoxy within the cylindrical walls and separated by at least 3mm from outer frame.
This architecture seemed to present itself as a very good way to construct a transformer with very tight magnetic coupling, while still having an open-frame solenoid magnetic circuit, and unlike an ignition coil, the idea here was to place the primary in the center.
There is much info about transformers in the most common shapes and much about solenoid inductors, and many scholarly articles about transformers in general to very advanced, complicated and difficult to understand pulse transformers such as were constructed to power klystrons at CERN.
Info that explains the detail of a sophisticated closed magnetic-loop transformer design presents formulas that expresses design using what is known abut a core's permeability, magnetic flux density, saturation, hysteresis of core materials, eddy currents, energy, work, power, ampere-turns, reflected inductance, primary and secondary coupling coefficients, core losses, types of specialized ferrites, magnetic curie points, reluctance, inductance, and efficiency, isolation of windings, etc. .
I remain in the dark, too stubborn to light a match to make dinner and spend my time cursing the darkness and whining about not knowing how to wind my wires. I do this rather than lighting one match, starved intellectually, kept from understanding the math that reveals the hidden secrets of designing a solenoid transformer using engineering rather than trail and error techniques.
A new Sparky is on it's way from China, sent to me free of freight charges, sent by means of Chinese international economy airmail, and guaranteed to arrive before Mar. 31, 2018.
.
Will I find a way to wind my windings before then?
In the meantime, I am trying to memorize the info in this excellent .pdf published by the IEEE.
FUNDAMENTALS OF
MAGNETICS DESIGN:
INDUCTORS AND TRANSFORMERS
Thursday September 15, 2011
Arthur Williams
Chief Scientist
Telebyte Inc.