Hi Mads, thanks for your kind words 😊
I would like to highlight some of the notes and things on my website that might be of interest here, to help people find them.
Here’s a walkthrough of the main things:
[1] “Deriving the equivalent circuit of a Tesla coil”PDF:
https://bartmcguyer.com/notes/note-11-TcEquations.pdf I wrote [1] because I couldn’t find a toy-model derivation of the ubiquitous equivalent circuit for a Tesla coil. This note provides one by approximating the secondary coil as a transmission line. It gets… surprisingly messy, because there are two 100+ year old mysteries that re-emerge if you do this.
The first mystery has to do with reciprocity, uniqueness, and energy conservation, and was noticed at least as early as 1904 by the German physicist Paul Drude. Funny enough, Antonio C. M. de Queiroz had started an English translation of that paper a while ago, so I worked with some friends to finish it, giving:
[2] “Translation of an Article by Paul Drude in 1904”PDF:
http://arxiv.org/abs/1303.1588 That first mystery was a big surprise to me and really difficult to figure out, so much so that I published a paper about it. To dig in, I recommend starting with a short introduction here:
[3] “An old puzzle about reciprocity and Tesla coils” Webpage:
https://bartmcguyer.com/notes/note-2-OldPuzzle.html The full paper’s online here, and you’ll need it to understand [1]:
[4] “Paul Drude's Prediction of Nonreciprocal Mutual Inductance for Tesla Transformers” PDF:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0115397 As a bonus, [4] provides a graphical way to understand how some rather different-looking equivalent circuits in RF and microwave textbooks come from the Telegrapher’s Equations.
The second mystery is the surprising lack of an analytical model for the self-capacitance of the secondary solenoid, which I think is well known to the Tesla coiling community. In short, you can’t derive an equivalent circuit for a Tesla coil without also deriving some model for this self-capacitance. If you approximate the secondary as a uniform transmission line, the model you get is something I like to call the “Miller” self-capacitance, after the famous electrical engineer who derived it in 1918. I showed experimentally that it is correct in very controlled conditions:
[5] “Test of the Miller self-capacitance of a solenoid inductor” PDF:
https://bartmcguyer.com/notes/note-12-MillerCapTest.pdfHowever, while I hoped that perhaps the underappreciated Miller self-capacitance might be the answer, in general, it seems to account for only about half or so of the whole self-capacitance, depending on how you count. To investigate this, I used the Virtual Secondary Database from Paul Nicholson’s Tesla Secondary Simulation Project collaboration to test different models numerically:
[6] “Exploring the self-capacitance of single-layer solenoid inductors with the TSSP's VSD” PDF:
https://bartmcguyer.com/notes/note-14-SelfCapTSSP.pdf In short, the widely known empirical Medhurst formula from 1947 does remarkably well, but some cruder models are pretty decent too. As a bonus, near its end, [6] suggests a practical way to estimate the self-capacitance in situ by measuring the lowest secondary resonance when the topload is disconnected or removed.
Backing up, it’s actually pretty interesting to dig deeper in to how a secondary coil can behave as a transmission line. Here’s a note that derives toy-model transmission lines starting from a network model for the solenoid:
[7] “Transmission-line models for single-layer solenoid inductors” PDF:
https://bartmcguyer.com/notes/note-13-CoiledLines.pdf Switching gears, I noticed a while ago that the laser-guided spark community, who typically use Marx generators, was becoming interested in Tesla coils, because, as enthusiasts know, they’re very good at growing long sparks. However, as enthusiasts also know, Tesla coils have trouble with streamer loading. To get around this, I wondered if you could modify a Marx generator to mimic a Tesla coil, in a way that wouldn’t have the same streamer-loading trouble. To test this, I built a prototype “Marx coil” and published a paper about it. Here’s a short introduction to the paper:
[8] “Can a Marx generator produce sparks like a Tesla coil?” Webpage:
https://bartmcguyer.com/notes/note-7-MarxCoil.html And here’s the full paper:
[9] “Investigation of a Marx Generator Imitating a Tesla Transformer” Main PDF:
https://bartmcguyer.com/pdf/2018_RSI_McGuyer_MarxCoil.pdf Supplementary PDF:
https://bartmcguyer.com/pdf/2018_RSI_McGuyer_MarxCoil_Supplement.pdf Supplementary video:
https://bartmcguyer.com/media/2018_RSI_McGuyer_MarxCoil_Supplement_Video.mov In the spirit of there being no such thing as a new idea, Mads did something remarkably similar at nearly the same time:
https://highvoltageforum.net/index.php?topic=2755 Coming across that post inspired me to join this forum and post about the Marx coil:
https://highvoltageforum.net/index.php?topic=2796 Last, while working on the Marx coil, I stumbled on a derivation of the “larger than resonance” (LTR) capacitance formula commonly used to size the primary tank capacitor in spark-gap Tesla coils driven by neon sign transformers:
[10] “Deriving the LTR primary capacitance formula for NSTs” Webpage:
https://bartmcguyer.com/notes/note-1-LTR.html 
