Updated the tesla coil model

I changed the pipe diameter, torus, and coil in order to conform to the new calculations I did. This ended up lowering the price by like $100 so it should be able to fit into tier 2, as long as I source the microwaves myself (hopefully free off offerup).

Redid calculations

After changing the secondary, I had to redo all of the calculations. I think this actually made the coil more optimized because I was able to calculate the resonant frequencies more accurately. Since I was more familiar with all the formulas I was able to do it a lot quicker than last time but it was still very inconvenient. However, I don't want to pump kilowatts of power into an untuned coil, because dual MOT SGTCs are capable of real power and I wouldn't want to put that to waste.

The secondary coil now has a diameter of 4" and a height of 24".
It requires 1,047 feet of 26AWG magnet wire for 1000 turns at a height of 20".

It has an inductance of 206831.196uH and a self capacitance of 7.132pF.

The toroid has a large diameter of 17" and a pipe diameter of 4". The inner diameter is 9". This means that the capacitance is 18.659pF which allows us to calculate the resonant frequency of the secondary circuit, which is 256.212kHz.

Next, the primary tank capacitor (MMC) ideally should have 0.221uF of capacitance and rated triple the amount of input voltage, so at least 13kV. I rounded down a bit to save cost, and made an MMC with 7 per string and 14 strings in parallel to achieve a capacitance of 0.2uF and a 14kV rating.

Lastly, the primary coil has an inductance of about 0.001929mH when matching the resonant frequency. This means that there will be 5 turns for testing purposes, but the math says that 3 turns will be ideal. There will be a 5" inner diameter of the primary coil, 0.25" wire diameter, 0.25" spacing, 10" outer diameter, and ~10' of wire.

I believe the secondary is slightly underpowered (more suitable for ~750W of input rather than 1.5kW), however it should definitely give good results and save a large amount of cost.

Disaster strikes

Turns out all my calculations have to be redone unfortunately. They are correct, but I need 1500 ft of 22AWG magnet wire, and 500ft is like $25. That would be $75 of just wire. Not to mention the $40 PVC pipe I'd need. While these specs are typically recommended for such a high power (1.5kW) coil, I think I'm going to redo the calculations with a smaller secondary. I found a 4" x 2ft long PVC pipe for pretty cheap so I'll redo all the math and stuff with that as the base.

Made CAD

Created the coil in Fusion 360, just for a 3D reference. Making a coil with 900 turns was not a good time for my computer and for some reason the copper material wasn't showing up. I'm pretty sure it was because I made the wire size accurate to the actual design so it was really thin and only visible when zoomed in, so I decided to make it the full amount of turns as well.

Finished all calculations

First, I had to set the power supply in stone. Voltage doublers are very fragile and the diodes get fried easily, so I decided to instead put two MOTs in series and one as a ballast. After that, I calculated the secondary coil and got the results:
24in. height
6in. diameter
~900 turns
22AWG
415ft.

Then, I found the electrical values:
603.9mm height
1724.7 meters
33.77mH inductance
28.153pF capacitance

After that I worked o the topload design:
17in. full diameter
4in. part diameter
18.659pF

Calculated the resonant frequency which was 200.983kHz using the inductance 33.77mH and capacitance of 0.000018569uF.

Finally got to the tank capacitor and found that it would need to withstand 3x the voltage of the power supply (so about ~15kV) and calculated that the capitance of the MMC should be 0.1845uF.
I then designed the MMC and tried to get as close to this as possible.
0.1uF, 2kV per cap. 7 capacitors per string, with 13 strings in parallel. The total capacitance is 0.1857uF with a voltage rating of 14kV. It uses 91 caps.

The inductance of the primary coil using the capacitance of the MMC and resonant frequency is 0.0033769mH. This means that I should use ~4 turns of 0.315in. copper tubing (due to the skin effect). It has an 11.04in. outer diameter and a 107in. length.

Lastly, I designed the RF ground which is basically a separate earth ground from my house in which I can tie the bottom of the secondary to.

Research

Spent most of the school day and a couple hours at home researching transformers, power inputs, and safety.

First, I looked at the three main types of transformers used for spark-gap coils.
The neon sign transformer, microwave oven transformer, and oil ignition transformer. Each one has it's own pros and cons.

NST - Relatively safe and decent power, but expensive for reliable (non-GFCI) ones
MOT - Very high power and cheap, but not very safe and requires a voltage doubler
Oil Ignition Transformer - Lower power and cheap, but isn't made to run for a while and could overheat quickly.

After looking and browsing eBay for an unspeakable amount of time, I decided on going with a MOT with a voltage doubler. This is because most NSTs were $60+ for the basic ones, and the oil ignition transformers were around $40 each. I found MOTs for ~$20, and I can use a bunch of really cheap diodes (1N4007) in series with some microwave oven capacitors in order to double/multiply the voltage up cheaply. The other thing is that I need a ballast with the MOT so I'll either wind an inductor or use a few light bulbs.

I also looked at the math equations on DeepFriedNeon and did some calculations to find the desired spark length.

TLDR: Single-MOT design w/ ballast and voltage doubler.