Also see CuriousMarc's companion video, which shows how the spark gap works with a coherer for primitive radio transmissions. https://www.youtube.com/watch?v=9zG_DlxyugQ
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"So where is the spark gap in this unit? It turns out to be the ceramic cylinder. I opened up the cylinder and found a stack of eight metal disks with (maybe) carbon electrodes in the center. The disks are separated by mica washers to leave 0.33 mm gaps between each pair. This forms a series of 7 tiny spark gaps.
This type of spark gap is known as a "quenched spark gap". Spark gap transmitters were the first form of radio transmitter, used from 1887 to 1920. They used a spark to transmit Morse code via radio waves (details). The quenched spark gap was one type of spark gap used in these transmitters, as shown in the diagram below.
By combining multiple small gaps, the quenched spark gap could cool off efficiently."
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"Spark gaps generate radio waves across a wide spectrum; inventor David Hughes first noticed this interference in 1878."
A similar circuit is in every plasma cutter.[1] For the same reason; you need a high voltage pulse to ionize the working gas (usually air) and start the arc.
I miss TechShop, too. If making is your passion theres good news: it isn't dead. Current virus issue excluded there are many smaller maker spaces you can join in the bay.
I have small tools. TechShop had the big stuff - CNC mills, waterjets, plasma cutters. I used all of those. The smaller maker spaces are at the low-end 3D printer level. Maybe a wood shop. There's Humanmade in SF, which has much of the old TechShop gear, but it's an hour away and twice as expensive as TechShop.
That schematic of a Tesla coil is the same as a spark-gap transmitter, except of course the latter is designed to emit as much as possible and has an antenna connected where the output torus would be; see page 375 of this excellent book: https://archive.org/details/principlesunderl00unit
(Although very old, that book is great at explaining the basics of what radio actually is.)