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Probably your biggest problem will be to build a form that will house the windings.
As for the coil itself, you need to provide more information as to the PI on which the coil will be used to provide more specific answers.
However, without that info, I would recommend trying to match the inductance of any new coil to the stock coil if the PI is a factory made unit.
If the PI is a home made unit, then you have a lot more flexibility, since the coil and PI can be tailored to what you are trying to seek. A good place to start is a coil with something like 300 uh to 350 uh and see if it works ok. One could tweak the damping with an additional resistor across the windings inside the coil housing or inside the coil connector, if you already have a working coil.
For a 24" diameter coil, this would mean a coil of maybe 12 to 13 turns in the windings. The actual inductance could be measured and it will vary because of the type of insulation used. As an example, a coil made with magnet wire will have a higher inductance than one made using insulated hookup wire. My guess is a coil made with Litz will have an inductance somewhere between one made with magnet wire and one made with hookup wire.
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