An interesting new paper concerning a professional 500 Kv Tesla coil gives us precious information on how to design the coils: Transformer form: Flat spiral with peripheral excitation gives the largest coupling factor. Number of turns in secondary: Coupling reduces with increasing the number of turns. One turn primary and minimum number of turns in secondary (enough to give the desired step-up voltage coefficient) should be used. Conductor cross section shape: Strip conductors give larger coupling than round conductors. A compromise between high voltage performance and coupling should be found. Conductor dimensions: Wider strips give stronger coupling. Transformer diameter: Larger diameter gives larger coupling. A compromise between transformer inductance (speed) and coupling should be found. http://fr.arxiv.org/abs/1109.3081
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