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If you are using a standard NST, there is a significant amount of leakage inductance and capacitance associated with its own secondary windings, so there is a definite resonant frequency associated with the NST itself.The spark gap does interesting things to the spectral content of the current.

The number of cycles of ringing before “significant” decay is approximately equal to the Q of the mode in question.Complicating all of this is that true arcs can present negative differential resistance, and that NSTs are designed to have saturable cores (partly out of economy, partly to provide “free” protective current-limiting). It’s like my input

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