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It does take energy flow to maintain an arc, and the longer the arc, the
more energy per second. I've seen estimates for long Tesla Coil
discharges ranging between 300w/foot and 1Kw/foot. I don't know if this
applies to 18" sparks, I think it's more valid for sparks many feet in
length.
From the appearance of long tesla coil sparks, I suspect that afeet-per-watt constant exists, but that it only applies to the fully-lit