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Cap-driven x-former?

Original poster: FIFTYGUY-at-aol-dot-com 


     I bought a HV transformer many years ago (from Mouser, probably) that has
a unique feature that I have never figured out.
     It's a 5KV, 300mA secondary, 110V primary. Single phase, no windings
connected to ground at all. From my recent TC research, I learned that this
X-former also has magnetic shunts (which have since resisted all my 
attempts to
remove them without destroying the unit). Makes a pretty impressive Jacob's 
driver with the high, but self-limited current.
     What has puzzled me is why it has a third winding that requires the use
of a cap to make the transformer run. The third winding is center tapped, and
it's inside (wound closer to the core) of the secondary. The center tap is not
used, but the seller's ad mentioned the cap requirement, and they included a
cap and a connection drawing.
     With the cap, it's works great. Without, the HV leads barely put out any
spark. How does this thing work, and can this "extra winding with cap"
principle be applied to other existing HV transformers as well?
     More specs: Seller advertised it as out of a copier power supply. Inked
on the side of the unit is "General Electric part # 9T68Y5022G10". Made for
Eastman Kodak (with an Eastman Kodak part #).
     Cap is a 10uF 1000VDC oil-filled type.

-Phil LaBudde