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Big Primaries, Small Caps

Dear List,

I'm curious about Tesla coils with large primaries and small tank caps.
John Freau and others have articulated numerous times over the years that
coils so designed have lower gap losses and longer sparks relative to coils
using big tank caps and few primary turns.  I'm curious as to why this is
so.  It seems to me that the bigger bang size delivered by a larger cap
would thump the secondary harder, yielding longer sparks.

Can someone in the know provide an explanation?  I'm not an engineer, but I
am an experienced comm/nav technician, so I can grasp pretty deep concepts.
 However, a side trip into Calculus land will lose me pretty quickly.

Best Regards,

Gregory R. Hunter