Sounds like you are describing a Rapid Start - Hot Cathode Ballast for 2 lamps - typical of F40T12 lamps and HO/VHO lamps of 4' and 8' length.
Unless something changes between tonight and Friday, I will have a whole weekend off!!! Ya, Baby!.
Plan to post a few Audio Xover [passive] schematics, a couple simple motor drawings, and whatever I can draw/convert/post. I'll add a couple Ballast drawings - especially the RS hot Cathode Ballast you are asking about.
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Scott " 35 " Thompson Just Say NO To Green Eggs And Ham!
It is a property of most materials that they will give up electrons much more easily when hot - meaning temperature. This was common nuisance with tube devices that had to be turned on to warm up for several minutes before they would begin working.
Cold cathodes typically employ a much higher discharge voltage so they can emit adequate electrons at typical room temperatures. Alas, this is much less efficient.
Hot cathodes have a heater (basically a little tungsten filament with a special coating) that emits lots of electrons to travel through the gas in the tube and make it glow.
Hot cathodes are quite a bit more efficient. About the only advantage of a cold cathode is the instant start..