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Every book I've looked up on the topic of a cyclotron explains it using a two-Dee model, and I understand it well. But Serway shows a picture of the first cyclotron with only one "Dee", how does this model work? Doing some research I found that it has a "Dee dummy/grounded" but I don't quite understand.

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An educated guess: that pioneering device used the more straightforward method that you have read about, but it has been disassembled for the photo so that you can see its interior.

If you can find a reliable source that Lawrence's early cyclotrons actually functioned with just one dee, that source will have enough detail that I can give you a better answer. But I think the photo is just like a car at a car show parked with the hood open: educational, but not an operating condition.

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