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Oct 27, 2016 at 14:41 comment added Buzz As a general matter, you cannot use any configuration of static electric fields to raise the energy of a charge moving around a circular orbit. The reason is simply that when the charge comes around to where it started, which means that it is at the same potential; hence its kinetic energy cannot have changed. With static cavities, the charge would be slowed down by the fringing fields outside the cavities before it could be accelerated back to its original speed inside the cavity. So ideally (but not in real accelerators), the fields shouldn't cycle on until the charges are already inside
Oct 27, 2016 at 13:24 comment added Sparkler To my understanding, acceleration takes place in RF-cavities, within which the electrons move approximately straight so I'm not sure what you mean by "With a constant electric field, they would accelerated around half their orbit, then decelerated over the other half".
Oct 27, 2016 at 13:16 history answered Buzz CC BY-SA 3.0