Theoretically,

Ok, Ok, but an electric car is still a car. Why would a car need an engine? A railway car has no engine. The word has its meaning, and by forcing it to name your thing only makes those that know the word question your knowledge of the word if not your whole design, get that? It won't make your design any more clear or catch the right audience. You can't just pick up words and use them however you like. A coil like the one you described probably won't produce synchrotron radiation as electrons inside metals won't accelerate to near speed of light. But why would I bother explaining? I've only used a synchrotron for 10 years.