An accelerating electron or proton emits light via synchrotron radiation, but an accelerating ring of charge does not and Larmor suggests that a standing wave of charge wouldn't either {1}.
Are there any other special cases where accelerating charges don't emit light?
{1} "[S]teady motion which does not involve radiation is really a state of stationary undulation arising from the superposition of a wave-train traveling outwards on another travelling inwards". (Page 511)
