Assume we have a particle lying in the xy-plane with an initial velocity in the x-direction. If an external, constant and uniform magnetic field is applied in the z-direction, the particle, assuming it has a positive charge, will begin to do circular clockwise laps. However, it seems to me that this negliges energy loss from radiation, and that the trajectory of the particle should decay in an exponential fashion. I have never seen a derivation of this, and a search on the forum and google did not provide any results. Am I mistaken?