The Relativistic Cyclotron Radiation in the Circular Rotating Frame of the Moving Heavy Particle

In the current paper we tackle the task of determining the formula for the cyclotron radiation as measured from a frame co-moving with the particle being accelerated. In the case of cyclotrons, as opposed to synchrotrons, the magnetic field is constant, resulting into spiral trajectories for light particle, like electrons and into circular trajectories for heavier particles, like protons, as we will demonstrate in the current paper. This due to the fact that the braking force is a very small percentage of the accelerating (Lorentz) force, as will be shown later in our paper. These proofs have never been attempted before owing to the difficulty of dealing with rotating frames. Our paper is divided into two main sections, the first section deals with cyclotron radiation measured in the inertial frame of the lab, the second section deals with cyclotron radiation as measured in a frame co-rotating with the particle along a circular path, at a uniform speed.