A cyclotron consists of a constant magnetic field and a variable rf-electric field. This configuration imprints a continuous acceleration to the particle till relativistic effects break the synchrony between the motion and the field switching. Particles in a cyclotron move in spiraling trajectories.
In a synchrotron, the magnetic field varies in strength to maintain synchrony between the particle angular frequency and the field switching. Particles in a synchrotron move in closed orbits. Read more