A cyclic particle accelerator in which the magnetic field (to turn the particles so they circulate) and the electric field (to accelerate the particles) are synchronized with the traveling particle beam. While the cyclotron uses a constant magnetic field and a constant frequency electric field, both are varied in the synchrotron. This allows for construction of large rings that can accelerate particles to much higher energies than a cyclotron which has a limited magnet size. The synchrotron uses multiple separate bending magnets and narrow bore tubes to connect them. It can be used to produce high energy protons and other particles such as carbon ions that are used to treat cancer. In addition the energy of the particles can be varied as needed which is very difficult in a cyclotron.