The development of the synchrotron resulted from the need for energies at about the GeV range.
Particles are first injected from another accelerator into the synchrotron, which is essentially a doughnut shaped vacuum tank surrounded by a ring of magnets. Unlike the cyclotron a single large diameter magnet is not required, making it possible to build synchrotrons with diameters measured in tens or hundreds of metres.
At ISIS the 70MeV H– ions produced in the linac are converted to protons, and accelerated to 800MeV in a 52 m diameter synchrotron.
As with the cyclotron, the synchrotron employs magnetic fields to send the beams of charged particles in a circular path and electric fields to accelerate their speed. With the synchrotron, however, the magnetic field rises in step with the velocity of the particles. This keeps them moving in a circle of nearly constant radius, rather than the widening spiral experienced in the cyclotron.
The frequency of the electric field changes to match the increasing speed of the particles. However, at high energies the particles move so close to the speed of light that they make a circuit in constant time. Instead of increasing speed, they simply gain more momentum via an increase in mass.