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How does a synchrotron keep particles moving in a ring with a constant radius?

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Diagram of a linear proton resonance accelerator, or linac, showing protons entering from a source, passing through a series of labeled drift tubes powered by a radio-frequency source, and exiting as a beam through a cavity. — particle accelerator The accelerator is a large-diameter tube within which an electric field oscillates at a high radio frequency. Within the accelerator tube are smaller diameter metallic drift tubes, which are carefully sized and spaced to shield the protons from decelerating oscillations of the electric field. In the spaces between the drift tubes, the electric field is oriented properly to accelerate the protons in their direction of travel.

In a synchrotron, particles are kept moving in a ring with a constant radius by synchronizing the strength of the magnetic field with the increasing energy of the particles.12

As the particles are accelerated by radio-frequency voltages, their momentum increases. To prevent the particles from spiraling outward, the magnetic field generated by the ring's dipole magnets is increased in tandem with the particle energy. This precise adjustment ensures that the radius of the orbit remains approximately constant throughout the acceleration process. While the magnetic field provides the "bending" force to maintain the circular path, additional magnets, such as quadrupoles, are used to focus the beam and keep it narrow and intense as it travels through the vacuum chamber.12