(disputed — see talk page) Synchrocyclotrons have not been built since the isochronous cyclotron was developed.
Isochronous cyclotrons maintain a constant RF driving frequency and compensate for the relativistic mass gain of the accelerated particles by increasing the magnetic field with radius. Isochronous cyclotrons are capable of producing much greater beam current than synchrocyclotrons.
See also
Cyclotron — this contains a mathematics section that assumes constancy of mass, and an extensive see also section.
In this instrument, the oscillator (radio-frequency generator) that accelerates the particles around the dees is automatically adjusted to stay in step with the accelerated particles; as the particles gain mass, the frequency of accelerations is lowered slightly to keep in step with them.
The largest synchrocyclotron is the 600-cm (236-in) phasotron at the Dubna Joint Institute for Nuclear Research in Russia; it accelerates protons to more than 700 MeV and has magnets weighing 6,984 tonnes.
Synchrocyclotrons cannot be adapted to make allowance for such large increases in mass.