¹The largest synchrocyclotron still in use was constructed just outside St Petersburg in Russia with iron

Figure 4: Schematic of cyclotron. Charged particles are injected near the center of the cyclotron. They spiral outward as they gain energy in crossing the voltage gap, which is controlled by the alternating voltage source.

material costs made them impractical.

The synchrotron consists of a ring instead of a disk, a design which sharply reduces the amount of material required. The trimmed weight comes at the price of complexity in keeping the beam closely confined to a pencil-thin ring of constant radius. As the particles are accelerated around the ring, the magnetic field must be carefully increased in order to keep them circulating at a fixed radius. At the same time, the voltages at the gaps must be synchronized with the beam’s velocity.

A synchrotron accelerates a large number of charged particles at a time. Because the magnetic field and electric field must always be adjusted for a particular position and speed of the particles, these particles must be treated together, and are therefore grouped. Then the big problem is to keep these groups from spreading, counteracting drifting and repulsive forces between the equally charged particles. To do this, one needs to create a stable equilibrium around the ideal position of the particles within the synchrotron ring. To have a stable equilibrium means that if the particles deviate from the ideal position, they tend to return to it. For example, a marble at the bottom of a salad bowl is in stable equilibrium. The synchrotron provides a kind of “salad bowl” to keep the particle group together and on track; it counteracts lateral deviations (away from the beam axis) through a process called transverse focusing and longitudinal deviations (along the beam axis) through phase focusing.