Late to the party but here is how you operate a synchrotron such as the CERN Proton Synchrotron Booster:
- You inject the beam from the production facility (currently linac4) and it starts to circulate in the ring. In a specific section of the ring there is a particular element called Radio Frequency (RF) cavity. It produces an electric field oriented along the beam direction and oscillating back and forth. The beam revolution time and the electric field frequency are synchronized so that the beam passes through the RF cavity when the field is vanishing.
- You increase a bit the current in the magnets of the ring. This causes the beam to move on a slightly inwards path, completing a turn in a shorter time. Now, when it goes through the RF cavity, it feels some of the longitudinal electric field getting some boost from it. As the energy increases the beam goes back to the usual path. If the beam is not fully relativistic you need to increase the RF frequency accordingly to compensate for the higher velocity.
- You keep repeating step 2, increasing the current in the magnets to its maximum allowable value. Congrats: you now have the beam at top energy!
- You extract the beam sending it wherever is needed.
- You ramp down the currents in the magnets preparing the ring to receive another pulse from the linac and go back to step 1.
Now, what does the linac do while the PSB cycles? The answer is... nothing, it just waits! You can run diagnostic pulses, or send the beam to some other users, but the PSB (or any other synchrotron) does not accept any proton if not configured for injection. This is a disadvantage of synchrotrons compared to linacs or cyclotrons: they cannot deliver continuous beams, but a single pulse which is at most as long as its circumference, then you need to wait for the next cycle.
Others mentioned that the CERN PSB is made up by four rings. That is true, but quite irrelevant here. The reason for that is that a single ring would take too many cycles to fill the PS leaving part of the beam circulating in the PS at injection energy for an unbearable long time, while it gets disrupted by collective effects and intra-beam forces (in particular space charge). Four rings operating simultaneously deliver four times more beam current to the PS, cutting its filling time, so that it can initiate its acceleration procedure faster.
Note that the PS delivers the beam to the SPS and only then the beam reaches the LHC. All these rings operate in a similar manner, receiving the beam at their lowest acceptable energy and accelerating it before delivering to the next ring. Each ring has to complete several cycles to fill up the next one. The only exception is the LHC which, once at top energy, does not deliver the beam to another ring (at least yet, see CERN-FCC) but it squeezes it down to produce collisions.