The Nucleus Resolved, Ch Beams and the edges of the chart: emittance, heavy ions, high spin and the drip lines
Problem
The accelerating gap of a synchrotron has synchronous phase ϕs=30∘, measured from the zero-crossing on the rising part of the radiofrequency wave, and the machine runs well below the transition energy, so that a particle gaining more energy per turn also arrives earlier on the next pass. Someone argues: 'A particle that arrives 5∘ early meets the wave earlier, where the voltage is still rising towards its peak, so it receives a larger kick than the synchronous particle. That larger kick makes it arrive even earlier next time, so the effect runs away and the particle is lost from the bunch.' State what is wrong with this argument and describe correctly what happens to the early particle over many gap crossings.