IN PARTICLE ACCELERATORS

The effects of charged particle beams crossing a third-order resonance in an accelerator are studied. A 20% emittance growth or 2.5% of trap-fraction can be used to define the critical or tolerable resonance strength, which is found to follow simple scaling laws vs tune-ramp rate and initial emittance. One scaling law can be derived by solving Hamilton’s equations of motion in a perturbative approach. Such scaling laws can be used to evaluate the performance of high power accelerators, such as fixed-field alternatinggradient accelerators (FFAGs) and cyclotrons [6].