Resonance crossing experiment at a proof of principle fixed field alternating gradient accelerator

An experimental study of crossing a third order uncoupled resonance was performed in a proof of principle fixed field alternating gradient with various widths of resonance and crossing speed. We observed that part of the beam is transported to a larger amplitude when the crossing speed is relatively small. We derived an adiabatic parameter from a particle trapping model as a useful index for avoiding beam deterioration due to resonance crossing. It relates the crossing speed to the resonance width and the amount of nonlinear detuning. When the adiabatic parameter is more than 7, resonance crossing will not affect a beam.