Electromagnetic design and tuning of the four-vane radio frequency quadrupole with nonuniform intervane voltage profile

Equipartitioning is an efficient beam-dynamics design scheme also for radio frequency quadrupole (RFQ). To realize an equipartitioned RFQ, it is essential to reproduce the nonuniform intervane voltage profile required from the beam dynamics. We developed a cavity design and tuning method to this end. The dimensions of a voltage-ramped four-vane cavity were determined by a three-dimensional rf simulation. To produce the desired vane voltage profile, the longitudinal variation of the cross-sectional shape was adjusted using the least-squares method based on the simulated responses of the vane-base width to the quadrupole-mode field. In the low-level tuning, slug-tuner positions were determined based also on the least-squares solutions obtained from the simulated tuner responses to the field profile. Finally, the deviation of the quadrupole-mode field was within 1.5% from the design profile, and the mixed dipole modes were 1% of the quadrupole-mode field after only two iterations of tuner adjustment; they are sufficiently smaller than the requirement of 2%.