Study of longitudinal mechanisms and correlations in the definition of RFQ transverse acceptance

The Radio Frequency Quadrupole (RFQ) is a linear accelerator that focuses, bunches, and accelerates a continuous input of charged particles while preserving the beam emittance. This paper focuses on the study of the transverse acceptance of an RFQ and how this concept can be used in the design of frontend structures. A simple and fast system to qualify a source and low energy transfer line has been developed in terms of the number of particles delivered in the RFQ acceptance. Multi-particle simulation results show a dependence of the RFQ transverse acceptance on the particle phase in the radio frequency period. The usually referred-to acceptance value is, in fact, just an average value over the 360° phase range, whereas a modulation has been found between more and less favorable phase values, with different patterns depending on the specific structure. We use as a study case three RFQs designed and operated at CERN to investigate such correlations.