Simple lumped circuit model applied to field flatness tuning of four-rod radio frequency quadrupoles

Abstract

The field flatness of any radio frequency quadrupole (RFQ) is an important parameter that needs to be carefully tuned because it can affect beam transmission efficiency. In four-rod RFQs, the heights of a set of tuning plates determine the quality of the field flatness. The goals of this paper are (a) to show that by using a lumped circuit model of a four-rod RFQ, the field flatness profile for any tuning plate height distribution can be quickly calculated, (b) to derive a perturbative solution of the model so that insights into the physics of the tuning process and its effects can be understood, and (c) to compare the predicted field profiles to measurements.