Full three-dimensional approach to the design and simulation of a radio-frequency quadrupole

Abstract

We have developed a new full 3D approach for the electromagnetic and beam dynamics design and simulation of a radio-frequency quadrupole (RFQ). A detailed full 3D model including vane modulation was simulated, which was made possible by the ever advancing computing capabilities. The electromagnetic (EM) design approach was first validated using experimental measurements on an existing prototype RFQ and more recently on the actual full size RFQ. Two design options have been studied, the original with standard sinusoidal modulation over the full length of the RFQ; in the second design, a trapezoidal modulation was used in the accelerating section of the RFQ to achieve a higher energy gain for the same power and length. A detailed comparison of both options is presented supporting our decision to select the trapezoidal design. The trapezoidal modulation increased the shunt impedance of the RFQ by 34%, the output energy by 15% with a similar increase in the peak surface electric field, but practically no change in the dynamics of the accelerated beam. The beam dynamics simulations were performed using three different field methods. The first uses the standard eight-term potential to derive the fields, the second uses 3D fields from individual cell-by-cell models, and the third uses the 3D fields for the whole RFQ as a single cavity. A detailed comparison of the results from TRACK shows a very good agreement, validating the 3D fields approach used for the beam dynamics studies. The EM simulations were mainly performed using the CST Microwave-Studio with the final results verified using other software. Detailed segment-by-segment and full RFQ frequency calculations were performed and compared to the measured data. The maximum frequency deviation is about 100 kHz. The frequencies of higher-order modes have also been calculated and finally the modulation and tuners effects on both the frequency and field flatness have been studied. We believe that with this new full 3D approach, the enhanced computing capabilities and the calculation precision the electromagnetic design software offer, we may be able to skip the prototyping phase and build the final product at once, although we recognize that prototyping is still needed to establish and validate the fabrication procedure.