Instability and halo for double-periodic focusing structure

This paper presents a comprehensive investigation into the beam transport issue in the double-period focusing structure of low energy proton/ion cryogenic superconducting linear accelerators (CSLA). The structure, con-sisting of a large period corresponding to a cryogenic refrigeration module and a small period of focusing so-lenoid, is modeled with solenoids and drifts to study the impact of higher-order resonances on beam halo in transverse phase spaces without considering the acceleration. Numerical simulation reveals that the double -period structure can cause beam envelope instability even when the small periodic zero-current phase advance (sigma 0f) is less than 90 degrees, making it more susceptible than the fully periodic structure. The study identifies that 2:1 resonance remains a major factor contributing to the formation of beam halo, particularly in the double -period structure. Furthermore, through exploration of different matching modes, the paper elucidates that not only 2:1 resonance but also higher-order resonances can lead to beam halo formation for space charge dominated beam. The oscillation frequency spectrum of the matched envelope is obtained using fast Fourier transform. It is recommended that particle oscillation frequencies avoid matching the identical fundamental frequency and its multiples of the matched envelope. Overall, the findings of this study can serve as valuable references for the design and optimization of CSLA.