Matched phase sweep method for the optimization of bunching factor in dual rf systems of high-intensity hadron synchrotrons

The scheme of multiturn painting beam injection in a dual harmonic rf system is widely employed in high-intensity proton or heavy ion synchrotrons to alleviate space charge effects. With a momentum offset of the injected beams, a large bunching factor can be achieved at the end of multiturn painting injection process. However, the momentum offset can increase the instantaneous beam peak current during the first <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>4</a:mn></a:math> synchrotron period, causing a reduced bunching factor during the beam injection process. To address this issue, a matched phase sweep method is developed. By matching the synchrotron oscillation frequency and beam injection period, an optimal curve for phase sweeping can be directly obtained. The effectiveness of the method has been checked via simulations and machine study, which are in good agreement. The matched phase sweep method is employed for the increase of the beam power in the upcoming upgrade project of the China Spallation Neutron Source and can also be generally applied for the operation in the presence of dual harmonic rf system in high-intensity hadron synchrotrons.