Longitudinal painting with large amplitude second harmonic rf voltages in the rapid cycling synchrotron of the Japan Proton Accelerator Research Complex

In the rapid cycling synchrotron (RCS) of the Japan Proton Accelerator Research Complex (J-PARC), the longitudinal painting is important to alleviate the space-charge effects. It is known that the momentum offset injection and applying the second harmonic rf voltage improves the bunching factor, which is defined as the ratio of average and peak current. Our simulation studies show that the large-amplitude second harmonic, 80% to the fundamental, is optimum, and the second harmonic phase sweep improves the bunching factor at the beginning of the injection period. We performed the beam tests of longitudinal painting in the J-PARC RCS. We proved that the longitudinal painting with the 80% second harmonic, the momentum offset of -0.2%, and the second harmonic phase sweep improved bunching factors significantly.