Source of spill ripple in the RF-KO slow-extraction method with FM and AM

The RF-knockout (RF-KO) slow-extraction method with frequency modulation (FM) and amplitude modulation (AM) has brought high-accuracy irradiation to the treatment of a cancer tumor moving with respiration, because of a quick response to beam start/stop. However, a beam spill extracted from a synchrotron ring through RF-KO slow-extraction has a huge ripple with a frequency of around 1 kHz related to the FM. The spill ripple will disturb the lateral dose distribution in the beam scanning methods. Thus, the source of the spill ripple has been investigated through experiments and simulations. There are two tune regions for the extraction process through the RF-KO method: the extraction region and the diffusion region. The particles in the extraction region can be extracted due to amplitude growth through the transverse RF field, only when its frequency matches with the tune in the extraction region. For a large chromaticity, however, the particles in the extraction region can be extracted through the synchrotron oscillation, even when the frequency does not match with the tune in the extraction region. Thus, the spill structure during one period of the FM strongly depends on the horizontal chromaticity. They are repeated with the repetition frequency of the FM, which is the very source of the spill ripple in the RF-KO method.