Improvement of extraction efficiency from a slow extraction synchrotron by applying the constant spiral step condition

An operating condition for high extraction efficiency of a synchrotron with a slow extraction method is presented. With this condition, the separation between a particle injected into the electrostatic septum and a particle circulating in the synchrotron (the spiral step) becomes independent of the momentum of the particle (the constant spiral step condition). In a synchrotron with the Hardt condition, the spiral step varies according to the momentum of the extracted particle. So the extraction efficiency of the circulating beam with large momentum deviation becomes low because of the beam loss at the entrance of the electrostatic septum (ES). In a synchrotron with the constant spiral step condition, the beam loss at the entrance of the ES decreases. Therefore, the extraction efficiency of the synchrotron with the constant spiral step condition can become higher than that with the Hardt condition despite the loss of particles with large momentum deviation in the middle of the ES. Analogous to the Hardt condition, setting the horizontal chromaticity of the synchrotron to an appropriate value provides the constant spiral step condition. Particle tracking simulation results indicate that the extraction efficiency of the synchrotron with the constant spiral step condition is slightly higher than that with the Hardt condition. Adequate extraction efficiency is achieved with the horizontal chromaticity set between the Hardt condition and the constant spiral step condition. The magnetic strength of the sextupole magnets in the synchrotron should be set high enough to get horizontal chromaticity of the ring at any value in this range. Furthermore, it is desirable to design a synchrotron so that the constant spiral step condition becomes close to the Hardt condition.