Dynamic fringe field effect of the rapid ramping quadrupole magnets at a Rapid Cycling Synchrotron

For a DC quadrupole magnet, the normalized magnetic fielddistribution along the beam trajectory is mainly determined by themechanical structure of the magnet and remains almost independent ofthe exciting current. However, the magnetic field measurementresults of the Rapid Cycling Synchrotron (RCS) at the ChinaSpallation Neutron Source (CSNS) show that the normalized magneticfield distribution along the beam trajectory varies during theexciting current ramping process for rapid rampingmagnets. Consequently, for rapid ramping quadrupole magnets, thereare significant differences between the dynamic and static magneticfield gradient distribution. And the changes in the distribution ofthe magnetic field gradient can cause time dependent tune-shiftsduring the exciting current ramping process. For RCS, the tune iscrucial, and the shifts of tune may lead to the beam approaching theresonance line, thereby causing beam loss. The impact of the fringefield effect of the rapid ramping quadrupole magnets on beamdynamics at CSNS-RCS was detailly studied. A new method forcorrecting the time-dependent tune shifts caused by the dynamicfield distribution, based on waveform compensation at the quadrupolemagnets, has also been proposed for the RCS of CSNS. Relatedsimulation and experiment have been conducted, and the simulationresults and experimental results are consistent with theoreticalstudy results.