The large-bore magnets in the injection system of a high-intensity proton synchrotron are placed close to each other as compared to their bore sizes. In such cases, the magnetic cores interfere with the fringe fields of adjacent magnets. Moreover, the incoming beam passes through several kinds of time-varying fields along the injection line and the nonlinear field region of the ring quadrupole magnet. The beam behavior under these conditions is analyzed by using the Runge-Kutta method. Although the interference of the magnetic fields does not result in emittance growth, it produces a closed-orbit distortion. Field fluctuations of the time-varying field cause an emittance growth and the nonlinear field deforms the beam profile in phase space of the incoming beam. These effects lead to the modification of the injection scheme. This study focuses on the particle tracking with magnetic field interferences during the early stage of beam commissioning, when the space charge force is not important.
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