These years

a new type of accelerator

namely induction synchrotron

has been a focus of improving the intensity of high energy ion beams.Combining the advantages of radio-frequency synchrotron and linear induction accelerator

an induction synchrotron may improve the performance of accelerators evidently.As a key factor to determine the principle of acceleration

the longitude dynamics of the accelerators should be studied first.In some aspect

the longitude dynamics of induction synchrotron is similar to a radio-frequency synchrotron

but it has some unique characteristics.In this paper

the longitude dynamics of induction synchrotron is analyzed.The software of ISync

based on multi-particle tracing

is programmed to simulate the longitude dynamics.The simulation results are in accordance with the theoretical analysis.The aberration and oscillation of time spectrum are discovered in the simulation.The origin of the phenomena is analyzed

and ways of suppressing the phenomena are proposed.The work can be of help for future works on induction synchrotron.