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Space-charge effects play an important role in high intensity particleaccelerators and were studied using a variety of macroparticle tracking models.In this paper, we propose a symplectic particle-in-cell (PIC) model and comparethis model with a recently published symplectic gridless particle model and aconventional nonsymplectic PIC model for long-term space-charge simulation of acoasting beam. Using the same step size and the same number of modes for thespace-charge Poisson solver, all three models show qualitatively similaremittance growth evolutions and final phase space shapes in the benchmarkexamples. Quantitatively, the symplectic PIC and the symplectic gridlessparticle models agree with each other very well, while the nonsymplectic PICmodel yields different emittance growth value. Using finer step size, theemittance growth from the nonsymplectic PIC converges towards that from thesymplectic PIC model.

A symplectic particle-in-cell model for space-charge beam dynamics simulation