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