Abstract
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.
Highlights
The nonlinear space-charge effects from particle interactions inside a charged particle beam play an important role in high-intensity accelerators
The computational cost is linearly proportional to the number of macroparticles, which makes the simulation fast for many applications. Those grid-based, momentum conserved, PIC codes do not satisfy the symplectic condition of classic multiparticle dynamics
Violating the symplectic condition in multiparticle tracking might not be an issue in a single pass system such as a linear accelerator
Summary
The nonlinear space-charge effects from particle interactions inside a charged particle beam play an important role in high-intensity accelerators. The computational cost is linearly proportional to the number of macroparticles, which makes the simulation fast for many applications. Those grid-based, momentum conserved, PIC codes do not satisfy the symplectic condition of classic multiparticle dynamics. We propose a symplectic PIC model for self-consistent space-charge long-term simulation. This model has the advantages of the computational efficiency of the PIC method and the symplectic property needed for long-term dynamics tracking. We carried out long-term space-charge simulations and compared this model with the symplectic gridless particle model and the nonsymplectic PIC model in two beam dynamics applications.
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