Abstract
Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multi-particle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance growth than the particle-in-cell model in the illustrative examples.
Highlights
In high intensity accelerators, the nonlinear space-charge effect from charged particle interactions inside the beam has significant impact on beam dynamics through the accelerator
The particle-in-cell method is an efficient method in handling the space-charge effect self-consistently
Those grid based, momentum conserved, PIC codes do not satisfy the symplectic condition of classic multiparticle dynamics
Summary
The nonlinear space-charge effect from charged particle interactions inside the beam has significant impact on beam dynamics through the accelerator. Most of those multiparticle tracking codes use the particle-in-cell (PIC) method to include the space-charge effect self-consistently in the simulation [1,2,3,4,5,6,7,8,9,10,11]. 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. In a circular accelerator, violating the symplectic condition may result in undesired numerical errors in the long-term tracking simulation This issue together with the numerical grid heating was brought up during the 2015 space-charge workshop at Oxford [12].
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