Symplecticity of transfer maps is important for reliable evaluation of space-charge dominated beams in accelerators. Unfortunately, most simulation codes that include collective effects, such as space charge, do not use canonical phase-space variables and therefore are not symplectic in the presence of electromagnetic fields. In this paper, we present a numerical method to extract symplectic transfer maps using particle tracking simulation code IMPACT-T for space-charge dominated beams. We demonstrate this method by obtaining symplectic transfer maps in the photo-injector (113 MHz SRF gun) section of the Coherent electron Cooling (CeC) Proof of Principle (POP) experiment.
Bachhawat et al. (Thu,) studied this question.