Machine learning-based symplectic model for space-charge effect simulation

Symplectic simulation of space-charge effects is important for high-intensity particle accelerators. In this work, we propose to use a generative model to efficiently simulate space-charge effects in JuTrack, a Julia-based particle tracking code. The one-step symplectic transverse transfer map of the particles is obtained by differentiating the predicted space-charge Hamiltonian. This model effectively preserves the phase-space structure and reduces non-physical effects in long-term simulations by ensuring symplecticity in the calculation.