In the last two decades, numerical and experimental studies have extensively explored the impact of the space charge on bunched beams in both linear accelerators and storage rings. However, fully accounting for space charge effects over the entire accelerator is computationally intensive, especially in storage rings, where simulations must track beam dynamics over many turns and extended time periods. In many cases, space charge forces cannot be neglected, motivating the development of an alternative computational model. Here, we explore space charge-induced nonlinear dynamics using a model that approximates the Coulomb force by concentrating its effects at discrete locations along the accelerator. This approach enables efficient analyses of the full six-dimensional phase space evolution under space charge effects. Future work will apply this model to further investigate the interplay between space charge and beam-beam interactions in colliders, as well as to assess long-term stability criteria in ring accelerators.

In the last two decades, numerical and experimental studies have extensively explored the impact of the space charge on bunched beams in both linear accelerators and storage rings. However, fully accounting for space charge effects over the entire accelerator is computationally intensive, especially in storage rings, where simulations must track beam dynamics over many turns and extended time periods. In many cases, space charge forces cannot be neglected, motivating the development of an alternative computational model. Here, we explore space charge-induced nonlinear dynamics using a model that approximates the Coulomb force by concentrating its effects at discrete locations along the accelerator. This approach enables efficient analyses of the full six-dimensional phase space evolution under space charge effects. Future work will apply this model to further investigate the interplay between space charge and beam-beam interactions in colliders, as well as to assess long-term stability criteria in ring accelerators.

JuTrack is a novel accelerator modeling and tracking package developed in the Julia programming language. Taking advantage of compiler-level automatic differentiation (AD), JuTrack allows rapid and accurate derivative calculations for arbitrary differentiable functions. This paper introduces the core capabilities of JuTrack, including lattice modeling and particle tracking, and demonstrates how AD-derived derivatives enhance the efficiency of beam physics studies through several practical examples.