Simulation of the Effect of an in-Vacuum Undulator on the Beam Dynamics of ALS

The femtoslicing project at the Advanced Light Source (ALS) requires that a short period (3 cm) and narrow gap (5 mm) in vacuum undulator to be installed. The combination of the short period and the narrow gap raised concern of the impact on the beam dynamics. A 3D field model was established based on numerical data using 8 longitudinal and 4 transverse harmonics. At first fourth-order symplectic integrator was used. It was to our surprise that the dynamic aperture decreased by 30%. To understand the cause of the drastic change in the dynamic aperture, the field model was implemented in a differential algebraic code and the Taylor map of the undulator was obtained. Tracking result using the Taylor map showed little change in the dynamic aperture, which was latter corroborated using the symplectic integrator with 150 slices per period (as opposed to 10 before). Yet it is simply too time consuming to use the symplectic integrator with such thin slices. For this case, Taylor proves to be a much faster alternative.