Longitudinal Beam Dynamics for the Heavy-Ion Synchrotron Booster Ring at HIAF

To accelerate high-intensity heavy-ion beams to high energy in the booster ring (BRing) at the High-Intensity Heavy-Ion Accelerator Facility (HIAF) project, we take the typical reference particle 238U35+, which can be accelerated from an injection energy of 17 MeV/u to the maximal extraction energy of 830 MeV/u, as an example to study the basic processes of longitudinal beam dynamics, including beam capture, acceleration, and bunch merging. The voltage amplitude, the synchronous phase, and the frequency program of the RF system during the operational cycle were given, and the beam properties such as bunch length, momentum spread, longitudinal beam emittance, and beam loss were derived, firstly. Then, the beam properties under different voltage amplitude and synchronous phase errors were also studied, and the results were compared with the cases without any errors. Next, the beam properties with the injection energy fluctuation were also studied. The tolerances of the RF errors and injection energy fluctuation were dictated based on the CISP simulations. Finally, the effect of space charge at the low injection energy with different beam intensities on longitudinal emittance and beam loss was evaluated.