Single bunch instability analysis based on SILF design

BackgroundShenzhen Innovation Light Source Facility (SILF), as a fourth-generation synchrotron light source, employs a vacuum chamber with a 12 mm radius and numerous insertion devices with gaps as low as 4 mm, resulting in significantly high beam-coupling impedance. The ultra-low transverse emittance (~90 pm·rad) and small momentum compaction factor (6.6×10-5) make the beam highly sensitive to collective effects, which become critical factors limiting machine performance.PurposeThis study aims to investigate the impact of 3rd Harmonic Cavity (3HC) on single-bunch instabilities in SILF and compare the effectiveness between active and passive 3HC configurations for beam instability suppression and threshold enhancement.MethodsThe broadband impedance of SILF storage ring was calculated based on the lattice design and impedance model. Firstly, the resistive-wall impedance and geometric impedance were modeled and analyzed using ECHO and CST programs respectively, yielding a total longitudinal broadband impedance of approximately 110 mΩ. Then, single-bunch instability simulations were performed using ELEGANT program under three operational modes: without 3HC (mode A), with active 3HC (mode B), and with passive 3HC (mode C). For modes A and B, single bunch simulations with 105 macro-particles were tracked for 105 turns at optimum voltage and phase configurations under zero current conditions. Finally, for mode C, multi-bunch simulations with 5%~20% filling rates were conducted using 104 macro-particles per bunch and tracked for 2×105 turns to establish the electromagnetic field in the passive 3HC, with the detuning frequency adjusted to achieve a bunch-lengthening factor of approximately 4.ResultsComputational results show that both active and passive 3HCs extend the RMS bunch length from 2.5 mm to approximately 11.9~12.0 mm, achieving more than 4-fold bunch lengthening, and maintain energy spread at 1.0‰ up to 0.9~1.3 nC single bunch charge, satisfying the 300 mA design requirement. For Transverse Mode Coupling Instability (TMCI), the single bunch charge thresholds reach 2.5 nC and 2.4 nC for active and passive 3HC respectively at chromaticity of +3, compared to only 1.0 nC without 3HC at chromaticity above +1. The performance difference between active and passive 3HC is less than 5% across all chromaticity settings, demonstrating their comparable effectiveness in suppressing single-bunch instabilities.ConclusionsResults of this study demonstrate that the 3HC is essential for SILF to achieve high-performance operation with single bunch charge exceeding 1 nC. The minimal performance difference (< 5%) between active and passive 3HC indicates that either configuration is viable for SILF implementation.