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Description
We present a systematic multi-bunch longitudinal beam dynamics study for the Elettra 2.0 storage ring equipped with a double RF system (main RF cavity plus passive third-harmonic cavity). The higher-order modes (HOMs) of the main RF cavity, obtained from 3D eigenmode simulations, are used as input to coupled-bunch instability models. For these HOMs, we compute growth rates using a simple harmonic-oscillator (SHO) model and an extended model including the nonlinear double-RF potential and Landau damping, and determine the HOM detuning required to bring all growth rates below the damping capability of the longitudinal feedback. The analytical predictions are benchmarked against multi-bunch tracking in Elegant. In parallel, we optimise the double-RF parameters for both uniform and non-uniform fillings using mbtrack2 tracking with the albums algorithm. For the operational main-cavity detuning, we identify narrow third-harmonic cavity detuning windows that avoid Robinson-type and PTBL instabilities while providing near-flat RF potentials, bunch-lengthening factors up to 4.4 and lifetime improvements up to 3–4. These results define a robust working point for the Elettra 2.0 double-RF system.
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