Beam breakup current limit in multiturn energy recovery linear accelerators

CBETA, the Cornell BNL Energy-Recovery-Linac (ERL) Test Accelerator, is the first multiturn ERL with superconducting radio frequency (SRF) cavities cavities and will therefore be the first ERL whose current could be limited by the beam break-up (BBU) instability. To investigate the threshold current, we calculate HOMs in CBETA's cavities, including their construction errors, and simulate the BBU threshold current with the established simulation code BMAD. For some construction errors, this current limit is not sufficiently large and means of increasing it are investigated. We find that some means that have been shown effective in single turn ERLs are not practical for multiturn ERLs. To make sure that simulations are trustworthy for CBETA, we revisit the BBU theory for multiturn configurations, and compare to simulation results. We also further explore the scaling law of the BBU threshold current for the case with symmetric ERLs, and a new scaling factor has been found. BBU suppression with lattice chromaticity has been investigated assuming bunches with a Gaussian energy spread. The ability to simulate BBU effect with multiple particles per bunch has been added into BMAD, and agreement with the derived theoretical formula is found. CBETA is currently under beam commissioning at Cornell University. Our simulations show that an optimized optics will push the BBU threshold current beyond the design current, for all realistic cavity production errors.