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This paper uses theory and simulation of the Beam Break-Up instability (BBU)for multi-turn ERLs to determine and to optimize the current limit of theCornell Brookhaven Energy-Recovery-Linac Test Accelerator (CBETA). Currentlyunder construction at Cornell University's Wilson Laboratory, the primarystructures of CBETA for beam recirculation include the Main Linac Cryomoduleand the Fixed Field Alternating Gradient beamline. As the electron bunches passthrough the MLC cavities, Higher Order Modes (HOMs) are excited. Therecirculating bunches return to the cavities to further excite HOMs, and thisfeedback loop can give rise to BBU. We will first explain how BBU effect issimulated using the tracking software BMAD, and check the agreement with theBBU theory for the most instructive cases. We then present simulation resultson how BBU limits the maximum achievable current of CBETA with different HOMspectra in the cavities. Lastly we investigate ways to improve the thresholdcurrent of CBETA.

Beam break-up current limit in multi-turn ERLs and CBETA