  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 the
Cornell Brookhaven Energy-Recovery-Linac Test Accelerator (CBETA). Currently
under construction at Cornell University's Wilson Laboratory, the primary
structures of CBETA for beam recirculation include the Main Linac Cryomodule
and the Fixed Field Alternating Gradient beamline. As the electron bunches pass
through the MLC cavities, Higher Order Modes (HOMs) are excited. The
recirculating bunches return to the cavities to further excite HOMs, and this
feedback loop can give rise to BBU. We will first explain how BBU effect is
simulated using the tracking software BMAD, and check the agreement with the
BBU theory for the most instructive cases. We then present simulation results
on how BBU limits the maximum achievable current of CBETA with different HOM
spectra in the cavities. Lastly we investigate ways to improve the threshold
current of CBETA.
