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

## TL;DR

This paper analyzes the Beam Break-Up instability in multi-turn ERLs like CBETA, using theory and simulation to determine current limits and explore methods to enhance the threshold current for stable operation.

## Contribution

It combines theoretical analysis and simulation to evaluate BBU effects on CBETA's current limit and proposes strategies to improve the threshold current.

## Key findings

- Simulation results show BBU limits current based on HOM spectra.
- Agreement between BMAD simulations and BBU theory is confirmed.
- Strategies to increase CBETA's current threshold are discussed.

## Abstract

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.