  MESA (Mainz Energy recovery Superconducting Accelerator) is an energy
recovery linac (ERL) which is under construction at Johannes Gutenberg
University in Mainz. It will be operated in external beam (EB) mode with 150
$\mu$A electron beam at 155 MeV and energy recovery (ER) mode with 1 mA (first
stage) and later 10 mA (second stage) electron beam at 105 MeV. An important
factor which may limit performance of the machine is a beam breakup (BBU)
instability which may occur due to excitation of higher-order modes (HOMs) in
superconducting RF cavities. This effect occurs only when the injected beam
current exceeds a threshold value. The aim of the present work is to develop a
software for reliable determination of the threshold current in MESA, find main
factors which may change its value and finally make a decision concerning
capability of MESA operation at 10 mA and need for additional measures for
suppressing BBU instability.
