The multipass regenerative multibunch beam breakup instability is specific to recirculating linacs (linear accelerators) and energy recovery linacs operating in continuous wave mode where particle bunches pass multiple times through the same superconducting RF cavities with extremely high quality factor. Parasitic electromagnetic modes excited in the cavities can affect bunch dynamics in such a way, that on its subsequent passes it excites the modes further and a positive feedback loop is formed. The term "regenerative" means that the effect on a single bunch during its passage through the machine is negligible but the instability develops in time due to persisting fields in the cavities (in opposite to "cumulative" instabilities developing in space when the effect accumulates during the single passage of a bunch through the machine).

Analysis in the time domain (bunch tracking) and the frequency domain (complex current plot technique) may be used to study the instability. Usually only dipole modes are considered, however, in the present work similar approaches are applied to monopole and quadrupole modes and illustrated with simulation results for the S-DALINAC and MESA facilities. An approximated stability analysis technique with better performance for the case of multiple recirculations is proposed. Countermeasures including betatron phase advance adjustment and additional betatron coupling are considered and a universal criterion for assessment of their effectiveness is proposed. A strategy to study the instability experimentally at S-DALINAC is described. A simple model of a damped oscillator with feedback is proposed as a universal example illustrating the phenomenon in general.