Transverse Mode Coupling Instabilities

Transverse Mode Coupling Instabilities (TMCI) emerged between 1974 and 1980 as the main limitation of dense bunches in electron synchrotrons and storage rings. A two-particle model allows one to calculate the Beam-Break-Up (BBU) instability in linacs. Extending this to synchrotrons show that the BBU instability is suppressed below a threshold intensity by synchrotron oscillations. The classical theory of head-tail modes together with general properties of coupling impedances are used to show how single bunches become unstable when head-tail modes couple together: This is the TMCI threshold. Above threshold, observations both in proton and electron synchrotron can be described by BBU theory.