Transverse instabilities for multiple nonrigid bunches in a storage ring

Review of collective beam instabilities in electron-positron storage rings

“…For theoretical analysis of mecha nisms of excitation and suppression of multibunch instability, taking into account the motion of parti cles inside a bunch, models of both macroparticles and continuous medium can be used. Commonly, the methods of perturbation theory are applied to the Vlasov equation, which allows (introducing a series of simplifications) for reducing the analysis of insta bility to solving the problem on eigenvalues for the coherent modes of oscillations [1,[79][80][81][82]. Interac tion of the beam with the elements of the vacuum chamber is described in terms of frequency depen dent transverse impedance.…”

Beam Instabilities in Hadron Synchrotrons

“…In the case of flat chambers, the intensity threshold is higher in one plane than in the other and linear coupling can be used to raise the TMCI intensity threshold [152]. Note finally that with many bunches the TMCI intensity threshold can be considerably reduced [144]. Fig.…”

“…This analysis was extended in Ref. [144] to include also the coupling between the modes (and the possibility to have different head-tail modes in the different bunches). In the case of gaps between bunch trains, a time-domain approach is usually better suited.…”

Collection of Formulas Describing Storage Ring Coherent Instabilities

“…The nontrivial situation arises when the coherent tune shift is of the order of ω s . Then modes can not be considered separately and coupling can lead to new Coupled-Bunch-Coupled-Mode (CBCM) instability in the multibunch system [6].…”