Transverse mode coupling instability of colliding beams

Abstract

In high brightness circular colliders, coherent and incoherent beam dynamics are dominated by beambeam interactions. It is generally assumed that the incoherent tune spread introduced by the beam-beam interactions is sufficiently large to cure any instabilities originating from impedance. However, as the two counterrotating beams interact they can give rise to coherent dipole modes and therefore modify the coherent beam dynamics and stability conditions. In this case, coherent beam-beam effects and impedance cannot be treated independently and their interplay should be taken into account in any realistic attempt to study the beam stability of colliding beams. Due to the complexity of these physics processes, numerical simulations become an important tool for the analysis of this system. Two approaches are proposed in this paper: a fully self-consistent multiparticle tracking including particle-in-cell Poisson solver for the beambeam interactions and a linearized model taking into account finite bunch length effects. To ensure the validity of the results a detailed benchmarking of these models was performed. It will be shown that under certain conditions coherent beam-beam dipole modes can couple with higher order headtail modes and lead to strong instabilities with characteristics similar to the classical transverse mode coupling instability originating from impedance alone. Possible cures for this instability are explored both for single bunch and multibunch interactions. Simulation results and experimental evidences of the existence of this instability at the LHC will be presented for the specific case of offset collisions.

Impact of the resistive wall impedance on beam dynamics in the Future Circulare+e−Collider

“…In this situation, coherent beam-beam effects and impedance are not independent any more and their interplay should be taken into account [34]. This subject, along with the mitigating effect of beamstrahlung, equally linked to the colliding beams, is an important topic, which deserves future investigations.…”

Modeling of the emittance growth due to decoherence in collision at the Large Hadron Collider

“…The results are mostly in between the predictions of the weak-strong model and the strong-strong model without chromaticity. This observation may be interpreted as an impact of the multiple coherent modes developing in the presence of beam-beam interactions and chromaticity [22,23]. The frequency of most of these modes will be within the incoherent spectrum, such that the assumption behind the derivation of Eq.…”

Analysis of transverse beam stabilization with radio frequency quadrupoles

“…Complementary to the studies carried out with PyHEADTAIL, the second accelerator physics model used here is the CMM implemented in the BimBim code. It includes amongst others the effects of impedance and chromaticity, but neglects for instance multiturn wake fields and Landau damping from magnetic octupoles [27]. The former is a valid approximation for the wake fields present in the LHC as they decay on a time scale faster than the revolution period [18].…”