Beam-beam Instability Research Articles

Impedance modelling and collective effects in the Future Circular e+e− Collider with 4 IPs

The FCC-ee impedance model is being constantly updated closely following the vacuum chamber design and parameters evolution. In particular, at present, a thicker NEG coating of 150 nm (instead of previous 100 nm) has been suggested by the vacuum experts, and a more realistic impedance model of the bellows has been investigated. Moreover, also the transverse impedance has been updated by considering the same sources as for the longitudinal case. Therefore, the FCC-ee impedance database is getting more complete and the impedance model is being refined. In this paper we describe the presently available machine coupling impedance in both longitudinal and transverse planes, and study the impedance-driven single bunch instabilities (with and without beam-beam interaction) for the new FCC-ee parameter set with 4 interaction points (IPs). The results are compared with the previously obtained ones and a further possible mitigation of the beam-beam head-tail instability (X-Z instability) is proposed.

Coupling effects of beam-beam interaction and longitudinal impedance

Recent studies have shown a novel coherent head-tail instability induced by beam-beam interaction with a large Piwinski angle. The instability has become an important issue during the designs of CEPC and FCC-ee. Simulations have further revealed that the longitudinal impedance has a strong impact on the beam stability, squeezing the horizontal stable tune area seriously. The cross-wake force has been introduced to represent beam-beam interaction. A mode coupling theory based on the localized wake (impedance) force has been developed to explain the instability. However, the theory did not consider the effects of longitudinal impedance. In this paper, we develop a new transverse mode coupling analysis method that could be used to study the beam-beam instability with and without longitudinal impedance. The result shows that the distortion of longitudinal phase space trajectory and the incoherent synchrotron tune shift induced by longitudinal impedance would reduce the stable tune area.

Cross-wake force and correlated head-tail instability in beam-beam collisions with a large crossing angle

This paper discusses novel coherent beam-beam instability in collisions with a large crossing angle. The instability appears in the correlated head-tail motion of two colliding beams. A cross-wake force, which is localized at the collision point, is introduced to represent the head-tail correlation between colliding beams. A mode-coupling theory based on this localized cross-wake force enables us to explain the correlated heal-tail instability. The use of a collision scheme with a large crossing angle is becoming popular in the design of electron--positron colliders. An example thereof is the SuperKEKB project, in which a collision with a large crossing angle is performed to boost the luminosity to $0.8\ifmmode\times\else\texttimes\fi{}{10}^{36}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Future circular colliders will also be designed with a large crossing angle. Strong-strong simulations, which have shown the first coherent head-tail instability, can limit the performance of proposed future colliders. The mechanism whereby this instability occurs is mode coupling due to the cross-wake force. This instability may affect all collider designs based on the crab waist scheme.

Coherent Beam-Beam Instability in Collisions with a Large Crossing Angle

Coherent Beam-Beam Instability in Collisions with a Large Crossing Angle

Coherent Beam-Beam Instability in Collisions with a Large Crossing Angle.

In recent years the "crab-waist collision" scheme [P. Raimondi, Proceedings of 2nd SuperB Workshop, Frascati, 2006.; M. Zobov etal., Phys. Rev. Lett. 104, 174801 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.174801] has become popular for circular e^{+} e^{-} colliders. The designs of several future colliders are based on this scheme. So far the beam-beam effects for collisions under a large crossing angle with or without crab waist were mostly studied using weak-strong simulations. We present here strong-strong simulations showing a novel strong coherent head-tail instability, which can limit the performance of proposed future colliders. We explain the underlying instability mechanism starting from the "cross-wake force" induced by the beam-beam interaction. Using this beam-beam wake, the beam-beam head tail modes are studied by an eigenmode analysis. The instability may affect all collider designs based on the crab-waist scheme. We suggest an experimental verification at SuperKEKB during its commissioning phase II.

Fundamental beam-beam limit from head-on interaction in the Large Hadron Collider

The beam-beam limit at hadron colliders manifests itself in the form of degraded luminosity lifetime and/or reduced beam lifetime. In particular, for increasing beam intensity, the nonlinear beam-beam force causes incoherent emittance growth, while the (linear) coupling force between the two colliding beams can result in coherent beam-beam instabilities. These phenomena may be enhanced (or suppressed) by lattice errors, external noise, and other perturbations. We investigate the luminosity degradation caused both by incoherent emittance growth and by coherent beam-beam instability. The resulting beam-beam limit for an ideal machine and the of question how it is affected by some of the aforementioned errors are discussed in theory and simulation.

Response of colliding beam-beam system to harmonic excitation due to crab-cavity rf phase modulation

During 2008 and 2009 dedicated beam experiments with crab cavities were performed in the KEKB. The goal was to measure the impact of crab-cavity radio frequency (rf) noise on the beam quality. These experiments were performed as a validation of the crab-cavity beam dynamics models in view of the possible use of crab cavities in the upgrade of the CERN Large Hadron Collider (LHC). An unexpected strong beam-beam instability was observed during the course of the experiments as a kind of frequency response. Understanding this finding required extensive multiparticle and single particle simulations plus an extra experimental session to consolidate the observations.

Importance of beam-beam tune spread to collective beam-beam instability in hadron colliders.

In hadron colliders, electron-beam compensation of beam-beam tune spread has been explored for a reduction of beam-beam effects. In this paper, effects of the tune-spread compensation on beam-beam instabilities were studied with a self-consistent beam-beam simulation in model lattices of Tevatron and Large Hodron Collider. It was found that the reduction of the tune spread with the electron-beam compensation could induce a coherent beam-beam instability. The merit of the compensation with different degrees of tune-spread reduction was evaluated based on beam-size growth. When two beams have a same betatron tune, the compensation could do more harm than good to the beams when only beam-beam effects are considered. If a tune split between two beams is large enough, the compensation with a small reduction of the tune spread could benefit beams as Landau damping suppresses the coherent beam-beam instability. The result indicates that nonlinear (nonintegrable) beam-beam effects could dominate beam dynamics and a reduction of beam-beam tune spread by introducing additional beam-beam interactions and reducing Landau damping may not improve the stability of beams.

Saturation of the coherent beam-beam instability

The nonlinear regime of the beam-beam instability for flat beams is considered. Excitation of coherent modes and mode interaction is studied above the threshold of instability. It is shown that the exponential growth of the linear approximation may saturate, leading to a finite growth of transverse emittance.

Simulation of the head-tail instability of colliding bunches

A numerical simulation of a possible coherent beam-beam instability of the head-tail type is presented. The studied model employs a linearized coherent beam-beam interaction and takes complete account of the bunch length, including the deformation of the colliding bunches during their overlap. Measured head-tail mode spectra from the VEPP-2M collider are compared with the results of the analytical model and tracking. A computer code for evaluation of the coherent mode increments, which was used for analysis of possible ways to stabilize the beam-beam system, is described.

Spin depolarization due to beam-beam collisions

The effect of the beam-beam interaction on spin depolarization in a proton-proton collider has been studied. The employed method is based on a matrix formalism for spin advance and for perturbed betatron particle motion in a ring. Calculations were done for a collider with one interaction point and two installed Siberian Snakes in each ring. A matrix for spin advance after an arbitrary large number of turns is found. Performed study indicates that spin depolarization due to beam-beam collisions is suppressed if the beam-beam interaction is stable and if the operation point is far enough from spin resonances. Meanwhile, in the absence of snakes or under beam-beam instability, spin is a subject of strong depolarization. Analytical estimations are confirmed by results of computer simulations.

Phase averaging of the beam-beam instability

In this paper we study the beam-beam instability in long bunches. A common effect of the finite bunch length and of the modulation of β-functions results in significant suppression of the strengths of the beam-beam resonances in the core region as well as in the excitation of strong synchro-betatron resonances in the tails of colliding bunches. For large amplitudes of synchrotron oscillations the calculations predict essential difference in the strengths of beam-beam resonances for two cases: when colliding bunches have equal vertical ( β z ∗ ) and horizontal ( β x ∗ ) β-functions, and when together with β x ∗ ⪢ β z ∗ the cross sections of the colliding bunches are very flat. The region of the discussed parameters is specific for the future B- and Φ-factories.

Renormalized Fokker-Planck equation for the problem of the beam-beam interaction in electron storage rings

It is shown that the beam-beam interaction in electron storage rings is equivalent to an additional source of noise for the particle betatron oscillations. A weak white noise acting upon a nonlinear oscillator causes a fast loss of coherence in its phase. This loss of coherence induces a broadening of the resonances, thus avoiding the problem of the divergent perturbative series which arises in the study of nonintegrable Hamiltonian systems. A “renormalized” Fokker-Planck equation is established which contains new diffusive terms corresponding to the presence of resonances. The solution of this equation is exhibited explicitly in a simplified case. This allows an analytical approach to the problem of the beam-beam instability, which sets an upper limit to the maximum attainable luminosity in storage rings.

Laboratory observations of RF emissions at ωpeand (n+ ½)ωcein Electron beam-plasma and beam-beam interactions

Electric field emissions at frequencies of (n + ½)fce have been generated in a large-scale electron beam experiment in the giant NASA vacuum facility in Ohio. These emissions arise when a contrastreaming beam configuration exists, the primary beam consisting of monoenergetic electrons (50 eV to 5 keV) and the other beam of lower-energy ‘backscattered’ secondary electrons. It is suggested that the same mechanism could also be the source of the observed emissions at auroral latitudes. In the absence of the beam-beam instability, weak oscillations were observed at the plasma frequency. In the latter case no significant modifications of the primary beam velocity distribution occurred, and the beam configuration is adequately described by single-particle motion in the ambient magnetic field.