Experimental stabilization of transverse collective instabilities in the LHC with second order chromaticity

Schenk, Michael; Buffat, Xavier; Carver, Lee; Maria, Riccardo De; Li, K.; Métral, E.

doi:10.1103/physrevaccelbeams.21.084401

Cited by 10 publications

(19 citation statements)

References 7 publications

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“…This is in accordance with both, experiments and simulations, that were carried out on the rf quadrupole and with second-order chromaticity in the LHC, presented in Refs. [5,7], and confirms the interpretation of these results. All the theory derived for nonlinear chromaticity can also be directly applied to the rf quadrupole.…”

Section: Discussionsupporting

confidence: 87%

“…This section demonstrates that the stability diagram theory developed by Scott Berg and Ruggiero in Ref. [8] for detuning with longitudinal action (which corresponds to a detuning from second-order chromaticity as explained in [7]) is a special solution of Eq. (29) derived in this paper.…”

Section: Appendix A: Vlasov Solution For the Airbag Beam With Linear mentioning

confidence: 71%

“…The functions g l 1 ðr; ϕÞ are the eigenmodes of the free (Z ⊥ 1 ≡ 0) Vlasov equation [Eq. (7)], where l denotes the azimuthal mode number. The corresponding eigenvalues are Ω ðlÞ ¼ ω β;0 þ lω s , for l ∈ Z.…”

Section: A Linear Chromaticitymentioning

confidence: 99%

“…The reason why a larger amount of second-order chromaticity is required when using a positive sign has already been discussed previously in Refs. [2,7]. It is due to the fact that the specific azimuthal mode has a negative real coherent frequency shift combined with the one-sided frequency spreads (and stability boundary diagrams) that are introduced by ξ ð2Þ as illustrated, e.g., by Fig.…”

Section: Fig 4 Comparison Of the Betatron Frequency Distributions Omentioning

confidence: 99%

“…Although the theory developed in this paper is valid for arbitrary orders, the second-order chromaticity is of particular interest here given the experimental observations made in the Large Hadron Collider (LHC) at CERN [6,7]. Both LHC measurements as well as tracking simulations indicate that second-order chromaticity introduces two beam dynamics effects: (i) it changes the effective impedance, i.e., the overlap sum of the beam spectrum with the impedance, leading to a modification of the transverse dipole modes and the associated coherent frequencies, and (ii) it introduces a betatron frequency spread as a function of longitudinal action which leads to a dispersion integral and Landau damping [8].…”

Section: Introductionmentioning

confidence: 99%

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Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

Schenk

Buffat

et al. 2018

Phys. Rev. Accel. Beams

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This paper extends the existing Vlasov theory for transverse coherent beam instabilities to account for nonlinear chromaticity. It confirms the hypothesis that nonlinear chromaticity has two effects on the beam dynamics: (i) it changes the effective impedance which results in a modification of the coherent frequencies of the head-tail modes, and (ii) it can introduce betatron detuning with longitudinal action and provide Landau damping of transverse modes. Based on the new formalism, these two mechanisms are identified and studied analytically with both an airbag and a Gaussian beam. To complete the study, the theory is successfully benchmarked against the circulant matrix solver BimBim as well as the PyHEADTAIL macroparticle tracking code.

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Section: Discussionsupporting

confidence: 87%

Section: Appendix A: Vlasov Solution For the Airbag Beam With Linear mentioning

confidence: 71%

Section: A Linear Chromaticitymentioning

confidence: 99%

Section: Fig 4 Comparison Of the Betatron Frequency Distributions Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

Schenk

Buffat

et al. 2018

Phys. Rev. Accel. Beams

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Impedance and Collective Effects

Métral

Rumolo

Herr

2020

Particle Physics Reference Library

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As the beam intensity increases, the beam can no longer be considered as a collection of non-interacting single particles: in addition to the "single-particle phenomena", "collective effects" become significant. At low intensity a beam of charged particles moves around an accelerator under the Lorentz force produced by the "external" electromagnetic fields (from the guiding and focusing magnets, RF cavities, etc.). However, the charged particles also interact with themselves (leading to space charge effects) and with their environment, inducing charges and currents in the surrounding structures, which create electromagnetic fields called wake fields. In the ultra-relativistic limit, causality dictates that there can be no electromagnetic field in front of the beam, which explains the term "wake". It is often useful to examine the frequency content of the wake field (a time domain quantity) by performing a Fourier transformation on it. This leads to the concept of impedance (a frequency domain quantity), which is a complex function of frequency. The charged particles can also interact with other charged particles present in the accelerator (leading to two-stream effects, and in particular to electron cloud effects in positron/hadron machines) and with the counter-rotating beam in a collider (leading to beam-beam effects). As the beam intensity increases, all these "perturbations" should be properly quantified and the motion of the charged particles will eventually still be governed by the Lorentz force but using the total electromagnetic fields, which are the sum of the external and perturbation fields. Note that in some cases a perturbative treatment is not sufficient and the problem has to be solved self consistently. These perturbations can lead to both incoherent (i.e. of Coordinated by E. Metral

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Wake field, impedance and collective instability

Métral¹

2021

J. Inst.

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The first mention of the impedance concept appeared on November 1966 in the CERN internal report Longitudinal instability of a coasting beam above transition, due to the action of lumped discontinuities by V.G. Vaccaro. Then, a more general treatment of it appeared in February 1967 in the CERN yellow report Longitudinal instabilities of azimuthally uniform beams in circular vacuum chambers of arbitrary electrical properties by A.M. Sessler and V.G. Vaccaro. The concept of wake field came two years later, in 1969, in the paper The wake field of an oscillating particle in the presence of conducting plates with resistive terminations at both ends by A.G. Ruggiero and V.G. Vaccaro. This was the beginning of many studies, which took place over the last five decades, and today, impedances and wake fields continue to be an important field of activity, as concerns theory, simulation, bench and beam-based measurements. Building a reliable impedance or wake field model of a machine is the first necessary step to be able to evaluate the machine performance limitations, identify the main contributors in case an impedance reduction is required, and study the interaction with other mechanisms such as optics nonlinearities, transverse damper, noise, space charge, electron cloud, beam-beam (in a collider), etc. Beam collective instabilities, and their mitigation, cover a wide range of effects in particle accelerators and they have been the subjects of intense research. As the machines performance was pushed new mechanisms were revealed and nowadays the challenge consists in studying the interplays between all these intricate phenomena, as it is very often not possible to treat the different effects separately. With the increasing power of our computers this becomes easier but the need to continue and develop theories remains, to have a better understanding of the interplays between all these effects: the subject of impedance and beam instabilities in particle accelerators is far from being exhausted, as testified by the many new instability and stabilizing mechanisms which have been recently explained or discovered. Furthermore, in the context of the studies for possible future accelerators, some uncharted territories remain such as, for instance, the collective instabilities during the necessary ionization cooling for a muon collider.

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Experimental stabilization of transverse collective instabilities in the LHC with second order chromaticity

Cited by 10 publications

References 7 publications

Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

Impedance and Collective Effects

Wake field, impedance and collective instability

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