Thresholds for loss of Landau damping in longitudinal plane

Karpov, Ivan; Argyropoulos, Theodoros; Shaposhnikova, E.

doi:10.1103/physrevaccelbeams.24.011002

Cited by 13 publications

(20 citation statements)

References 12 publications

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“…The reason for the discrepancy was in shorter wavelengths of possible perturbations examined in the last reference. The problem of the LLD threshold calculation appeared to be solved until a recent article of I. Karpov, T. Argyropoulos and E. Shaposhnikova [6] demonstrated that all the previous results were, in fact, incorrect: actually, there is no LLD threshold for such impedance, and the previous claims were all based in the insufficiency of the accepted limits on wave numbers q of the perturbations or insufficient number of the mesh points. This conclusion was demonstrated in several independent ways, leaving no doubt of its correctness.…”

Section: Introductionmentioning

confidence: 99%

Convective instabilities of bunched beams with space charge

Burov

2019

Phys. Rev. Accel. Beams

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For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For sufficiently strong space charge (SC), the instability threshold of the wake-driven coherent tune shift normally increases linearly with the SC tune shift, as independently concluded by several authors using different methods. This stability condition has, however, a very strange feature: at strong SC, it is totally insensitive to the number of particles. Thus, were it correct, such a beam with sufficiently strong SC, being stable at some intensity, would remain stable at higher intensity, regardless of how much higher! This paper suggests a resolution of this conundrum: while SC suppresses TMCI, it introduces head-to-tail convective amplifications, which could make the beam even less stable than without SC, even if all the coherent tunes are real, i.e. all the modes are stable in the conventional absolute meaning of the word. This is done using an effective new method of analysis of the beam's transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the saturating convective instability, SCI, and the absolute-convective instability, ACI.

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Section: Introductionmentioning

confidence: 99%

Convective instabilities of bunched beams with space charge

Burov

2019

Phys. Rev. Accel. Beams

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“…In addition, another incorrect interpretation is given (see e.g. [66]) that the observed continuous spectrum after saturation is of the discrete van Kampen type, instead of recognizing that the linearity no longer applies and continuous spectra of the type presented in this work should instead be implied. We conclude with the expectation that particle trapping, the associated nonlinearities and the various trapping scenarios will certainly find their way into beam physics in the future as well.…”

Section: X2 Solitary Structures On Hadron Beams In Synchrotronsmentioning

confidence: 82%

“…The privilege of being the most general method is therefore reserved for the Schamel method, since it is as general as the BGK method, it is in addition complete and can also deal with undisclosed solutions. A8 Holes in synchrotrons and storage rings exist above a threshold only and are van Kampen modes This threshold statement is only valid if there is a certain band of incoherent sychrotron frequencies, as for the applicability of the Landau damping [65,66,89]. For structures that arise from coherent seeds, however, there is a loss of linear Vlasov dynamics at all, which not only implies the lack of a threshold for the invalidity of Landau damping but the overall existence of hole equilibria and the exclusion of van Kampen modes to describe these structures in favor of the current theory (see also Sect.X2).…”

Section: A3 the Thumb-tear Drop Relation Is A Linear Dispersion Relat...mentioning

confidence: 99%

Pattern formation in Vlasov-Poisson plasmas beyond Landau caused by the continuous spectra of electron and ion hole equilibria

Schamel¹

2021

Preprint

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The data that supports the findings of this study are available from the corresponding author upon reasonable request. CONTENT I. INTRODUCTION p.2 II. THEORY OF ELECTRON HOLE EQUILIBRIA p.4 III. THE GALLERY OF ELEMENTARY MODES p.7 III.1 The harmonic mode (single wave) III.2 The privileged sech 4 (x) -solitary mode III.3 The Gaussian e −x 2 -solitary mode III.4 The Second Order Gaussian e − sinh 2 (x) -solitary mode III.5 The sech 2 (x) -soliton IV. HOLES CAUSED BY TWO TRAPPING SCENARIOS p.12 IV.1 The cnoidal electron hole (CEH) IV.2 The Schamel-Korteweg-de Vries solitary electron hole (SKdV-SEH) IV.3 The modified second order Gaussian SEH IV.4 The undisclosed logarithmic Schamel SEH V. THE CLASS OF NEGATIVELY POLARIZED SOLITARY ELECTRON HOLES (npSEHs) p.15

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“…Feedbacks are working very well, but they cannot, at the moment, damp all types of instabilities: BNS or Landau damping still usually needs to be used (after optimisation of all the many machine and beam parameters available), and there is still a lot to be done on Landau damping and its possible loss, both in the transverse and longitudinal plane (see for instance Refs. [7][8][9]47]).…”

Section: Discussionmentioning

confidence: 99%

“…The Sacherer stability diagram in the longitudinal plane is justified only for low-frequency impedances and in other cases should be used with caution. More advanced methods (van Kampen modes and Lebedev equation) together with particle simulations are available for accurate threshold estimations, also based on a realistic impedance model, since a constant Im(Z /n) may not give converging LLD thresholds [47]. Landau damping can be significantly increased by additional, higher harmonic RF system, but its limitations in bunch-Fig.…”

Section: Landau Dampingmentioning

confidence: 99%

General mitigation techniques for coherent beam instabilities in particle accelerators

Métral

2021

Eur. Phys. J. Plus

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An important number of coherent beam instability mechanisms can be observed in a particle accelerator, depending if the latter is linear or circular, operated at low, medium or high energy, with a small or a huge amount of turns (for circular machines), close to transition energy or not (below or above), with only one bunch or many bunches, with counter-rotating beams (such as in colliders) or not, if the beam is positively or negatively charged, if one is interested in the longitudinal plane or in the transverse plane, in the presence of linear coupling between the transverse planes or not, in the presence of nonlinearities or not, in the presence of noise or not, etc. Building a realistic impedance model of a machine is a 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 (linear and nonlinear), RF gymnastics, transverse damper, noise, space charge, electron cloud, and beam–beam (in a collider). Better characterising an instability is the first step before trying to find appropriate mitigation measures and push the performance of a particle accelerator, as some mitigation methods are beneficial for some effects and detrimental for some others. For this, an excellent instrumentation is of paramount importance to be able to diagnose if the instability is longitudinal or transverse, single bunch, or coupled bunch, involving only one mode of oscillation or several, and the evolution of the intrabunch motion with intensity is a fundamental observable with high-intensity high-brightness beams. Finally, among the possible mitigation methods of coherent beam instabilities, the ones perturbing the least the single-particle motion (leading to the largest necessary dynamic aperture and beam lifetime) and easiest to implement for day-to-day operation in the machine control room should be preferred.

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Thresholds for loss of Landau damping in longitudinal plane

Cited by 13 publications

References 12 publications

Convective instabilities of bunched beams with space charge

Convective instabilities of bunched beams with space charge

Pattern formation in Vlasov-Poisson plasmas beyond Landau caused by the continuous spectra of electron and ion hole equilibria

General mitigation techniques for coherent beam instabilities in particle accelerators

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