Paper  Title  Other Keywords  Page 

TUA1I2  New Understanding of Longitudinal Beam Instabilities and Comparison with Measurements  impedance, synchrotron, coupling, proton  45 


Beam instabilities driven by broad and narrowband impedance sources have been treated separately so far. In this contribution, we present the generalised beam stability analysis based on the concept of van Kampen modes. In the presence of broadband impedance, the loss of Landau damping (LLD) in the longitudinal plane can occur above a certain singlebunch intensity. For significantly higher intensities, the broadband impedance can drive violent radial or azimuthal modecoupling instabilities. We have shown that the synchrotron frequency spread due to RF field nonlinearity, counterintuitively, reduces the singlebunch instability threshold. We have also demonstrated that a multibunch instability driven by a narrowband impedance source can be significantly affected by LLD when adding broadband impedance. These findings are supported by macroparticle simulations and beam observations in the Super Proton Synchrotron and the Large Hadron Collider at CERN.  
Slides TUA1I2 [1.517 MB]  
DOI •  reference for this paper ※ doi:10.18429/JACoWHB2023TUA1I2  
About •  Received ※ 01 October 2023 — Revised ※ 06 October 2023 — Accepted ※ 13 October 2023 — Issued ※ 13 October 2023  
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WEA1I2  Analytical and Numerical Studies on Kicked Beams in the Context of HalfInteger Studies  resonance, spacecharge, coupling, emittance  188 


In the context of the halfinteger studies an investigation of the dynamics of the kicked beam has revealed surprising properties. The coupling of space charge with chromatic ity in addition to usual damping/nondamping dynamics, exhibits new properties typical of a linear coupling. This proceeding covers the status of these studies carried out with analytical and numerical approaches and the prelimi nary results of experimental investigations in the CERN PS Booster.  
Slides WEA1I2 [24.966 MB]  
DOI •  reference for this paper ※ doi:10.18429/JACoWHB2023WEA1I2  
About •  Received ※ 02 October 2023 — Revised ※ 07 October 2023 — Accepted ※ 13 October 2023 — Issued ※ 24 October 2023  
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THAFP03  Measurement of Stability Diagram at IOTA at Fermilab  experiment, kicker, pickup, impedance  400 


Funding: Fermilab Nonlinear focusing elements can enhance the stability of particle beams in highenergy colliders by means of Landau Damping, through the tune spread which is introduced. We propose an experiment at Fermilab’s Integrable Optics Test Accelerator (IOTA) to investigate the influence of nonlinear focusing elements on the transverse stability of the beam. In this experiment, we employ an antidamper, an active transverse feedback system, as a controlled mechanism to induce coherent beam instability. By utilizing the antidamper, we can examine the impact of the nonlinear focusing element on the beam’s transverse stability. The stability diagram, a tool used to determine the system’s stability, will be measured using a recently demonstrated method at the LHC. This measurement is carried out experimentally by selecting specific threshold gains and measuring them for a range of phases. The stability diagram is represented by gei¿ on the complex plane. The experiment at IOTA adds insight towards the stability diagram measurement method by supplying a reduced machine impedance, to investigate the impedance’s effect on the stability diagram, as well as a larger range of phase measurements. 

Slides THAFP03 [1.331 MB]  
Poster THAFP03 [1.692 MB]  
DOI •  reference for this paper ※ doi:10.18429/JACoWHB2023THAFP03  
About •  Received ※ 06 October 2023 — Revised ※ 09 October 2023 — Accepted ※ 10 October 2023 — Issued ※ 12 October 2023  
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THBP12  Slow vs Fast Landau Damping Threshold Measurement at the LHC and Implications for the HLLHC  octupole, experiment, simulation, emittance  470 


The mechanism of Loss of Landau Damping by Diffusion (L2D2) was observed in dedicated experiments at the LHC using a controlled external source of noise. Nevertheless, the predictions of stability threshold by L2D2 models are plagued by the poor knowledge of the natural noise floor affecting the LHC beams. Experimental measurements of the stability threshold on slow and fast time scales are used to better constrain the model. The improved model is then used to quantify requirements in terms of Landau damping for the HLLHC.  
DOI •  reference for this paper ※ doi:10.18429/JACoWHB2023THBP12  
About •  Received ※ 29 September 2023 — Revised ※ 07 October 2023 — Accepted ※ 10 October 2023 — Issued ※ 30 October 2023  
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THBP37  Refining the LHC Longitudinal Impedance Model  impedance, cavity, simulation, injection  559 


Modelling the longitudinal impedance for the Large Hadron Collider (LHC) has been a longstanding effort, especially in view of its HighLuminosity (HL) upgrade. The resulting impedance model is an essential input for beam dynamics studies. Increased beam intensities in the HLLHC era will pose new challenges like RF power limitations, beam losses at injection and coupledbunch instabilities throughout the acceleration cycle. Starting from the existing longitudinal impedance model, effort has been made to identify the main contributing devices and improve their modelling. Loss of Landau damping (LLD) simulations are performed to investigate the dependence of the stability threshold on the completeness of the impedance model and its broadband cutoff frequency. Plans to perform beam measurements to estimate the cutoff frequency, by investigating the LLD threshold in operation, are also discussed.  
Poster THBP37 [5.606 MB]  
DOI •  reference for this paper ※ doi:10.18429/JACoWHB2023THBP37  
About •  Received ※ 01 October 2023 — Revised ※ 06 October 2023 — Accepted ※ 10 October 2023 — Issued ※ 14 October 2023  
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THBP42  Longitudinal Loss of Landau Damping in Double Harmonic RF Systems below Transition Energy  synchrotron, impedance, spacecharge, proton  575 


Landau damping plays a crucial role in ensuring singlebunch stability in hadron synchrotrons. In the longitudinal plane, loss of Landau damping (LLD) occurs when a coherent mode of oscillation moves out of the incoherent synchrotron frequency band. The LLD threshold is studied for a purely inductive impedance below transition energy, specifically considering the common case of double harmonic RF systems operating in counterphase at the bunch position. The additional focusing force due to beaminduced voltage distorts the potential well, ultimately collapsing the bucket. The limiting conditions for a binomial particle distribution are calculated. Furthermore, the contribution focuses on the configuration of the higherharmonic RF system at four times the fundamental RF frequency operating in phase. In this case, the LLD threshold shows a nonmonotonic behavior with a zero threshold where the derivative of the synchrotron frequency distribution is positive. The findings are obtained employing semianalytical calculations using the MELODY code.  
Poster THBP42 [1.710 MB]  
DOI •  reference for this paper ※ doi:10.18429/JACoWHB2023THBP42  
About •  Received ※ 30 September 2023 — Revised ※ 08 October 2023 — Accepted ※ 10 October 2023 — Issued ※ 14 October 2023  
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