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3958691f-4882-4187-870e-d2df6c2f151e | plinginstability”,Part. Accel.,vol.20,p.79,1986. https:
//cds.cern.ch/record/167026
[25]S.A.Antipov,V.Gubaidulin,I.Agapov,E.C.CortésGarcía,
andA.Gamelin,“Spacechargeeffectsinfourth-generation
lightsources:ThePETRAIVandSOLEILIIcases”,Phys.
Rev. Accel. Beams, vol. 28, no. 2, p. 024401, Feb. 2025.
doi:10.1103/PhysRevAccel... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5106.pdf | 3 |
bfff43e8-a809-4eb5-bcea-0f4cf0f74b2c | record/558880/files/17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5106
MC5.D06: Coherent and Incoherent Instabilities Measurements and Countermeasures 2509WEP: Poster session WEP5106
Content from this work m... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5106.pdf | 3 |
d8ad3886-f772-44df-b144-7393103363fa | COUPLED-BUNCH INSTABILITIES WITH A DEFOCUSING
HIGHER-HARMONIC RF SYSTEM
R. Heine∗, W. Keusgen, Technische Universität Berlin, Berlin, Germany
L. Intelisano, I. Karpov, European Organization for Nuclear Research, Geneva, Switzerland
Abstract
Longitudinal coupled-bunch instabilities limit the beam
intensity in many synch... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 0 |
881ae392-ccfa-4327-973a-d8ff7a65d28e | rateofcoupled-bunchinstabilities. Theinfluenceofbeam
parameters such as the bucket filling factor, narrowband
impedance properties, and RF system configuration is high-
lighted. RegimesinwhichBLMisadvantageousordisad-
vantageous are compared to the ones for a single-harmonic
RF (SRF) system. The results are based on se... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 0 |
4ba151d2-ff70-4b8f-99a4-67eb3568dbec | and, in the worst case, to beam loss. To lift the intensity
limitations due to CBI, double-harmonic RF systems (DRF)
have been implemented in several synchrotrons [ 1,2]. Al-
thoughtheimpactofDRFsystemsonCBIiswellunderstood
and discussed in the literature [ 3,4], the interplay among
different beam parameters, impedance... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 0 |
ad31253c-b3f7-47a3-b298-318cd346276c | stabilitydiagrammethod andshed lighton thegrowthrate
behaviour for different RF settings.
∗ruben.nicholas.heine@cern.chMAIN EQUATIONS AND DEFINITIONS
Tosimplifythecalculation,wemovefromconjugatecoordi-
natesparticleenergy, Δ𝐸,andRFphasedeviation, 𝜙,ofthe
conventionalequationsofmotiontoenergy, ℰ,andphase,
𝜓, of the s... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 0 |
8eafa180-42ee-43e2-9eb8-d824655b848f | A small perturbation function ̃ℱis added to this station-
ary distribution, which is periodic in 𝜓and satisfies the
linearised Vlasov equation [ 6].
The perturbation’s phase advance from bunch to bunch
is2𝜋𝑙/𝑀, where𝑀is the number of equidistant bunches,
and𝑙is the coupled-bunch mode. The Lebedev equation
provide... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 0 |
8eb90f45-15b8-482b-9080-d41d231218c7 | integrals defined in [ 9].17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5107
2510 MC5.D05: Coherent and Incoherent Instabilities Theory, Simulations, Code DevelopmentWEP5107 WEP: Poster session
Content from ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 0 |
36426425-f435-4db6-9932-899efb8cf477 | The general solution is then found from
det∣𝛿𝑝𝑘+𝜁𝑀
ℎ𝐺𝑝𝑘(Ω)𝑍𝑘(Ω)
𝑘∣ = 0. (7)
Mostimpedancesourcesinacceleratorsarewelldescribed
by the resonator model according to 𝑍(𝜔) = 𝑅/(1 +
𝑖𝑄(𝜔/𝜔𝑟−𝜔𝑟/𝜔)), where𝑅is the shunt impedance, 𝜔𝑟
the resonant frequency, and 𝑄the quality factor of the reso-
nance.
... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 1 |
7326d166-fb33-4c2d-a850-fe5175b76f0f | DOUBLE RF-SYSTEMS
The voltage of a DRF system is described by
𝑉RF(𝜙) = 𝑉 0[sin(𝜙+𝜙 𝑠0)+𝑟𝑣sin(𝑟ℎ𝜙+𝑟ℎ𝜙𝑠0+Φ2)],
(9)
with𝑉0denoting the voltage magnitude of the main RF sys-
tem,𝜙𝑠0thephaseofthesynchronousparticle,and 𝑟𝑣and
𝑟ℎthevoltagemagnitudeandharmonicnumberratiosofthe
two RF systems. For the sake of... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 1 |
6dd2f5bf-9cbe-4b2f-b3ec-5e919aa25107 | 𝜔𝑠(ℰ), changes depending on 𝑟ℎand𝑟𝑣. This function is
animportantcontributortothefinalstabilitybehaviourofthebeamaccordingtoEq. (6). Whileanoveralllargesyn-
chrotronfrequencyspreadisadvantageousforbeamstability,
the local derivative of 𝜔𝑠(ℰ)at the location of the potential
instability, Ωunstable= 𝜔𝑠(ℰunstable)... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 1 |
4b3a5095-beb9-446a-93de-92c853df7adc | distribution has been derived in [ 10]:
𝜁th,SRF=ℎ𝜙4max𝜔𝑟
16𝑀𝑅𝜔0min
𝑥∈[0,1](1−𝑥)1−𝜇/𝐽1(𝑥𝜔𝑟𝜙max
𝜔0ℎ),
(10)
where𝐽1is the Bessel function of the first kind and order.
In the case of DRF, analytical approximations for CBI
[5,11], as well as for loss of Landau damping in bunch
shorting mode [ 12] havebeen p... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 1 |
5c5d2725-d719-45d9-b8c3-26b19f8647ea | theCBIthresholdinBLMdropstozero: 𝑟𝑣,0= 1/𝑟3
ℎ. The
reason for the decrease of 𝜁thfor𝑟𝑣→ 𝑟𝑣,0is the com-
pensation of the third-order terms of the RF-voltage for
BLM, leading consequently to 𝜔′𝑠(ℰ) = 0 for𝑟𝑣= 𝑟𝑣,0.
Beyond the compensation regime, 𝜔′𝑠(ℰ)switches sign and
for𝑟𝑣> 2𝑟𝑣,0BLMoffershigherint... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 1 |
5b3c2b3d-e93f-47a5-b3ba-f0b3f1cb97a8 | Thegoodagreementbetweenexactandapproximatesolu-
tionscanbeseeninFigure 2. Onlyfor 𝑟𝑣→ 1/𝑟ℎ,theresults
deviate more strongly, as the region of validity shrinks for a
flat potential well.
LONG BUNCHES
In contrastto short bunches, the location of the instability
for long bunches is difficult to predict and might drasti... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 2 |
657f603e-7ad3-46a8-8afd-5dc2fb1958e1 | are calculated for a given growth rate to allow a comparison
with macro-particle simulations. For the given 𝑟𝑣= 0.2,
𝜔𝑠(ℰ)has a local maximum around 𝜙max≈ 1.4, causing
significant 𝜁th-drops for certain 𝜔𝑟. In the parameter space
coloured in blue, the instability has moved to the part of
thebunchwithlow ∣𝜔′𝑠(ℰ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 2 |
de9636e9-7d2f-4a99-8bfa-3ee69b4615b2 | threshold gains, while the blue areas mark regions with
lowered thresholds.
Increasing the distribution parameter, 𝜇, will push the
instability more towards the centre; thus, the blue areas
of relative 𝜁th-loss shrink or disappear, while the red gain
regionsremainunchanged. Theoppositeeffectholdsfora
decreased 𝜇.GRO... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 2 |
f86b77ab-73a1-4bbf-ad75-283f8898db8c | old is observable, due to the decrease of |𝜔′𝑠(ℰ)|. Despite
the longer bunch length ( 𝜙max= 1), the small angle approx-
imationremainsagoodestimateoftheintensitythreshold
behaviourat ℑ{Ω} ≈ 0 . Furthermore,theintensitythreshold
hasa linear growthrate-dependency,if 𝜙maxor𝑟𝑣aresuffi-
ciently small. Linearity is not... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 2 |
4e3f6e56-230d-4649-ad78-54b0db3cb927 | CONCLUSION
In this study,we investigatedthe effect of a DRF systemin
BLMontheintensitythresholdsforCBI.Theapproximated
scaling factor of ∣1−𝑟𝑣𝑟3
ℎ∣for DRF-systems in BLM was
comparedtothestabilitydiagrammethodtoassessitsvalid-
ityrange. Moreover,wepresentedthecondition 𝑟𝑣≥ 2/𝑟3
ℎ
to ensure an increased intensity ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 2 |
dc1c431b-c15f-4dd9-bce3-f8c310e26d86 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5107
2512 MC5.D05: Coherent and Incoherent Instabilities Theory, Simulations, Code DevelopmentWEP5107 WEP: Poster session
Content from this work may be used under the terms of the CC BY 4.0 licence (© 2026). Any distribution of this work must maint... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 2 |
9fd5dc65-6757-46d2-bb2f-4aae8af6dc2a | REFERENCES
[1]A. Hofmann, S. Myers, “Beam Dynamics in a Double RF
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[2]C. M. Bhat et al., “Stabilizing effect of a double-harmonic
RF system in the CERN PS”, in Proc. PAC’09 , Vancouver,
Canada, M... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 3 |
6d73a636-eb6c-43e4-95aa-d569a9a4e116 | pp.58–66, 1986. doi:1/zero.alt4.1/zero.alt4/zero.alt47/BF/zero.alt41129839
[6]A. W. Chao, Physics of Collective Beam Instabilities in High
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1993.
[7]R.Heine etal.,“Thresholdsoflongitudinalmulti-bunchin-
stabilitiesindoubleharmonicRFsystems”,in Proc.IPAC’25 ,Taipei, T... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 3 |
50f72442-1446-4378-a59b-bf6f13ce90f2 | bunchinstabilityevaluationforFCC-hh”, in Proc.IPAC’19 ,
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[11]M. Zobov et al., “Bunch length control in DAFNE by a
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vol.354, pp. 215-223, 1995.
doi:1/zero... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 3 |
ad6091f5-56b1-4fe3-9596-edd3b5234019 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5107
MC5.D05: Coherent and Incoherent Instabilities Theory, Simulations, Code Development 2513WEP: Poster session WEP5107
Content from this work may be used under the terms of the CC BY 4.0 licence (© 2026). Any distribution of this work must maint... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5107.pdf | 3 |
24874d76-275f-47cb-9399-4fcd05ebcf69 | LONGITUDINAL BEAM STABILITY IN HL-LHC∗
I. Karpov†, R. Calaga, B. E. Karlsen-Bæck, H. Timko, and M. Zampetakis,
European Organization for Nuclear Research, Geneva, Switzerland
Abstract
Recentstudiesshowedthatthebroadbandimpedancein
synchrotronscansignificantlyalterthelongitudinalmulti-
bunchinstabilitythreshold. Theresu... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
e3bc5850-017e-4de3-8399-197062b9ba7f | impedancemodel. Futurebenchmarkmeasurementsarepro-
posedtoprobethemulti-bunchinstabilitythresholddriven
bythepartiallycompensatedmainRFcavityimpedance. Fi-
nally,possiblemitigationmeasurestoincreasetheinstability
threshold are discussed.
INTRODUCTION
Interaction of a charged particle beam with the beam-
coupling impeda... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
e96376e1-0fdc-46af-8296-36192a1c5015 | fined by the broad-band (BB) impedance, both evaluated
separately. IntheLargeHadronCollider(LHC),LLDwas
observed since 2010 [ 2], cured by applyingthe controlled
longitudinalemittanceblow-upduringacceleration[ 3]. The
longitudinal CBIs were measured only in dedicated ma-
chinedevelopment(MD) studies[ 4,5]. The instabil... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
5b19cfe0-4c81-4db7-9bdd-9792165869d1 | ∗Researchsupported bythe HL-LHC project
†ivan.karpov@cern.chmeasurements [ 10]. However, recent beam-based evalu-
ations with two different techniques indicated about 70%
higherIm 𝑍/𝑘andalowerresonantfrequencyofthecorre-
sponding effective BB resonator impedance [ 11,12]. The
High-Luminosity (HL) LHC upgrade requires... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
7d8d56fb-bcf8-4c91-a178-0d793ade47da | jected beam and the LHC RF bucket leads to oscillations
of bunch phase and length. These oscillations vary from
bunchtobunchduetothebunchparameterspreaddefined
bytheinjectorcomplex. Theinjectedbunchtrain,moreover,
affectsthecirculatingbeamduetotheactionofthebeam-
basedfeedbackloops. Inaddition,uncontrolledlongitudinal
... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
47ebe6c4-c445-47f2-bf98-1cb835de9580 | feasible in the LHC scenario with up to ∼3000 circulat-
ing bunches. Therefore, a semi-analytical analysis at in-
jection and collision energies was performed based on
solvingthelinearisedVlasovequationwiththenumerical
code MELODY [ 16]. It computes the growth rates of the
uniformly filled ring for a combination of res... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
24725e6c-3e6b-400a-a8dc-7b5374467c07 | and𝑅bb= 44kΩ[11,12]. The lowest threshold of lon-
gitudinal CBI is expected to be defined by HOMs of the
Double Quarter Wave (DQW) crab cavities [ 19], which will
be installed during the Long Shutdown 3 (LS3). In the17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-9545... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 0 |
7ace57e5-67ba-41b0-be3a-7862f2f84858 | 1.1 1.2 1.3
Bunch length τ4σ(ns)123Particles per bunch, Np×1011
Imp. model + HOM (FB)
Meas.-based + HOM (FB)(FT)
(FT)Figure 1: Thresholds of longitudinal multi-bunch instability
fortwoimpedancemodelsatflatbottom andflattop. Stars
indicateaveragetargetbeamparameters, and theerror bars
cover a±10%spread.
worstcasescenari... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 1 |
31386eba-0165-472c-828d-d7b0ee057c5e | shape(𝜇 ≈ 2inLHC).Thebunchlengthpresentedinthis
workcorrespondstofourtimestheRoot-Mean-Squarebunch
length of the equivalent Gaussian bunch. It is computed
fromtheFull-WidthHalf-Maximum(FWHM)bunchlength
𝜏FWHMas𝜏4𝜎= 𝜏FWHM√2/ln2. Theresultsforboththe
presentimpedancemodelandthemeasurement-basedBB
impedance parameters... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 1 |
c15c5fbb-e637-4d6d-a2e0-47c3f77f9388 | Parameter Unit Flat bottom Flat top
Circumference, 𝐶m 26658.86
Harmonic #, ℎ 35640
Gamma trans., 𝛾tr 55.76
RF frequency, 𝑓rfMHz 400.79
Beam energy, 𝐸0TeV 0.45 7
RF voltage, 𝑉0MV 8 16
−10−5 0 5 10
(ω−ωRF)/ω0012ReZeff(ω) (MΩ)∆ω=−2π×13 kHz
Ga=Gm
a
Ga=Gm
a/4Figure 2: Effective FM impedance for nominal and reduced
direc... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 1 |
dc8ce2f6-73c4-44f5-ab11-29b3bea16e9f | itywithathresholdandgrowthratesimilartotheonedriven
by crab-cavity HOMs. Injecting several bunchtrains with
HL-LHC beam parameters should enable better assessment
of beam stability, accounting for relevant aspects of beam
accumulationat450GeV.Suchtestsarealsoimportantto
evaluate the stabilitymargin forthe fundamental m... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 1 |
6d24d5de-5155-453d-80f7-716bed6d7882 | at the detuned cavity resonant frequency. The RF feedback
contains analogue and digital branches with a combined
transfer function expressed in Laplace notation
𝐻𝑎,𝑑(𝑠) = 𝐺𝑎𝜏𝑎𝑠
1+𝜏𝑎𝑠+𝐺𝑑1
1+𝜏𝑑𝑠,(4)
where𝐺𝑎istheanaloguegain, 𝜏𝑎isthehigh-passfiltertime
constant, 𝐺𝑑is the digital gain, and 𝜏𝑑is the... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 1 |
43d623d6-2357-4aa5-9dc3-41f75bde9e7d | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5109
MC5.D05: Coherent and Incoherent Instabilities Theory, Simulations, Code Development 2515WEP: Poster session WEP5109
Content from this work may be used under the terms of the CC BY 4.0 licence (© 2026). Any distribution of this work must maint... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 1 |
506633c2-f635-4299-91bf-ce381fc5151b | 1.1 1.2 1.3
Bunch length τ4σ(ns)123Particles per bunch, Np×1011
Imp. model + HOM
Meas.-based + HOMIM + FM
MB + FMFigure 3: Thresholds of longitudinal multi-bunch instability
fortwoimpedancemodelsatflattop. Blacklinescorrespond
toHOM-driveninstability,while bluelinesrepresent FM-
driven instability (Fig. 2).
digitalgain... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 2 |
c08f7e3d-f62e-4540-b0c8-9c798f4747cc | The suppression of LLD-driven bunch oscillations was also
demonstrated [ 14]. Assuming a distribution function [ 24]
𝑔(ℰ) =⎧{
⎨{⎩1−ℰ2
𝑎ℰ2max, 0 ≤ ℰ < 𝑎ℰ max
1
1−𝑎(1−ℰ
ℰmax)2
, 𝑎ℰmax≤ ℰ < ℰmax,(5)
where0 < 𝑎 < 1 , we computed the modification of the
instability threshold due to the distribution flatness (Fig. 4).
... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 2 |
f96a8239-ccc4-4204-8ff3-3f739c02fc3b | the beam-based phase loop, which triggers a phase kick and
increasesRFnoise. Afterall,IBSwillreduceflatnessand
increase the bunch length with time.
Double-Harmonic RF System
The most robust solution to prevent the instability is a
double-harmonicRFsystem. Dependingontheharmonic
1.1 1.2 1.3
Bunch length τ4σ(ns)123Partic... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 2 |
4aa37b38-5f20-4abc-a439-72a276822f5f | ratio,𝑟ℎ,andthevoltageratio, 𝑟𝑣,bothCBIandLLDthresh-
oldsstronglyrisebyafactor 1+𝑟𝑣𝑟3
ℎwhenbothRFsystems
areinphaseatthebunchcentre[ 25,26]. Thesemi-analytical
resultsforcombinedNBandBBimpedancesourcesshow
thatanadditional800MHzRFsystemwith 𝑟𝑣= 0.15should
be sufficient to significantly improve beam stability (F... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 2 |
0979b2de-9a89-47c3-b77d-a5bbaa8b548d | narrow-bandimpedancesources. Dedicatedmeasurement
scenarios based on adjustments of RF feedback settings are
proposedto probe the predictedinstabilitythreshold under
realisticconditions. Wefindthatmitigationbybunchflatten-
ing is limited, while a double-harmonic RF system provides
a substantial increase in the stabilit... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 2 |
4d51e9d4-46fb-4502-b5a2-93692de683ed | REFERENCES
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ee4884aa-0991-4ab9-b1f0-7592230a33d1 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5109
MC5.D05: Coherent and Incoherent Instabilities Theory, Simulations, Code Development 2517WEP: Poster session WEP5109
Content from this work may be used under the terms of the CC BY 4.0 licence (© 2026). Any distribution of this work must maint... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5109.pdf | 3 |
64af5290-8729-4652-be19-421fc9a56a75 | STUDIES OF COUPLED-BUNCH INSTABILITY IN THE HL-LHC∗
C. C. Becker†1, R. Calaga, B. E. Karlsen-Baeck, I. Karpov, H. Timko
CERN, Geneva, Switzerland
1also at TU Wien, Vienna, Austria
Abstract
Beam dynamics studies, and in particular detailed
macroparticle simulations, are challenging forhigh-energy
hadron synchrotrons due... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 0 |
4c5789fa-459f-486b-a178-e1b141e3f0ca | whichcouldleadtocoupled-bunchinstabilities(CBI),onthe
beamstability. Thisisparticularlyimportantinthepresence
ofabroad-bandimpedance,whichwaspredictedtolower
the CBI threshold. In this contribution, particle-tracking
simulation setups for instabilities, driven by either broad-
or narrow-band impedances, are investigate... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 0 |
2484d476-8614-4726-811b-1df0c8289367 | metric discontinuities, resistive-wall effects, or non-ideal
deviceswithintheacceleratorandareresponsibleforsingle-
buncheffectssuchasthelossofLandaudamping(LLD).In
previous theoretical work [ 1], it was shown that the longi-
tudinalthresholdsforCBIandLLDarecloselylinkedand
that, especially when operating close to the ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 0 |
beb124f2-20ed-4446-801f-b668fd1afbc4 | the LHC, macroparticle simulations with the BLonD [ 3]
simulation suite are performed. However, the macroparti-
cle analysis of BB and HOM effects each come with their
∗Researchsupported bythe HL-LHC project
†clara.charlotte.becker@cern.chchallenges. Whilst the analysis of single-bunch LLD re-
quireshightimeresolution,... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 0 |
1b39d178-806c-4242-be0d-d454530b6481 | tion into the HL-LHC [ 4].
Table 1: HL-LHC Accelerator, RF and Beam Parameters at
Injection
Parameter Unit Value
Circumference, 𝐶 m26658.86
Harmonic number, ℎ 35640
Beam energy, 𝐸 GeV 450
Transition gamma, 𝛾tr 53.8
RF frequency, 𝑓RF MHz400.788
RF voltage, 𝑉0 MV 8
Bunch intensity, 𝑁pp/b2.3×1011
BothNBandBBimpedanc... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 0 |
2dc0e094-4fdc-4da7-abd2-02d921bc69a3 | 𝑅sh= (Im𝑍/𝑘)eff×𝑄×(𝑓r/𝑓rev). Thebunchshapeisbestde-
scribed by a binomial distribution function, which, neglect-
ing intensity effects, is given by the line density function
𝜆(𝑡) = 𝜆0⎛⎜
⎝1−sin2Δ𝑡
2
sin2𝜏full
2⎞⎟
⎠𝜇+0.5
, (2)
with the binomial exponent 𝜇, the normalisation constant
𝜆0,Δ𝑡isthetimecoordinat... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 0 |
ce7820c3-34b3-4b0a-885a-e5a845413b48 | 𝜇 = 1.5−2.0 , and the same value is assumed for the HL-
LHC era.
The bunch shape and length have a considerable effect
on the LLD threshold, since the threshold bunch intensity
scales as [ 6]
𝑁𝑝,th∝𝜙5max
𝜇(𝜇+1)𝜒(𝑦max,𝜇), (3)
where the phase and bunch length are transformed by
𝜙max= 𝜏full𝜔rf/2,𝑦max= 𝑘max𝜙... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
a59c5736-debb-4ffc-8338-8cad4cd646bb | distribution were set to be slightly above the expected LLD
threshold. Afterapplyinga 10°phasekick,oscillatorybe-
haviour of the bunch was observed, indicating LLD. The
bunch position oscillation amplitude was analysed for the
last2×104,3×104and5×104turns of9×104simulated
turns after the kick. For each number of macrop... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
4800d0d2-84e8-49ae-b2bf-019992c2f87e | plitude converged. The results are shown in Fig. 1. It was
alsofoundthat,forcaseswherethebunchishighlyunstable,
fewer macroparticles are required to replicate the dynamics
oftheinstability. SincetheprovidedHL-LHCparameters
areclosetothethresholdinmostcases,andthereforeproba-
blynothighlyunstable,itwasconcluded that 107... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
c54ca795-a16c-4acc-bc15-c0660e1607d1 | the DQW crab cavity with 𝑓𝑟= 582MHz,𝑅sh= 73kΩ,
and𝑄 = 1360 leads to the lowest instability threshold [ 9].
Solely this mode was used for the discussed simulation and
is represented as a single resonator impedance source. The
worst case scenario was considered, where all four crab
cavitieshaveexactlythesameresonantf... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
23082d4d-1426-46c4-8b65-10d342f19098 | complexityscaleswiththetotalnumberofmacroparticles.
To reduce the total number of macroparticles in the simula-
tion,oneshoulddeterminetheminimumamountofbunches
required to predict the behaviour of each bunch in a full
ring. To investigate this, the decay of the wake field and
thevoltageinducedbytwotrainsoftheso-called... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
793c782b-1430-4d12-9d95-bc796fd51142 | 105. Thelinedensityofthebunchesisagainthebinomial
distribution function (Eq. 2), with a full bunch length of
𝜏full= 1.46ns and an exponent of 𝜇 = 1.5.
Figure3illustrates the decay of the induced wake field
duringthegapsbetweenbunches,batches,ortrains. Figure 2
showsanexampleofthebeamprofileanditsinducedvoltage.
Count... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
da7a8d4a-2360-413e-865a-16a0db8c2429 | indicatethataninstabilitystartstoemerge,butmoreturns
areneededtoidentifyaninstabilitygrowthrate. However,
modellingasubstantiallylargeramountofturnsisdifficult
asthesimulationsarealreadyruntimelimited,evenusing
GPU execution on the CERN computing cluster HTCondor.17th International Particle Accelerator Conference, Deau... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 1 |
89f281bb-c69b-43ed-ae09-e00b20ade04d | Figure 2: Beam profile for two trains of four 72 bunch
batches (top). Resulting induced voltage (bottom) assuming
a single NB resonator.
Figure3: DecayofthewakefieldenvelopefortheNBres-
onator (blue). The vertical lines indicate the distance to the
next bunch (yellow), batch (green), and bunch train (red).
Therefore, f... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 2 |
a0b2780c-e83d-434c-bd48-6999bec3f446 | and turn9000. This was determined by identifying the turn
intervalyielding the bestlinear fit. The amplitude growsto
about0.35ns. Notably,thegrowthratesfortherespective
batches are consistent across the different trains. Especially,
forthethirdandfourthbatchtheevolutionisalmostidentical
intheanalysedtimeframe. Theseobs... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 2 |
db658c63-a1a6-4d43-a955-59c7346150fa | Theasteriskindicatesthattheamplitudetowhichthebunch
position grows is approximately a factor 0.1smaller than
for the rest of the bunches. For bunches number 72, the
instabilitytakeslongertodevelopthanfortheotherbunches.
Bunch no. 72 144 216 288
𝜏−1
train14* 5 7 10
𝜏−1
train29 5 7 10
Figure 4: Example of a bunch posit... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 2 |
6a83a2aa-ebec-4086-b84a-528d2b9345a8 | as well as coupled-bunch effects induced by NB impedance
fromthecrabcavities,werediscussed. Macroparticlecon-
vergence studies for simulating single-bunch LLD were per-
formed and suggestedthat 107macroparticles are required
fortheLHCcase. Withthisamountofmacroparticlesper
bunch,combined simulationsof BB andNB effects ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 2 |
fb2c3e2f-2d8f-4ec9-8b0a-4d0ed74a6995 | For the present studies, a short bunch length was set to
reduce the run time of the simulations. In the future, the
simulations shall be performed with more realistic bunch
parameters. Furthermore,foramorecompletedescription
of the HL-LHC beam dynamics at injection, phase kicks
due to the beam phase loop and the bunch ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 2 |
12979277-59ef-4790-b8fd-391c56b0811c | REFERENCES
[1]I. Karpov and E. Shaposhnikova, “Generalized threshold of
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oldsforlossoflandaudampinginlongitudi... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5110.pdf | 3 |
f39ecf4c-0525-4b5c-88bc-643ef4eaa7eb | [8]J. A. Mitchell, G. Burt, R. Calaga, S. Verdú-Andrés, and B. P.
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6a0b0336-9fb4-48fc-99c0-1f033dc9f752 | LONGITUDINAL MICROWAVE INSTABILITY STUDY AT
TRANSITION CROSSING IN THE CERN PS
J. Salinas, J. Flowerdew, A. Lasheen∗, M. Neroni,
European Organization for Nuclear Research (CERN), Geneva, Switzerland
Abstract
Thebeamqualityofhigh-intensityprotonandionbunches
in the CERN Proton Synchrotron (PS) is limited by a lon-
gitu... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 0 |
91f0f1b0-c7e5-49f2-adfe-909d724ed6c3 | the gamma transition jump. Remarkable agreement with
measurements is obtained for the instability thresholds and
micro-bunchstructures. Nonetheless,the characteristicsof
thesimulatedinstabilitystronglydependonthemodellingof
longitudinal space charge, which focuses the micro-bunches
but also introduces significant numer... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 0 |
d71ff2da-5681-4f5c-a4bf-12330793b5cb | satisfying 𝑓𝑟𝜏ℓ≫ 1(where𝑓𝑟is the resonance frequency
and𝜏ℓis the bunch length). For typical PS bunches with
lengthson the nanosecond scaleat transition, this points to
resonant frequencies above 1GHz.
Morerecently,theinstabilitywasobservedwithvarious
ionspecies[ 2],anditsobservation,alongwithprotonbeams,
is prese... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 0 |
d56b8f62-24eb-43c5-88c2-34c2fe342f95 | sition [4]. While this preserves global beam quality and
reproducibility compared to the turbulent microwave insta-
bilityregime, the enlargedemittanceimposes a minimum
on the smallest achievable bunch length for AWAKE. More-
over, following the impedance reduction campaign in the
∗alexandre.lasheen@cern.chSPS [5,6], t... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 0 |
d09b80b3-e3b4-4aa8-aa44-c1f036515fc4 | identifythesourceofbeam-couplingimpedancecausingthe
instability. Inparticular,an analysisofthespectral compo-
nentsofthemodulatedbunchprofileswasperformedbothat
transition crossing and from dedicated measurements using
long bunches with small momentum spread [ 8,9]. These
provided a more precise measurement of the modu... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 0 |
da4263d6-1fc7-4747-bd38-da797640ab03 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5111
2522 MC5.D06: Coherent and Incoherent Instabilities Measurements and CountermeasuresWEP5111 WEP: Poster session
Content from this work may be used under the terms of the CC BY 4.0 licence (© 2026). Any distribution of this work must maintain a... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 0 |
584102f8-ebef-4679-9836-66658fdf050f | Figure2: Emittanceblow-upduetomicrowaveinstabilityasafunctionofthebunchintensityandlongitudinalemittance.
Theexperimentalresults(left)arecompareddirectlywithBLonDsimulations(right). ThePSoperatesfortheAWAKE
experiment with a bunch intensity 𝑁𝑏= 30×1010p+ and longitudinal emittance 𝜀ℓ= 0.2eVs.
MEASUREMENTS AND TRACKI... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 1 |
b2916134-3c6a-42a8-9c66-c6f4272e23c0 | tensitywerefine-tunedinthePSinjector(PSBooster),while
theemittanceblow-upwascontrolledlinearlyusingtheded-
icated200MHzRFblow-upschemeinthePS.Anoverview
of the measured stability map is given on the left of Fig. 2.
Toclassifybunchesasstableorunstable,alogisticregres-
sion model was trained using a threshold blow-up rat... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 1 |
5c58d6fc-08b3-49d4-a3e7-e1245d57065e | gitudinal Dynamics) code [ 11] to benchmark against the
measured instability threshold. These included a detailed
PSimpedance model [ 12],including numerous accelerator
components (RF cavities, kickers, vacuum system elements,
etc.),andinparticularthehigh-frequencycomponentsex-
pected to drive microwave instabilities. ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 1 |
2ca0b1c9-211f-4b8b-bb1d-7127d1cf1fcd | Figure 3: Simulated bunch profile evolution at transition
crossingwiththeBLonDsimulationcode. Themodelsuc-
cessfully captures the post-transition focusing and subse-
quent micro-bunching.
timings for the RF phase jump were set together with an
improved modelling of the beam loops [ 16].
Anexampleofbunchprofileevolution... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 1 |
05c1b8a4-ed4f-4cd8-b097-da8a2ad47b0d | scaled down by approximately 20% to reproduce collective
effects beyond instability. This remains within the uncer-
taintyassociatedwiththeapproximationsmaderegarding
the vacuum chamber aperture geometry (a detailed aperture
model was not available). Additionally, the modulation at
1.3GHz was well reproduced. In simula... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 1 |
b33c6342-9e52-46a3-839a-21e02bd9b769 | Withthe overall instability behaviour establishedin simu-
lation,the experimental parameter scanwasreproduced by
initializingsimulatedbuncheswithidenticalconditionsto
measurements. The result of the scan is presented on the
right side of Fig. 2. The results are in good agreement with
themeasurements,displayinga20%offse... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
0fe7a775-adec-4cc6-befd-292b21e44942 | instead show a clear synchronous phase shift Δ𝜑𝑠. In some
cases,themicro-bunchevenappearstooscillatedistinctly
ahead of the main bunch, as shown in Fig. 4.
Figure 4: Measurements of a single proton bunch in the
PS showing the formation of micro-bunches after transition,
with a clear synchronous phase shift Δ𝜑𝑠. Red... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
eccb4bb0-6201-45c7-8b7e-af2c553d3742 | chronousphaseofthemicro-bunchisshiftedasitsenergy
loss is continuouslycompensated bythe RF system. Mean-
while,thestrongfocusingforcesoflongitudinalspacecharge
above transition allow these structures to persist for many
synchrotron periods.
IMPEDANCE REDUCTION AND
INFLUENCE OF SPACE CHARGE
With the acceptable agreement... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
b2e9822c-7fb6-451b-825c-8afb05c6170e | contributionsrevealedthattheinstabilitythresholdisdom-
inated by the longitudinal space charge impedance [ 17].
Abovetransitionenergy,thecapacitivenatureofthespace
chargeimpedancedrivesthenegativemassinstability. When
asmallinitialdensitymodulationoccurs,thelongitudinal
electric field generated by space charge decelera... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
563d3276-e38a-4eb4-bd64-da7d6d3c375a | ties remain regarding the modelling of longitudinal space
charge,implyingthatalternativesimulationmethodsneed
to be investigated to provide more accurate predictions of
howimpedancereductionwillaffecttheinstabilitythreshold,
notably semi-analytical solutions to the Vlasov equations.
CONCLUSION
Thisstudypresentsacompreh... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
87880449-f509-4ca5-9e81-d8f4778c5903 | stability threshold that currently limits the AWAKE beam.
Thesimulationsdemonstratethatwhilespecificnarrow-
bandimpedancesourcesdictatethespectralsignatureofthe
instability, the stability limit is strongly influenced by lon-
gitudinal space charge. Hardware shielding is planned to be
testedononemanifoldunitthisyearandt... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
c2bd6c00-b879-4acf-ab23-bfcc9c99d0c4 | and N. Mounet for modelling of the gamma jump scheme.17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5111
2524 MC5.D06: Coherent and Incoherent Instabilities Measurements and CountermeasuresWEP5111 WEP: Poster... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5111.pdf | 2 |
eff98ea7-cb4a-4bcb-b108-419162f1579a | REFERENCES
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2d3dfc86-f3f4-4ad8-9168-c9a3dbc09dc7 | BEAM-LOADING COMPENSATION AT TRANSITION CROSSING FOR
MIXED INTENSITY BUNCHES
O. Smedt1,2, A. Lasheen∗1, H. Damerau1
1European Organization for Nuclear Research, Geneva, Switzerland
2École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Abstract
To produce beam for the nTOF and East Area experimental
facilitie... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 0 |
c0701ace-c015-4371-93c0-cb451743f907 | further increases the intensity difference with respect to the
low-intensitybunchfortheEastArea. Inthiscontribution,
longitudinal dipole oscillations triggered by the intensity-
dependent phase jump at transition crossing are exposed.
A mitigation technique is derived analytically and demon-
strated in beam tests, by t... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 0 |
30c6cf79-86f5-4dbd-8b3b-c2024bfc099e | celerated for the nTOF facility [ 2]. This parasitic bunch has
an intensity of up to 6×1012p/b (’parasitic TOF bunch’).
WhenacycleisdedicatedtothenTOFfacilitytheequiva-
lentbunch(’dedicatedTOFbunch’)hasahigherintensity
of8.4×1012p/b.
TheSHiPexperimentintheNorthAreaoftheSPSwill
requirearound twomillion cyclesfrom the PS... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 0 |
8bd9ecb3-f029-4814-926d-858c66bd3ad2 | The parasitic TOF intensity is currently limited by dipole
oscillations at transition crossing, induced by the difference
inbeamloadingbetweentheTOFandEASTbunches. These
dipoleoscillationscannotbemitigatedbythebeamphase
∗alexandre.lasheen@cern.ch
Figure1: MountainrangeplotofanEASTbunch(left)when
a parasitic TOF bunch i... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 0 |
ed51879c-a3a4-4daa-889d-fe7033ab6817 | crossing is shown in Fig. 1. After transition crossing, the
inter-bunchdistanceoscillateswithaninitialamplitudeof
37ns. ThelongitudinalRMSemittanceis0.38eVs170ms
after these oscillations begin.
Inthiscontributionweanalysethedipoleoscillations,and
develop a procedure to predict their amplitude. A method
for their compen... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 0 |
70c669d3-e09e-45fe-82f3-4f0637aee771 | 𝑉ind(𝜙𝑠)+𝑉RF(𝜙𝑠) =𝛿𝐸𝑠
𝑒, (1)
where𝛿𝐸𝑠is the energy gain per turn of the synchronous
particle,𝑒is the elementary charge, 𝑉ind(𝜙)is the beam
inducedvoltage,and 𝑉RF(𝜙)isthevoltageoftheRFsystem
withoutbeam. Thephase 𝜙iswithrespecttotheprinciple
harmonic of the RF system, ℎ. With knowledge of the beam
ind... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 0 |
84ed9ee0-8dc9-4c11-a838-ce238097486b | 2
02
phasepotential (arb. unit)
s,EAST
dipole oscillation
amplitudepotential before transition
potential after transitionFigure 2: Longitudinal potential in the EAST bucket before
and after transition crossing. The bottom of the potential
well moves almost instantly at transition. Therefore, the
EAST bunch becomes of... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5112.pdf | 1 |
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