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3c29dc0d-797e-4920-a6f9-fb96daa5b29e | mechanical apertures are small or where there are sensitive
elementsneartheaxis. Althoughtheobservedincreasein
transverse emittance is moderate (see Fig. 2c), its presence
indicatesthatthedisturbancenotonlydisplacesthebeam,17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 1 |
7cfa5e0b-55d2-4887-b2aa-fd9c67728ef5 | but also introduces additional mismatch components that
could amplify along the line. This underscores the impor-
tanceofensuring propertransversealignmentof thestems,
as wellas havingearlycorrection elements availablewhen
mechanical tolerances cannot be fully guaranteed.
In the longitudinal direction (see Fig. 3), the... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 2 |
796cec89-9a53-49b2-9148-31b2136ce3a5 | ical role in preventing bunching degradation. This effect
cannot be compensated for by the magnetic elements lo-
catedatthecavityexit,sincetheseactonlyonthetransverse
motionanddonotaffectthelongitudinaldynamics. Asan
additional consequence, this rotation also generates a slight
asymmetry in the field that manifests its... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 2 |
c4eba92a-8c6c-4baf-beb1-5cfe74d759ff | Figure 3: Effect of discrepancies on longitudinal dynamics.
ics simulations. Due to the high operating frequency and
compactgeometry,thestructureshowsprominentsensitivity
to geometric shifts. The single-cell study identifies trans-
verse and longitudinal stem displacements, together with
rotationsaroundthe 𝑥-axis,asth... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 2 |
fafd637d-d6ec-412c-a335-a33877ef7bdb | fabricationandassembly,providingguidancefordefining
mechanical tolerances in high-frequency IH-DTL cavities.
ACKNOWLEDGEMENTS
Initiative co-financed by the European Regional Devel-
opmentFund(ERDF)underthe2021-2027Multiregional
Operational Program for Spain and CDTI Innovation’s own
funds. In particular, this work has ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 2 |
c438c0d4-622a-4c4e-85b5-6b5feb21a091 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5083
MC5.D03: Calculations of EM fields Theory and Code Developments 2453WEP: Poster session WEP5083
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 attribution to th... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 2 |
39aef292-37f5-40d1-9448-517e49463f37 | REFERENCES
[1]H.P.Lietal.,“Studyand designofthecoupledcavitywith
ladder RFQ and IH-DTL structure for transportable neutron
source”,Nucl. Instrum. Methods Phys. Res. A, vol. 1056,
p. 168645, 2023. doi:1/zero.alt4.1/zero.alt416/j.nima.2/zero.alt423.168645
[2]K.Isokawa etal.,“Developmentof highgradientIH linac”,
Nucl. Ins... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 3 |
01381418-1c36-474c-8ab3-3405f26e3a83 | Nucl. Eng. Technol., vol. 56, p. 3536, 2024.
doi:1/zero.alt4.1/zero.alt416/j.net.2/zero.alt424./zero.alt44./zero.alt4/zero.alt41
[5] M.Otani etal.,“Interdigital H-modedrift-tubelinac design
with alternative phase focusing for muon linac”, Phys. Rev.
Accel. Beams, vol. 19,p. 040101, 2016.
doi:1/zero.alt4.11/zero.alt43/P... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 3 |
1adb1eab-3919-4ad1-98ba-93e655896357 | Apr.–May 2018.
doi:1/zero.alt4.18429/JACoW-IPAC2/zero.alt418-TUPAL/zero.alt475
[8]G.Moreno etal.,“Designandemsimulationsof750MHz
IH-DTL tank for carbon ion in medical applications”, in
Proc. 16th Int. Part. Accel. Conf. (IPAC’25), Taipei, Taiwan,
pp. 1502–1505, Jun. 2025.
doi:1/zero.alt4.18429/JACoW-IPAC2/zero.alt425-T... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 3 |
53fb366e-1369-4fc9-b139-059f382da7ec | Aug.–Sep. 2022.
doi:1/zero.alt4.18429/JACoW-LINAC2/zero.alt422-MOPOGE/zero.alt4517th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5083
2454 MC5.D03: Calculations of EM fields Theory and Code DevelopmentsWEP5083 ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5083.pdf | 3 |
6804b460-4f7c-4a71-b11e-99603b557254 | A GENERALIZED ANALYTICAL POTENTIAL FOR FAST RFQ BEAM
DYNAMICS MODELING
E. Laface∗, European Spallation Source ERIC, Lund, Sweden
Abstract
RadioFrequencyQuadrupoles(RFQs)arewidelyusedat
thefrontendoflinearacceleratorstofocus,bunch,andaccel-
eratelow-energyionbeams. Theirelectromagnetic fieldis
commonly evaluated with fu... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 0 |
12fc369d-e425-4af2-a3b4-2cd506425eb8 | regular solution of Laplace’s equation in cylindrical coordi-
natesandexpandedinangularandlongitudinal harmonics.
The classical two-term approximation is recovered as the
lowest-ordertruncation,whileequipotentialboundarycon-
ditions on the modulated vane surface define a finite matrix
problem for the modal coefficients... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 0 |
ca10dab1-a185-4b92-acfa-845d33755202 | component arising from periodic vane modulation.
In RFQ beam dynamics studies, the electromagnetic field
isoftenreconstructedwithnumericalsolversandthenim-
ported into particle tracking codes. Although accurate, this
approachcanbecomecomputationallyexpensivewhenre-
peatedfieldevaluationsarerequiredinparameterscans,tun-... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 0 |
3e725229-149f-4a2d-b79a-e58ee3d7d2cf | ThisworkdevelopsageneralizedanalyticalRFQpotential
that extends the classical two-term model while preserving
computational efficiency. Starting from Maxwell’s equa-
tions,itderivesthescalarpotentialincylindricalcoordinates
∗emanuele.laface@ess.euandexamineshowtruncationorderaffectsthereconstructed
field.
ELECTROMAGNET... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 0 |
3b6dfd3e-73e0-4e5d-b538-979dd258a09f | RFangularfrequency,and 𝜙𝑠isanarbitraryreferencephase.
To leading order, ⃗𝐸(𝑟,𝜃,𝑧,𝑡) ≃ −∇𝑈(𝑟,𝜃,𝑧) cos(𝜔𝑡 +𝜙 𝑠),
so the spatial potential satisfies ∇2𝑈 = 0.
ThisisthestartingpointfortheanalyticalRFQfieldmodel
considered here.
MODAL EXPANSION IN CYLINDRICAL
COORDINATES
The Laplace equation is solved in cyl... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 0 |
47326ea0-2b7e-4c57-bcf5-852d4a0c1930 | synchronousparticleand 𝜆 = 𝑐/𝑓istheRFwavelength. The
correspondinglongitudinalwavenumberis 𝑘 = 2𝜋/(𝛽𝜆) ,
and a convenient basis is 𝑍𝑛(𝑧) =cos(𝑛𝑘𝑧),𝑛 = 0,1,2,… ,
where a sine representation would be equivalent up to a
longitudinal phase shift.
Radial Dependence
Foramodeindexedby (𝑚,𝑛),theradialequationbe... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 0 |
8c2db6da-6a8e-4746-b420-4995132d7557 | where𝐼2𝑚isthemodifiedBesselfunctionofthefirstkind.
For𝑛 = 0, the radial equation reduces to 𝑟2𝑅″+ 𝑟𝑅′−
(2𝑚)2𝑅 = 0, whose regular solution is 𝑅𝑚0(𝑟) = 𝐴𝑚0𝑟2𝑚.
GENERALIZED RFQ SCALAR
POTENTIAL
Collecting the regular angular, longitudinal, and radial
modes, the most general scalar potential compatible with... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 1 |
1e2ecba7-e485-4d32-95d1-d04ec130c614 | 𝑈(𝑟,𝜃+𝜋/2,𝑧) = −𝑈(𝑟,𝜃,𝑧) , which suppresses angular
componentsincompatiblewithasigninversionundera 𝜋/2
rotation. Thevanemodulationalsointroducesalongitudinal
periodicity linked to the RF phase. Equation ( 3) provides
thecompleteregularbasis,whilesymmetryandboundary
conditions select the non-zero coefficients.... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 1 |
c5d45797-2986-4e9f-957e-79543f3296ab | the lowest-order truncation of the generalized expansion.
BOUNDARY CONDITIONS ON THE
MODULATED VANE SURFACE
Themodalcoefficientsaredeterminedbyenforcingthe
equipotentialconditiononthevanesurfaces. Letthevane
contourbedescribedbyalongitudinallymodulatedradius,
using a simplified cosine parameterization inspired by stan-... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 1 |
ef9542fb-7453-4336-b429-33adfc235a29 | FINITE TRUNCATION AND MATRIX
FORMULATION
Forpracticaluse,theinfiniteseriesmustbetruncated. Let
𝑀bethehighestangularorderand 𝑁thehighestlongitudinal
harmonic retained. The truncated potential is
𝑈𝑀𝑁(𝑟,𝜃,𝑧) =𝑀
∑
𝑚=0𝐴𝑚0𝑟2𝑚cos(2𝑚𝜃)
+𝑀
∑
𝑚=0𝑁
∑
𝑛=1𝐴𝑚𝑛𝐼2𝑚(𝑛𝑘𝑟)cos(2𝑚𝜃)cos(𝑛𝑘𝑧).(7)
Here𝑁𝑡deno... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 1 |
bf608bb9-5346-4295-a01d-80c17f659dcd | the number of retained modes, the system is square; if 𝑃
islarger,thecoefficientscanbeobtainedinaleast-squares
sense. Thisdefinesapracticalroutetocomputehigher-order
analytical RFQ coefficients directly from the vane profile.
ELECTRIC FIELD COMPONENTS
Once the scalar potential is known, the elec-
tric field follows as... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 1 |
70fca709-9ffc-4eca-96f2-1b305cba0f09 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5084
2456 MC5.D03: Calculations of EM fields Theory and Code DevelopmentsWEP5084 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 attribution to th... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 1 |
6ef1711d-aa5f-4869-9486-219d1a5ba8bb | FIELD ACCURACY AS A FUNCTION OF
TRUNCATION ORDER AND RADIUS
The generalized potential of Eq. ( 3) defines a hierarchy
of truncated analytical models. To quantify the effect of
truncation, the field reconstructed with a finite number of
terms is compared with a reference field obtained from a
much richer truncation of t... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 2 |
c9322880-2ae7-4936-bef4-280451810dfa | with𝑁𝑡retainedterms, and let ⃗𝐸(ref)(𝑟,𝜃,𝑧)denotethe ref-
erence field corresponding to 𝑁ref= 40. A convenient shell-
averaged relative RMS error, normalized to the reference
field energy [ 7], is
̄𝛿(𝑁𝑡)(𝑟1,𝑟2) =√
√
√
√
⎷⟨∥⃗𝐸(𝑁𝑡)−⃗𝐸(ref)∥2⟩
𝑟∈[𝑟1,𝑟2],𝜃,𝑧
⟨∥⃗𝐸(ref)∥2⟩
𝑟∈[𝑟1,𝑟2],𝜃,𝑧×100,
(8)
wh... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 2 |
a8673f24-feab-414c-ad4d-a21ffc2e642f | Range in 𝑟/𝑎 𝑁 𝑡= 2 𝑁𝑡= 4 𝑁𝑡= 8 𝑁𝑡= 12
0 ≤ 𝑟/𝑎 < 0.2 31.78 31.78 18.77 8.48
0.2 ≤ 𝑟/𝑎 < 0.4 16.86 16.86 10.75 5.51
0.4 ≤ 𝑟/𝑎 < 0.6 13.44 13.25 9.45 5.68
0.6 ≤ 𝑟/𝑎 < 0.8 15.35 13.25 10.56 7.35
0.8 ≤ 𝑟/𝑎 ≤ 1.0 25.30 15.98 13.97 10.64
The first two truncations remain similar over much of the
aperture,w... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 2 |
a920d27c-a4d2-46d9-ba5d-08022ef39597 | Nt=2
Nt=4
Nt=8
Nt=12Figure 2: Radial convergence of ̄𝛿(𝑁𝑡)versus normalized
radius𝑟/𝑎.
2 4 8 12
Truncation order Nt00.2
0.20.4
0.40.6
0.60.8
0.81.0
Normalized radial interval r/a31.78 31.78 18.77 8.48
16.86 16.86 10.75 5.51
13.44 13.25 9.45 5.68
15.35 13.25 10.56 7.35
25.30 15.98 13.97 10.64Mean relative RMS field... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 2 |
680aed19-fbb3-49df-8af4-d4b19c851680 | imposingequipotentialboundaryconditionsonthemodu-
lated vane surface, leading after truncation to a finite linear
system for the modal amplitudes.
A high-order internal reference was also introduced to
quantify the accuracy of truncated analytical models versus
the number of retained terms and transverse radius. The
ra... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 2 |
6a1cb18c-f6a5-4ce9-a4ab-d93982b8a3d7 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5084
MC5.D03: Calculations of EM fields Theory and Code Developments 2457WEP: Poster session WEP5084
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 attribution to th... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 2 |
2c6aff79-7186-4abd-8254-e53841a01365 | [3]A. Schempp, “RFQ Design and Performance,” in Proc.
LINAC’90 , Albuquerque, NM, USA, Sep. 1990, pp. 567–569.
[4]K. R. Crandall and T. P. Wangler, “PARMTEQ—A Beam
DynamicsCodefortheRFQLinearAccelerator,”LosAlamos
National Laboratory, LA-UR-81-2581, 1981.
[5]Z. Zhang et al., “Design of a radio frequency quadrupole for ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 3 |
6fab7e6e-7701-4255-9b66-9d1898fb4a12 | 1247–1250, Jun. 2014. doi:1/zero.alt4.5194/gmd-7-1247-2/zero.alt41417th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5084
2458 MC5.D03: Calculations of EM fields Theory and Code DevelopmentsWEP5084 WEP: Poster s... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5084.pdf | 3 |
c4dfd41f-3421-4083-bb96-cc0a6753f8ea | MODELING AND MEASUREMENTS OF THE IMPACT OF DIPOLE
FRINGE FIELDS IN THE EXTRA LOW ENERGY ANTIPROTON RING
S. Van der Schueren∗1, R. De Maria, D. Gamba, CERN, Geneva, Switzerland
M. Migliorati, University of Rome La Sapienza, Rome, Italy
1also at University of Rome La Sapienza, Rome, Italy
Abstract
The ELENA (Extra Low EN... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 0 |
c37fdd70-ae2f-4acf-98ee-6216cf5e5ce8 | INTRODUCTION
Fringefieldshavewellknownandlesswellknowneffects
onbeamdynamics. Toinvestigatewhicheffectsareimpor-
tantinsmall machines,weperformedmeasurements inthe
ELENAring[ 1]atCERN,forwhichtheopticsisdominated
by the dipole edges.
DIPOLE MODELS
Inthispaper,wewillcomparedifferentfringefieldmodels
using Xsuite [ 2]. T... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 0 |
6a8a639a-4ace-473d-86e9-93d6015e8950 | the transfer matrix of the dipole fieldmap, using the method
explained in the following subsection.
Accurate Modeling
Moreaccuratesimulationsthatwill serveas abenchmark
forourmodelswillbebasedonanelectromagneticfieldmap
obtainedfrominterpolatedmeasurementsusingBEM-based
magnetic field reconstruction [ 6]. To describe t... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 0 |
28020ca3-afff-4edb-b35a-15b1992baa8d | Parameter set 𝜃𝐸𝐹𝑖𝑛𝑡
Design parameters 17∘0.424
Acc-models parameters 16.45∘0.424
Fitted parameters 16.40∘0.399
trajectory. We have that ̂ 𝑠 =⃗𝑅′
0(𝑠),̂ 𝑥′(𝑠) = ℎ(𝑠) ̂ 𝑠(𝑠) and
̂ 𝑦(𝑠) = − ̂ 𝑥(𝑠) × ̂ 𝑠(𝑠) andℎ(𝑠) = 1/𝜌(𝑠) is the local curva-
ture, see Fig. 1for the specific case that will be used ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 0 |
8a633dc5-653f-47ab-8f72-1d66020fde82 | the magnetic scalar potential,
𝜙0(𝑥,𝑠) = −𝑎0(𝑠)−∞
∑
𝑛=1𝑎𝑛(𝑠)𝑥𝑛
𝑛!(6)
𝜙1(𝑥,𝑠) = −∞
∑
𝑛=1𝑏𝑛(𝑠)𝑥𝑛−1
(𝑛−1)!(7)
suchthatthecompletescalarpotentialcanbedeterminedby
Φ(𝑥,𝑦,𝑠) =∞
∑
𝑖=0𝜙𝑖(𝑥,𝑠)𝑦𝑖
𝑖!, (8)
𝑥
𝑠𝑦⊙
𝑠 =𝐿𝑚𝑎𝑔
2𝑥𝑠
𝑦
⊙
𝑠 = −𝐿𝑚𝑎𝑔
2𝑥
𝑠𝑦
⊙𝑠 = 0
𝜌(𝑠)
Figure 1: Frenet-Serr... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 0 |
a44efcf6-3fa9-4173-893f-2a189dc363b4 | Figure2: MultipoledecompositionoftheELENAdipoleup
to octupole component. Third order piecewise polynomials
areusedtodescribethelongitudinalbehaviour. Theuncer-
taintyofthefitwasestimatedbyvaryingthehighestorder
of the fitted polynomial and it was in the order of 0.0002%,
0.07%,0.8%,43%ofthemaximalvaluefor 𝑏1,𝑏2,𝑏3,�... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 1 |
d08d5130-641d-45d6-ab00-e4dfa0b3c21f | ordermultipolesincluded,whichleadstolargeuncertainties.
Weplan toinvestigateotheroptions,suchradial dependent
harmonic analysis and conversion to field derivatives.
To track the particles, one needs a description of the lon-
gitudinal behaviour of the functions 𝑎𝑛(𝑠),𝑏𝑛(𝑠). While
the lowest order component of a f... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 1 |
751c1b5e-ea51-49bd-b293-a93ce1dc97c3 | Runge-Kuttamethod[ 10],solvingtheHamiltonequations
with the Hamiltonian for a particle in an electromagnetic
field in Frenet-Serret coordinates,
𝐻𝜏=𝑝𝜏
𝛽0−(1+ℎ𝑥)
×(√(1+𝛿)2−(𝑝𝑥−𝑎𝑥)2−(𝑝𝑦−𝑎𝑦)2+𝑎𝑠) .(10)
This method will be referred to as fieldmap tracking , and
was used to determine the fitted parameters i... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 1 |
402bfa92-5f19-490f-a6ee-8839438871f5 | quadrupoles. The advantage of this setup is a very simple
lattice in which the effect of the dipoles can be isolated.
Themeasurementswereperformedat5.3MeV,rightafter
accelerating the beam from the injection energy of 0.1 MeV.
To exclude the effects of the Eddy currents, a compensa-
tion was added to the dipole currents... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 1 |
fff0389f-e3e5-482d-92a0-76c72497efe2 | behaviour of the machine.
Tune Measurements
Thetuneaspredictedbythedifferentmodelsisgivenin
Table2togetherwiththemeasurements. Whencomparing
the measurements in the horizontal plane, one can see an
improvementinallthreeoptimisedmodelsoverthedesign
model. Further improvement of the model is needed, al-
though a possible... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 1 |
95b1623e-96fe-46f8-a6df-13b6290db34c | Themeasurementswereperformedbothwithandwithout
electron cooler to investigate the non-linear effects of the
magnetic fields of the electron cooler on the beam. The
differenceinhorizontalplanecouldpossiblybeexplained
by a difference in horizontal orbit.
The deviation from the lumped fringe field map with the
measurement... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 1 |
97a5d1cb-230d-4330-b423-8ff61aab798f | Figure3: Comparisonofthetunemeasurementsasfunction
of frequency for all different models. The data with and
without electron cooler overlaps in the lower plot.
duces several simplifications on the non-linear dynamics.
Toincludeanaccuratedescriptionofthesextupolareffect
one would need to include the pole face curvature ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 2 |
a30ab479-c44e-4d56-b004-dc243519a123 | the models.
Althoughthevalueforthenon-linearchromaticitydoes
notagreewiththemeasurements,theyfallwellwithinthe
uncertainty on the octupole component of our model. To
explain the measurements, one would need an integrated
normalizedoctupolecomponentof −40m−2,whileourinte-
grated octupole field is −3±200 m−2, hence a dev... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 2 |
08dc8f39-5c1c-439e-936b-60203ab442b5 | optimized parameters. To describe the non-linear behaviour
of the machine, the lumped map with two parameters is not
sufficientandoneneedstoexplorebetterlumpedmapsor
resort to explicit tracking through the field map. To reach
a predictive description of the non-linear behaviour, im-proved fitting methods to determine t... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 2 |
be533251-6618-4371-a5ff-0d65ac95033c | thefieldmapandinterpolationmethodoftheELENAdipole.
WefurtherthankJ.RomainandL.Poncefortheirassistance
with the measurements.
REFERENCES
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[2]G. Iadarola et al., “Xsuite: An integrat... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 2 |
e30ce08a-f8b3-424b-bfd9-72593ce114b4 | [6]M. Liebsch, S. Russenschuck, and S. Kurz, “BEM-based
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gradient synchrotron”, Ann. Phys. , ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 2 |
e4c8d264-243b-4c2c-bc6b-d40688d77e77 | [9]H.A.Enge, FocusingofChargedParticles ,NewYork,NY,
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[10]J.D. Lambert, Numerical Methods for Ordinary Differential
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1e19e8c2-2300-41fd-ba8d-848595725087 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5085
MC5.D03: Calculations of EM fields Theory and Code Developments 2461WEP: Poster session WEP5085
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 attribution to th... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5085.pdf | 2 |
5db408fb-6745-496d-ab5c-215254832ac7 | [12]E. Forest, S.C. Leemann, and S. Schmidt, “Fringe effects
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fa4bd604-7d20-4d5a-9371-f8e06ebc6973 | ANALYTICAL SOLUTIONS FOR PARTICLE TRACKING IN PLANAR
CRYSTAL CHANNELLING
A. Iliopoulou∗1,2, B. Lindström1,3, S. Van der Schueren1,4, F. F. Van der Veken1, D. Veres1,5
1CERN, Meyrin, Switzerland,2University of Macedonia, Thessaloniki, Greece
3John Adams Institute at Royal Holloway, University of London, Egham, UK
4Sapie... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 0 |
09fb7962-1fe3-4228-90c4-f477734c8826 | propose a simplified Molière model that yields closed-form
analyticalsolutionsexpressedthroughJacobiellipticfunc-
tions. Toextendthetreatmenttobentcrystals,symplectic
integrators are applied to the equations of motion, ensuring
accuracyandlong-termstabilitythroughsymplecticity. This
semi-analytical approach to evaluate... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 0 |
398e8127-86b5-4458-b535-f84457ae63b4 | affecttheentirebeam,crystalsinfluenceonlytheintercepted
particles, leaving the rest of the beam untouched [15].
The implementation of crystals into simulations requires
studying the underlying particle–matter interactions, such
as channelling, dechannelling, volume capture, and volume
reflection [16]. Here we focus on ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 0 |
8ad0e3d1-3217-45f3-9f01-8eb6ee80124a | simulation library [21,22].
MODEL DESCRIPTION
Our model is derived from the Molière potential for a
“warm” atomic plane [16], approximating the sum of ex-
∗anastasia.iliopoulou@cern.ch
1Typically on the mm–cm scale.ponentials by a single exponential, leading to the relation
below:
𝑈(𝑥)=𝑈 N
cosh𝛽i
𝑎TF𝑥−1
,(1)
𝑈... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 0 |
e8c59b9c-8f55-4cdc-af51-af7b53a03d2d | CHANNELLING EQUATION
Underthecontinuumapproximation,assumingaclassical
particle trajectory with small angles relative to the crystal
lattice planes ( 𝜃≈tan𝜃=𝑝x
𝑝z), adiabatic invariance (no
energylosses),andathermallyaveragedcrystal,theparticle
transverse energy is considered a constant of motion:
𝐸T=1
2𝛽𝑝𝑐𝜃2+... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 0 |
a9ff9bbd-536f-45f7-9726-a7bb82eb1656 | i(𝜈𝑧+𝜙),−2𝑈N
𝐸T
,
𝜃(𝑧)=−2𝑎TF
𝛽i𝜈dn
i(𝜈𝑧+𝜙),−2𝑈N
𝐸T
,
2𝑁denotes the atomic density of the crystal, 𝑍the atomic number of the
lattice atoms, 𝑍ithe charge number of the incident particle and 𝑒the
elementary charge, as explained in Ref. [16].
3Basedonmeasurements,wetypicallyuse 𝑥c=√
0.9𝑑P
2butthisca... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 0 |
d83b61fe-f8b1-4070-ba93-6087db969ac8 | with
𝜈=−sgn(𝜃 in)𝛽i
𝑎TF√︄
𝐸T
2𝛽𝑝𝑐,
𝜙=−i F
−i
2𝑥in𝛽i
𝑎TF,−2𝑈N
𝐸T
,
where am(𝑢,𝑚) is the Jacobi amplitude, dn(𝑢,𝑚) is the
Jacobideltaamplitude, F(𝜙,𝑚)istheincompleteellipticin-
tegralofthefirstkind,and (𝑥in,𝜃in)aretheinitialconditions
of the particle entering the crystal.
Although the Jacobi ellip... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 1 |
b5b555f1-0855-4de7-bd80-58f9adadc16a | ,
while sn(𝑢,𝑚)andcn(𝑢,𝑚)are the Jacobi elliptic sine and
cosine functions, respectively, and 𝜈remains unchanged
after the transformation.
Bent Crystal
FortheaforementionedapplicationsintheCERNaccel-
erator complex, the crystals employed are bent, meaning
that the motion can be described by an effective potential,... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 1 |
c6b7ef3d-7bb0-4e70-90f2-a20bebf9824a | The Hamiltonian can be written as:
𝐻=𝛽𝑝𝑐
2𝜃2+𝑈 N
cosh𝛽i
𝑎TF𝑥
−1
+𝛽𝑝𝑐
𝑅𝑥,
and the splitting methods executed are4:
4Method1wasanalternativewaytosplittheHamiltonian,butwasshown
not to be convergent and hence abandoned; the naming is retained for
consistency with prior communication.
Figure 1: The first ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 1 |
ec1b25c2-ed4b-4736-a5fb-0306c6a1f2bb | alisedkick(K).Thetwosequencesthatcanbeselectedto
construct a full integration step (Fig. 1) are:
Version 1 (V1):𝑥 0−→
channel𝑥1−→
kick𝑥2−→
channel𝑥3,
Version 2 (V2):𝑥 0−→
kick𝑥1−→
channel𝑥2−→
kick𝑥3.
We can further divide the steps into symmetric sub-steps
toimproveprecisionthroughdifferentintegrationorders(O)
... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 1 |
1385188f-2a8f-4357-8b77-457041bc8241 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5086
2464 MC5.D11: Code Developments and Simulation TechniquesWEP5086 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 attribution to the author(s)... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 1 |
f05177c4-9b03-49cf-8c8c-ff679f374e1f | Figure 2: Comparison to the Mathematica solution for a
given order/version (O2/V1) and integration steps.
Figure3: Numberofpointsperperiod(N)toattainaspecific
accuracy thresholds for O8/V1.
against high-precision numerical solutions obtained with
Mathematica [27]. The general case tested corresponded to
a28Si(110)cryst... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 2 |
ba0118a1-fb7f-49eb-b797-579c1fb69265 | As an example, Fig. 3 illustrates the N–accuracy plot for all
models for O8/V1, representing the general trend observed
for every O/V configuration.
Regardingversionsandorders,theresultsshowthatO4
improves accuracy while having a similar runtime to O2
(Fig. 4), whereas higher orders are more computationally
expensive t... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 2 |
26b95e23-6e00-4382-9db4-33cb20f7f4e4 | different integration orders in M4.
tional stepwise Molière tracking approach and significantly
more accurate than the harmonic approximation.
Different configurations were compared, finding that
method 4, which implements a fourth order Yoshida in-
tegrator as straight channelling - bending kick - straight
channelling... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 2 |
8c1e8c9b-b072-4c54-9855-c89b14b9e84b | reflection, will be incorporated.
ACKNOWLEDGEMENTS
TheauthorswouldliketothankDr. GiovanniIadarolaand
Dr. Riccardo De Maria for their contributions to previous
related work and for helpful discussions.17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 267... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 2 |
9da7c615-9d82-4798-839c-a6583b627254 | REFERENCES
[1]D. E. Veres, M. Giovannozzi, and G. Franchetti, “Exploring
thepotentialofresonanceislandsandbentcrystalsforaslow
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[2]D. E. Veres, M. Giovannozzi, and G. Franchetti, “An inn... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
0a7ede59-fc10-4cdd-8c9c-3647d7db845c | thelargehadroncollider”,Phys. Rev. Accel. Beams,vol.28,
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[6]R. P. Flilleret al., “Results of bent crysta... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
4debcd18-bdaf-49cc-8d85-056a978cc81c | lider”,Eur. Phys. J. C, vol. 85, p. 1373, Dec. 2025.
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[9]E. Bagliet al., “Electromagnetic dipole moments of charged
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[10]J. Fuet al., “Novel Method for the Dir... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
56f360e8-ed6a-492f-b1f9-ab0ddd9f02f6 | surements of short-lived baryons using bent crystals at the
LHC”,Eur. Phys. J. C, vol. 80, no. 10, p. 929, Oct. 2020.
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[13]S. Redaelli, M. Ferro-Luzzi, and C. Hadjidakis, “Studies
forfuturefixed-targetexperimentsattheLHCintheframe-
work of the CERN physics beyondcolliders study”, inPr... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
39b15ac7-793b-4287-abb1-652031c8ecea | [16]V.M.Biryukov,Y.A.Chesnokov,andV.I.Kotov,Crystal
channeling and its application at high-energy accelerators.
Berlin, Germany: Springer, 1997.
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[17]D.Mirarchi,G.Hall,S.Redaelli,andW.Scandale,“Acrystal
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Nucl. Instrum. Methods Phys. ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
3b6ff243-f193-4ba9-8416-8a1d60085a48 | 2804, 2023.doi:10.18429/JACoW-IPAC2023-WEPA066
[20]F.F.VanderVekenet al.,“Recentdevelopmentswiththenew
tools for collimation simulations in Xsuite”, inProc. HB’23,
Geneva, Switzerland, pp. 474–478, Oct. 2024.
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[21]G.Iadarolaet al.,“Xsuite:anintegratedbeamphysicssim-
ulation framework”, i... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
632d353d-e668-49c6-9ca0-4fb1106dce35 | functions, with formulas, graphs, and mathematical tables,
New York, NY, USA: Dover Publications, 1974.
[25]G. B. Arfken, H. J. Weber, and F. E. Harris,Mathematical
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MA, USA: Academic Press, 2012.
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[26]H. Yoshida, “Construction of higher ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5086.pdf | 3 |
cafd8f58-ded3-4bed-b573-4bce1ce68819 | LINEAR AND NONLINEAR EFFECTS OF FRINGE FIELDS ON THE
SINGLE-PARTICLE DYNAMICS IN THE HELIUM LIGHT ION COMPACT
SYNCHROTRON
S. Van der Schueren∗, R. De Maria, H. Huttunen, European Organization for Nuclear Research,
Geneva, Switzerland
M. Migliorati, Istituto Nazionale di Fisica Nucleare, Rome, Italy
V. Korchevnyuk, Écol... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 0 |
b8638233-1b62-4a74-8938-275c9d9ce115 | forthefringefieldsofcurvedcombined-functionmagnets
with edge angles are not available in the literature. In this
workweinvestigatethelinearandnon-lineareffectsofthese
fringe fields through the framework of resonance driving
terms, providing an alternative approach to quantify their
influence on single-particle dynamics... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 0 |
1b2541d7-ff0c-48bf-b1fe-beab9a496dc6 | magnets, but also produce field-quality specifications for
magnetstobedesigned,thereforeaccountingforfringefield
effects earlier in the ring design process.
THE HELICS SYNCHOTRON
The HeLICS optics [ 4], computed with Xsuite [ 5] and
shown in Fig. 1, contains six combined-function dipole-
quadrupole magnets with design ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 0 |
968528f7-9ac4-451a-9c59-5c838dde789a | Dipoles in the Current Design of the HeLICS Ring
Parameter Design value
bending radius 2.74 m
bending angle 60 degrees
edge angle 30 degrees
(curved) magnetic length 2.87 m
dipole strength 1.65 T
quadrupole strength -0.50 T/m
magnetic field expansion in Frenet-Serret coordinates [ 6],
⃗𝑅(𝑥,𝑦,𝑠) = ⃗𝑅0(𝑠)+𝑥 ̂ 𝑥(�... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 0 |
dec9d864-846f-4da2-8748-7f95bdf75ea5 | length, and bent with bending radius 𝜌 =1
ℎinside the mag-
netic length.17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5087
MC5.D03: Calculations of EM fields Theory and Code Developments 2467WEP: Poster ses... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 0 |
82a7f10d-0e8a-482e-b905-8e0b8fd9ba60 | Themagneticfieldwilbespecifiedintermsofderivatives
on axis (Taylor coefficients),
𝑎𝑛(𝑠) = 𝜕𝑛−1𝑥𝐵𝑥(𝑥,𝑦,𝑠)∣𝑥=𝑦=0(3)
𝑏𝑛(𝑠) = 𝜕𝑛−1𝑥𝐵𝑦(𝑥,𝑦,𝑠)∣𝑥=𝑦=0(4)
𝑏𝑠(𝑠) = 𝐵𝑠(𝑥 = 0,𝑦 = 0,𝑠) (5)
from which the total magnetic field can be reconstructed
from the scalar potential B= −∇Φ[7]
Φ(𝑥,𝑦,𝑠) =∞
∑
... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 1 |
1c72868a-fb4b-4e25-abac-95dafd6edd60 | ELENAdipole[ 10,11]servedasamodel,andwillintroduce
higher-order components around the edge. If needed, the
full three-dimensional fieldmap can be extracted from the
magnetic components. An illustration of 𝑏1(𝑠),𝑏2(𝑠),𝑏3(𝑠)
canbefoundinFig. 3. Thedesignvaluesofthecomponents
in the body of the magnet will be referr... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 1 |
9fbaee5b-0de7-4c80-837e-368f9f1668e0 | servation point, and
ℎ𝑤,𝑗𝑘𝑙𝑚= −𝑏𝑤,𝑛Ω(𝑙 +𝑚)+𝑖𝑎 𝑤,𝑛Ω(𝑙 +𝑚+1)
𝑗! 𝑘! 𝑙! 𝑚! 2𝑗+𝑘+𝑙+𝑚
×𝑖𝑙+𝑚(𝛽𝑤,𝑥)𝑗+𝑘
2(𝛽𝑤,𝑦)𝑙+𝑚
2 (11)
withΩ(𝑖) = 1 if𝑖is even, and 0if𝑖is odd. The coordinates
can then be reconstructed using complex Courant-Snyder
coordinates ℎ𝑞,±= ̃ 𝑞±𝑖 ̃ 𝑝𝑞with̃ 𝑞, ̃ 𝑝the norm... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 1 |
477c2bfe-a25d-419c-a46f-0a134bac2acb | ditional resonance driving terms. To describe the magnetic
field,onecanusethepreviouslyintroducedgeneralmagnetic
field expansion.
Fringe fields
For an s-dependent field in a reference frame with cur-
vatureℎ(𝑠) =̄𝑏1Θ(𝑠), whereΘ(𝑠)is a step function that
is zero outside the magnet and one inside the magnet, the
tran... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 1 |
19c7bc9b-9d73-40dc-a94a-6c32c3d2bb83 | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5087
2468 MC5.D03: Calculations of EM fields Theory and Code DevelopmentsWEP5087 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 attribution to th... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 1 |
febd95fa-10f4-4f31-9d25-b3f63d047377 | Table 2: Hamiltonian Terms from FirstOrder Perturbation Theory ResonanceDriving Terms
Hamiltonian term Valuefora Combined-Function Magnetin PiecewiseCurvedFrame
ℎ1000= ℎ0100 −√𝛽𝑥
2(𝑏1(𝑠)−̄𝑏1Θ(𝑠))
ℎ1100= 2ℎ2000= 2ℎ0200 −ℎΘ(𝑠)𝛽 𝑥
4(𝑏1(𝑠)−̄𝑏1)−𝛽𝑥
4(𝑏2(𝑠)−̄𝑏2Θ(𝑠))
ℎ0011= 2ℎ0020= 2ℎ0002𝛽𝑦
4(𝑏2(𝑠)−̄𝑏2Θ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 2 |
7d99e6c5-b6e1-48b1-93af-bf92218f1f51 | 𝑝𝑦and are not present in the reference. The results can be
found in Tab. 2.
Application to the HeLICS ring
The first and second order resonance driving terms allow
to determine the closed orbit distortion and beta-beating.
Compared to a hard edgemagnet with edge angles, we find
ahorizontalclosedorbitdistortionwithama... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 2 |
c334a24a-42da-4a58-a255-2891eec78172 | of the coordinates in Eq. (12)and Eq.(13), one can further
reconstruct thespectrum of thering. Thisspectrum, taking
intoaccountuptosextupole-likespectrallines,isgivenin
Fig.5withhard-edgemagnetandfullmagnetdecomposi-tion with fringe fields and edge angles. In this figure, one
can see less dominant quadrupole-like lines... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 2 |
85c7a97d-c2a6-419c-a3f8-5fbf61b65d8e | tracking through the fieldmap, and compare the spectral
lines to lumped fringe field maps used in several tracking
codes. The derivation can easily be extended to higher-
orderresonancedrivingtermsandsecondorderperturbation
theory, to include effects like the well-known fringe field
integral [12].
CONCLUSIONS
Thetheory... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 2 |
a92ad6db-40ad-48f5-a433-48ec482a0d23 | magnet design is available, by creating a magnetic fieldmap
based on derivatives on axis.17th International Particle Accelerator Conference, Deauville, France JACoW Publishing
ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5087
MC5.D03: Calculations of EM fields Theory and Code Developments 246... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 2 |
f980f050-739d-4579-bc36-626119b2b9b4 | REFERENCES
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3ba365b6-3b43-4dba-83e6-f591ba7999dd | Taipei, Taiwan, Jun. 2025, pp. 2236–2239.
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Oct. 2023, pp. 73–80.
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[6]E. D. Courant,and H. S. Snyder,... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 3 |
cb3d484f-f3e6-46f0-9c56-65bc8a48456e | doi:1/zero.alt4.18429/JACoW-IPAC2/zero.alt424-TUPS/zero.alt49
[8]A. Franchi, L. Farvacque, F. Ewald, G. Le Bec and
K. B. Scheidt, “First simultaneous measurements of sextupo-
lar and octupolar resonance driving terms in a circular accel-
eratorfrom turn-by-turn beam position monitordata”, Phys.
Rev. Spec. Top. Accel. B... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 3 |
fee7687a-89bc-45dd-8819-03f7d96f1e65 | rati, “Modeling and measurements of the impact of dipole
fringe fields in the extra low energy antiproton ring”, pre-
sented at IPAC’26, Deauville, France, May 2026, paper
WEP5085, this conference.
[12]E.Forest,S.C.LeemannandF.Schmidt,“Fringeeffectsin
MAD part 1, Second order fringe in MAD-X for the module
PTC”,KEK,Tsu... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5087.pdf | 3 |
983d26ec-0548-45c4-b402-a4971ea8bf2f | HOM STUDY OF THE PERLE’S BOOSTER CAVITY
R. Roux†, Université Paris -Saclay, CNRS/IN2P3, IJCLab, Orsay, France
on behalf of the PERLE collaboration
Abstract
The injector for the PERLE ERL in construction at
IJCLab is based on a booster containing 4 superconducting
cavities to reach 7 MeV for 20 mA of cw current... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 0 |
e0a3f85c-d7a3-43e0-bf71-b0638123d473 | construction of the PERLE accelerator [1] near Paris in
France. PERLE is an Energy Recovery Linac (ERL) aim-
ing to reach 5 MW of electron beam power thanks to a high
current, 20 mA and an energy of 250 MeV . For this accel-
erator, an injector [2] providing such current but with an
energy of 7 MeV is required where... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 0 |
8f8c10dc-b156-4243-a4a3-e645914623d6 | the beam repetition rate, which is 40 MHz. The beam con-
sists of a train of electron bunches with a temporal length
of 10 ps. Given this short bunch length, the corresponding
frequency spectrum is broad, with a rms width of approxi-mately 16 GHz, as determined by the Fourier transform of
the bunch temporal profile.... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 0 |
3cbdf441-0dbf-4c5c-a21b-e12dd62d9960 | tion of the energy spread and bunch length. Because the
field decay times of the cavity are long compared to the
bunch spacing, these effects can accumulate over succes-
sive bunches, making the control of HOM excita tion essen-
tial for stable beam operation .
In this paper we will give the exhaustive list of all H... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 0 |
a53275a0-9077-4833-a10a-0263b03bd03e | relative to the nearest beam harmonic, the external quality
factor Q
ext, the longitudinal shunt impedance over quality
factor R/Q (R/Q)l and the transversal shunt impedance
over quality factor R/Q (R/Q)┴. While the Microwave stu-
dio does not directly provide the transversal shunt R/Q
(R/Q) ┴, it can be computed u... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 0 |
dc193cad-ef22-4bd0-85fc-f441aeb1a023 | Figure 1: longitudinal R/Ql as a function of frequency .
Figure 2: the transversal R/Q┴ as a function of frequency.
We now focus on the modes with a transverse or longi-
tudinal magnitude larger than one in order to assess their
potential impact on the beam . The results are summarized
in Table 1 and Table 2 fo... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 0 |
9cde2b55-7c8c-4a47-944d-3eb9e5f2162f | ISBN: 978-3-95450-252-3 ISSN: 2673-5350 doi: 10.18429/JACoW-IPAC2026-WEP5089
MC5.D04: Beam Coupling Impedance Theory, Simulations, Measurements, Code Development 2471WEP: Poster session WEP5089
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\WEP5089.pdf | 0 |
5c274433-7f7c-4a8d-9a85-e2bd295ee5d2 | frequency difference with respect to the nearest beam har-
monic of the beam .
Table 1: Transverse Modes Parameters
F (MHz) R/Q┴ (Ω) Qext ∆f (MHz)
1035.9 1.34 6.8x105 5.3
1068.57 8.2 2987 12.7
1128.32 26.4 3985 7
1130.97 27.1 15.7 9.5
1594.3 1.5 3.8x108 8
1631.6 4.0 6.5 11
1844.3 3.7 33 1.44
3011.6 1.34 ... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 1 |
2d1f0329-9457-4104-af67-baa6d25ee697 | 0.2 mm represents a large mechanical error, typically an
order of magnitude larger than standard fabrication toler-
ances . Hence, after mechanical adjustment s to reach the
correct frequency for the fundamental mode the risk of sig-
nificant HOM frequency shifts is minimal . In Table 1, two
modes are potentially c... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 1 |
8231b062-8e60-44e8-bffd-bae995cc8cbb | monic derived from the laser stability (source of the cur-
rent) is only 6x10 -6, namely 25 kHz for 4.6 GHz. Hence,
in order to reach an efficient energy transfer from the beam
harmonic to this mode, it requires practically the frequency
gap to be zero instead of 1.3 MHz which is very unlikely.
The results are sim... | D:\Daily_ihep\Conferences\IPAC2026\WEP\WEP5089.pdf | 1 |
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