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138f0de7-b490-48ca-984f-4a9fe02b0eaf | [0](𝑘;𝑠)∫𝜕
𝜕𝛿ℬ(𝑘,𝛿;𝑠)𝑑𝛿 = 0,
(13)
sincetheterm ∫𝜕
𝜕𝛿ℬ(𝑘,𝛿;𝑠)𝑑𝛿 vanishes,thus 𝒱[0]=
𝑁(constant), indicating the conservation of particle
numbers;
•for𝑚 = 1case, from Eq. (12) wehave
𝜕𝒱[1]
𝜕𝑠=𝜕
𝜕𝑠∫𝑑𝛿(𝛿 ⋅𝑉) = ∫𝑑𝛿(𝛿 ⋅𝜕𝑉
𝜕𝑠)
= 𝛼∫𝑑𝛿𝛿 ⋅∫𝑑𝑘𝑍∗
‖(𝑘;𝑠)𝑏∗(𝑘;𝑠)𝜕
𝜕𝛿ℬ(𝑘,𝛿;𝑠)
= ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 1 |
1dafd60b-2f17-4b24-b9e2-aadd4d515b0f | deviation 𝛿toobtainasetofrecursiveequations. For 𝑚 = 0
case,
𝑏[0](𝑘;𝑠) = 𝑏(0)
[0](𝑘;𝑠)+∫𝑠
0𝑖4𝜋𝜖0𝑟𝑒𝑐𝑁
𝛾𝑘𝑅56(𝜏 → 𝑠)×
𝑍‖(𝑘;𝜏)𝑏[0](𝑘;𝜏){𝐿,𝐷;;𝜏 → 𝑠}𝑑𝜏
= 𝑏(0)
[0](𝑘;𝑠)+∫𝑠
0𝐾[0](𝜏,𝑠)𝑏[0](𝑘;𝜏)𝑑𝜏,
(16)
where the kernel function 𝐾[0](𝜏,𝑠)is the familiar one,
whichcanalsobederivedfr... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 1 |
a40287e2-1b14-4fad-b4b1-9c97c12f9a24 | whichrequiresthezeroth-orderbunchingfactor. Similarly,
wecanobtainforthe 𝑚 = 2case. Ingeneral,byprinciple
of mathematical induction, we have
𝑏[𝑚](𝑘;𝑠) = 𝑏(0)
[𝑚](𝑘;𝑠)+∫𝑠
0𝐾[𝑚](𝜏,𝑠)𝑏[0](𝑘;𝜏)𝑑𝜏. (18)
So far we have obtained the slow and fast equations in
termsof𝒱[𝑚]and𝑏[𝑚]. Tocompletethetheory,west... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 2 |
fb5bbec2-0639-4c38-8eaf-2416a7d0b9b5 | (0](𝑘;0)∫∞
−∞𝑑𝛿0𝛿0𝑓0(𝛿;0)𝑒−𝑖𝑘(𝑠)𝑅56(𝑠)𝛿0
= −𝑖𝑘(𝑠)𝑅56(𝑠)𝜎2
𝛿0𝑏(0)
[0](𝑘;0){𝐿.𝐷.;𝑠}.
(22)
For the𝑚 = 2case, we have
𝑏(0)
[2](𝑘;𝑠) = 𝜎2
𝛿0[1−𝑘2(𝑠)𝑅2
56(𝑠)𝜎2
𝛿0]𝑏(0)
[0](𝑘;0){𝐿.𝐷.;𝑠}.
(23)
For the𝑚 = 3case and other higher order moments, they
all have analytical expressions.
SUMMA... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 2 |
5b700a08-d731-488e-a88d-a4a3e28b1c09 | ical solutions to the semi-analytical Vlasov solver [ 10].
Figure2: Sketchofsolvingthecoupledrecursiveequations.
HereweaddasidenotetoremindthatinRef.[ 11,12]the
energy spread increase due to collective effects is expressed
as
𝜎2
𝛿,coll=8
𝑛𝑏𝐶tot∫𝜆∗
0𝑑𝜆
𝜆2∣∫𝑠𝑓
0𝑑𝜏𝐼𝑏(𝜏)
𝛾𝐼𝐴𝑍‖(𝜆;𝜏)̃𝐺(𝜆;𝜏)∣2
,
(24)
... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 2 |
42ff5c1b-f618-4674-866d-ad532cdfb04e | Rev. ST Accel. Beams , vol. 5, p. 064401, 2002.
doi:1/zero.alt4.11/zero.alt43/PhysRevSTAB.5./zero.alt4644/zero.alt41
[2]Z.HuangandK.-J.Kim,“Formulasforcoherentsynchrotron
radiation microbunching in a bunch compressor chicane”,
Phys. Rev. ST Accel. Beams , vol. 5, p. 074401, 2002.
doi:1/zero.alt4.11/zero.alt43/PhysRevST... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 2 |
6f6902ef-41d6-4d87-9800-0ba0bec4a279 | radiation-inducedmicrobunchingsuppressionin multibend
beam transport or recirculation arcs”, Phys. Rev. Accel.
Beams, vol. 20, p. 024401, 2017.
doi:1/zero.alt4.11/zero.alt43/PhysRevAccelBeams.2/zero.alt4./zero.alt4244/zero.alt41
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formagnetizedbeams”, Phys.Rev.... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 2 |
4ba9492c-48ed-4526-8931-ac69a86fbaa7 | [9]S. Di Mitri et al., “Experimental evidence of intrabeam scat-
teringinafree-electronlaserdriver”, NewJ.Phys. ,vol.22,
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[10]C.-Y. Tsai et al., “Theoretical formulation of phase space
microbunching instability in the presence of intrabeam scat-
te... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 3 |
fef957e6-3214-4d53-ba76-7baeb5a42e2a | nomena in electron beam’s longitudinal phase space”, Sci.Rep., vol.11, p. 7895, 2021.
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[13]B. Liu, C.-Y. Tsai, Y. Jiao, W. Liu, F. Zeng, and W. Qin, “An-
alytical formulas of coherent-synchrotron-radiation induced
microbunching gain and emittanc... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 3 |
9300a062-4109-4a2d-893b-790219f0557e | QUICKESTIMATEOF CSR-INDUCEDMICROBUNCHINGINSTABILITY
IN A MULTIBEND TRANSPORT BEAMLINE
Cheng-Ying Tsai∗, School of Electrical and Electronic Engineering,
Huazhong University of Science and Technology, Wuhan, China
Abstract
Microbunching instability (MBI) driven by short-range
wakefields in high-brightness electron beams... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 0 |
ddafaf9f-66a5-4876-8860-22d38adb08e8 | length and introduce physically motivated simplifications
toderivethemaximumgain. Againspectrumisthencon-
structedbasedonphysicalinsightsintoMBIamplification
mechanisms. Theresultsshowgoodagreementwithdetailed
numericalcalculationsfromVlasovsolver. Thedeveloped
approachenablesquickandreasonablyaccurateestimatesof
the M... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 0 |
664b9c98-1578-449c-a79d-9cadb082885b | dominant role and may lead to transverse emittance growth
(see,e.g.,Refs[ 20–22])and/orlongitudinalMBI.Forabrief
review, see Ref. [ 23]. Study of MBI can be computationally
intensivethroughparticletrackingsimulationsbecauseof
sensitivity to the numerical noise. Existing linearized the-
ory is formulated based on Volter... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 0 |
d7af6b41-e35e-4163-a2e5-8c2da9fe970e | Therefore we need to solve the integral equation; otherwise,
intensetime-consumingparticletrackingsimulationswillbe
performed. This work is of practical importance: instead of
∗Email: jcytsai@hust.edu.cn. This work is supported by the Fundamental
Research Funds for the Central Universities (HUST) under Project No.
2021... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 0 |
05076ef7-3832-44c3-a0a6-7c355955e92b | a linear Volterra-type integral equation of the second kind,
𝑏(𝑘;𝑠) = 𝑏(0)(𝑘;𝑠)+∫𝑠
0𝐾(𝜏,𝑠)𝑏(𝑘;𝜏)𝑑𝜏, (1)
where𝑘 = 2𝜋/𝜆 being the modulation wavenumber,
𝑏(0)(𝑘;𝑠) = 𝑏(0)(𝑘;0){𝐿.𝐷.;0,𝑠} , the kernel function
𝐾(𝜏,𝑠) = 𝑖𝑘(𝑠)𝑅56(𝜏 → 𝑠)4𝜋
𝑍0𝐼𝑏(𝜏)
𝛾𝐼𝐴𝑍‖(𝑘;𝜏){𝐿.𝐷.;𝜏,𝑠},
(2)
with... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 0 |
1cd7fd86-a723-40ed-897c-9c1eb017d5a2 | 𝐺𝑐(𝑘;𝑠) =𝑏(𝑘;𝑠)
𝑏(𝑘;0), 𝐺(𝑘;𝑠) = |𝐺𝑐(𝑘;𝑠)|. (4)
For high-brightness electron beam, reduction of pure-
opticsbunchingduetoLandaudamping maybe neglected,
i.e., Eq. (1) can be approximatelywritten as
𝐺𝑐(𝑘;𝑠) ≈ 1+∫𝑠
0𝐾(𝜏,𝑠)𝐺𝑐(𝑘;𝜏)𝑑𝜏. (5)
THEORETICAL FORMULATION: SERIES
EXPANSION
Now we want to... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 0 |
f2a6d77b-c374-4ab0-8276-0f03bbd933fb | 𝑑0= 1. Ourstrategyconsiststhreesteps: first,weidentify
theoptimalwavelengthcorrespondingtothemaximumgain;
second,wederiveapproximateexpressionforthemaximum
gainignoringLandaudampingeffect;third,weincludeLan-
daudamping. Inwhatfollowsweconsider1-Dfree-space
steady-state CSR [ 16–19] with
𝑍‖,CSR(𝑘) = −𝑖𝐴𝑍0
4𝜋𝑘1/3... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 1 |
0ab9b850-3a93-4460-8e47-2e382cbaa55e | As the second step, substituting the series expansion
𝐺𝑐(𝑘𝑜𝑝𝑡;𝑠)into Eq. (5) gives(assume isochronousline)
𝑀
∑
𝑚=0𝑑𝑚𝑠𝑚
𝑓Λ𝑚≈ 1−𝑘𝑜𝑝𝑡ℤCSR𝑀
∑
𝑚=0𝑑𝑚Λ𝑚+1(Σ𝑚
56),(10)
whereℤCSR= 𝐴𝑘1/3
𝑜𝑝𝑡
𝜌2/3and
Σ𝑚
56≡𝑁𝑑
∑
𝑗=1∫
𝐵𝑅56(𝜏𝑗)𝜏𝑚
𝑗𝑑𝜏 ≈ 𝐿𝐵𝑁𝑑
∑
𝑗=1𝑅56(𝑠𝑗)𝑠𝑚
𝑗
(11)
comparing order ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 1 |
83ec0380-9daa-4d27-81c7-31b6950c5e5e | viaenergyspreadand largest ℋ𝑥viatransverseemittance.
Havingcompletedthethreesteps,fromEq. (5)weconstruct
MBI gain spectrum as
𝐺𝑐(𝑘;𝑠𝑓) ≈ 1+
𝐺𝑐(𝑘𝑜𝑝𝑡;𝑠𝑓)𝑘
𝑘𝑜𝑝𝑡𝑒1
2−𝑘2
2(𝑅2
56,eff𝜎2
𝛿0+ℋ𝑥,eff𝜖𝑥0).
(16)
If finite bunch length effect is to be included, we may multi-
ply𝐺𝑐(𝑘;𝑠𝑓)with a reductio... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 1 |
18ac44e2-92ed-4224-ba76-a037d739ac72 | to𝜎𝛿0= 1.23 × 10−5with no chirp. The initial Courant-
Snyder parameters of the beam are matched to the lattice:
𝛽𝑥0= 35.81m,𝛽𝑦0= 3m,𝛼𝑥0= 0,𝛼𝑦0= 0. The total
length of the arc is about 240 m. Description of the lat-
tice layout and relevant beam parameters can be found in
Refs. [7,9–11]. Figure 1 shows the bas... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 1 |
26c36297-d193-4f07-9409-8e1e0d21033e | Using Eq. (8) we estimate the optimal wavenumber 𝑘𝑜𝑝𝑡.
From the lattice information Fig. 1(c), we can evaluate Σ𝑚
56
andthecoefficients 𝑑𝑚fordifferentorders 𝑚. Withallthese
prepared, wecanconstruct theMBIgainspectrumshown
in Fig. 1(b).
Figure1: (a)Courant-Snyderopticsfunctions;(b)MBIgain
spectrum; (c,d) transpo... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 2 |
218fe0d4-6a4a-42e0-aea0-90ae52e1d4b8 | 𝑚=0𝑑𝑚𝑠𝑚Λ𝑚
are obtained, it is interesting to plot MBI gain 𝐺(𝑠)along
thebeamline. Figure3 showsthe comparison from Vlasov
solverand our model estimate. A good agreement is found.
SUMMARY AND OUTLOOK
Inthispaperwehavedevelopedaquickestimatetoevalu-
ateMBIgainingenericmulti-bendbeamlines. Startingfrom
Volterra in... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 2 |
ac27c0fa-fa12-4f2d-a923-b0394ed82dcc | only the 1-D free-space steady-state CSR is included and
the same radius of curvature for all bending magnets are
assumed, the present formulation is straightforward to ex-
tendtoincludeotherrelevantimpedancemodelsandwith
differentbendingradiialongthebeamline. Thequickesti-
mate does not really solve the equation; ther... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP10.pdf | 2 |
2673dfa3-2e32-48e9-825d-b66223d57ce0 | [2]Z.HuangandK.-J.Kim,“Formulasforcoherentsynchrotron
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a2a3d5c8-400f-44c4-8991-fc8610094add | BUNCHED-BEAM THEORY OF OF MICROBUNCHING INSTABILITY
Cheng-Ying Tsai∗, School of Electrical and Electronic Engineering,
Huazhong University of Science and Technology, Wuhan, China
Abstract
Conventional theory of single-pass microbunching in-
stability (MBI) is primarily based on the coasting-beam
approximation, which as... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 0 |
d17284fd-5e08-4a96-bb25-73bde6a262e1 | gain, or the amplified bunching factor, exhibits a depen-
dence on the initial modulation phase, a feature absent in
theexistingcoasting-beammodel. Theproposedbunched-
beamformulationmayofferadditionalphysicalinsightsinto
theunderlyingmechanismofMBI,particularlyinregimes
wherethefiniteextentofthebunchplaysanon-negligib... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 0 |
41d6b375-9737-47e5-85ad-bacd30289894 | ofthegoverningequationforthebunchingfactor. Whenthe
total bunch length is comparable to the modulation wave-
length, the existing theory is no longer valid. An intuitive
way to estimate the bunched-beam MBI gain is to convo-
lute the MBI gain with finite-bunch spectrum. However this
method may be lack of theoretical fo... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 0 |
081b47db-1e4f-4623-bdcb-d0fa2abb4de3 | Research Funds for the Central Universities (HUST) under Project No.
2021GCRC006 and National Natural Science Foundation of China under
projectNo. 12275094.with|𝑓1| ≪ ̄𝑓0and the normalization condition
∫∞
−∞∫∞
−∞𝑓(𝑧,𝛿)𝑑𝑧𝑑𝛿 = 𝑁 (here𝑁is the number of elec-
trons). Note that the unperturbed term has 𝑧dependen... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 0 |
64dbe191-0c93-43a0-beca-14795d7813d9 | and𝑏(𝑘;𝑠)thebunchingfactordefinedasFouriertransform
of the line density function. We define the beam sigma
matrixas Σ = (𝜎2
𝑧𝜎𝑧𝛿
𝜎𝑧𝛿𝜎2
𝛿),inwhichthechirpparameter
ℎ =𝜕𝛿
𝜕𝑧=𝜎𝑧𝛿
𝜎2𝑧. TheGaussianphasespacedistributioncan
be described as
̄𝑓0(𝑧,𝛿;0) =𝑁
2𝜋√
detΣ𝑒−1
2Z𝑇Σ−1Z
=𝑁
2𝜋√𝜎2
𝑧0𝜎2
𝛿0−... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 0 |
1ee775b4-ffea-443b-a435-4a9d158ae77e | Forfinite-bunch-lengthcase,asimplifiedexpressionof ̄𝑓0
can be written as
̄𝑓0(𝑧,𝛿;0) =𝑁
2𝜋𝜎𝛿0𝜎𝑧0𝑒−(𝛿−ℎ𝑧)2
2𝜎2
𝛿0−𝑧2
2𝜎2
𝑧0 (7)
and the perturbed part can be formulated as
𝑓1(𝑧,𝛿;0) = 2Δ cos(𝑘0𝑧0+𝜑)⋅̄𝑓0(𝑧,𝛿;0) (8)
withΔthe modulation amplitude, 𝑘0= 2𝜋/𝜆0the modula-
tion wavenumber and 𝜑the ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 1 |
8ac0c42f-45ef-4746-bebd-a7fc9a442095 | 𝑁∬𝑓(𝑧,𝛿;0)𝑒−𝑖𝑘𝑧𝑠𝑑𝑧𝑠𝑑𝛿𝑠
= ∬1
2𝜋𝜎𝑧0𝜎𝛿0[1+2Δcos(𝑘0𝑧0+𝜑)]×
𝑒−𝛿2
0
2𝜎2
𝛿0−𝑧2
0
2𝜎2
𝑧0−𝑖𝑘𝑧𝑠𝑑𝑧𝑠𝑑𝛿𝑠
=1
2𝜋𝜎𝑧0𝜎𝛿0∬[1+2Δ cos(𝑘0𝑧0+𝜑)]×
𝑒−𝛿2
0
2𝜎2
𝛿0−𝑧2
0
2𝜎2
𝑧0−𝑖𝑘(𝑧0+𝑅56𝛿0)𝑑𝑧0𝑑𝛿0
=1√
2𝜋𝜎𝑧0𝑒−𝑘2
2𝑅2
56𝜎2
𝛿0[(∗)+2Δ⋅(∗∗)],
(10)
where
(∗) =√
2𝜋𝜎𝑧0𝑒−𝑘2
2𝜎2
�... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 1 |
3d0bb063-0594-4b42-bab5-8818dbad2fe9 | 2(1+𝐾2)𝜁2cosh(𝐾𝜁2+𝑖𝜑). (13)
The function Ξ(𝐾,𝜁,𝜑) is
Ξ(𝐾,𝜁,𝜑) = 𝑒−𝐾2𝜁2
2+Δ⋅ℛ(𝐾,𝜁,𝜑), (14)
with its amplitude and phase shown in Figs. 2 and 3.
Figure 2: Amplitude of the function Ξ(𝐾,𝜁,𝜑) .
Figure 3: Phase of the function Ξ(𝐾,𝜁,𝜑) in degree.
A few remarks about the pure-optics bunched-beam
bunch... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 1 |
98c0410a-4428-4d2b-b4c5-2f564e2e841d | •Under coasting beam approximation ( 𝜁 ≫ 1), nonzero
value only exits when 𝑘 = 𝑘0;
•For finite bunch beam, nonzero value may exist for
𝐾 ≠ 1andthisbecomesevidentforsmaller 𝜁orshorter
bunches;
•For𝜁 < 2, i.e., a bunch only takes half modulation
wavelength, the bunching factor can be larger than 1;
•For short bunch... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 2 |
df6d02ff-9be7-4b73-b842-77084ab92d04 | equation for the bunching factor
𝑏(𝑘;𝑠) = 𝑏(0)(𝑘;𝑠)+∫𝑠
0𝒦[𝑠;𝜏,𝑏(𝑘,𝜅)]𝑑𝜏 (17)
where the kernel function becomes
𝒦[𝑠;𝜏,𝑏(𝑘,𝜅)] = 𝑖4𝜋
𝑍0𝐼𝑏(𝜏)
𝛾𝐼𝐴𝑘(𝑠)𝑅56(𝜏 → 𝑠)×
∫∞
−∞𝑑𝜅
2𝜋𝑍‖(𝜅;𝜏)𝑏(𝜅;𝜏)𝑒−𝜎2
𝛿0
2[𝑘𝑅56(𝑠)−𝜅𝑅56(𝜏)]2−𝜎2
𝑧0
2(𝑘−𝜅)2
(18)
For the coasting beam case, 𝜎𝑧0→ ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 2 |
66870621-803d-4b37-86bb-9e42b27e5b62 | INTUITIVE CONVOLUTION APPROACH
Oncethecoasting-beam(CB)bunchingfactorisobtained,
to estimate the bunched-beam case, a basic idea is to con-
volute the coasting-beam bunching factor to bunched-beam
formfactor. Hereweremindthattheconvolutionoperator
itselfisdimensional. AssumingGaussiandistribution,we
define
ΞGaussian(𝑘... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 2 |
aa3799c6-043b-4c61-a001-c61993e302f1 | takeintoaccounttheeffectofbunchedbeamonthekernel
function. Therefore it is believed that this expression Eq.
(21) may not be valid for a general case. As an ongoing
work, it will be worth comparing the solution of Eq. (17)
with Eq. (21) obtained from intuitiveapproach.
SUMMARY
Inthispaperwehavederivedthegeneralizedinte... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 2 |
767c96a2-76a2-42c0-9803-458f46c30c9e | REFERENCES
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[2]Z.HuangandK.-J.Kim,“Formulasforcoherentsynchrotron
radiation microbunching ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 3 |
c823032b-ea1c-4feb-8939-94ea8a1886ba | tion machines”, Phys. Rev. Accel. Beams , vol. 19, p. 114401,
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beam transport or recirculation arcs”, Phys. Rev. Accel.
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7b2d4b07-cf2c-4f0e-80f3-f0a918704cf0 | doi:1/zero.alt4.1/zero.alt416/j.nima.2/zero.alt419./zero.alt46./zero.alt461
[8]C.-Y.Tsai,“Analternativeviewofcoherentsynchrotronra-
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7a4ef890-db3d-46ac-82b9-6abaeef58999 | [11]C.-Y. Tsai and W. Qin, “Semi-analytical analysis of high-
brightness microbunched beam dynamics with collective
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[12]G. Perosa and S. Di Mitri, “Matrix model for collective phe-
nome... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP11.pdf | 3 |
856cd82b-9d62-4d1c-bc3d-de8a5dcaebba | SUPPRESSION OF EMITTANCE VARIATION
FOR THE HALF STORAGE RING
Xiaoyu Liu, Zhenghe Bai∗, Penghui Yang, Gangwen Liu, Zhouyu Zhao, Guangyao Feng
National Synchrotron Radiation Laboratory, USTC, Hefei, China
Abstract
The Hefei Advanced Light Facility (HALF) is a
diffraction-limitedstorageringlightsource.TheHALFstor-
agering... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 0 |
db763c93-23d6-4b46-a734-4f4df1515f6c | in 2028, is a diffraction-limited storage ring light source
operatinginthesoftX-rayandVUVspectralrange[1].To
achieve a natural emittance below 100pm·rad , enhanced
nonlineardynamicsperformanceandmorestraightsections,
the HALF storage ring design adopts a modified hybrid
six-bend achromat (H6BA) lattice as its baseline ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 0 |
816ced03-bdf9-403b-a48f-02c7d1ca8423 | x/uni00000003/uni0000003e/uni00000050/uni00000040
/uni00000013 /uni00000018 /uni00000014/uni00000013 /uni00000014/uni00000018 /uni00000015/uni00000013
/uni00000056/uni00000003/uni0000003e/uni00000050/uni00000040
Figure 1: Linear optical functions and magnet layout of the
HALF lattice. In the lower layout, bends are in ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 0 |
e8861a7f-cab5-448e-acce-e947c4e438ca | long straight sections. Table 2 shows the main parameters
of the IDs at HALF.
∗baizhe@ustc.edu.cnTable 1: Main Parameters of the HALF Storage Ring
Parameter Value
Energy 2.2GeV
Circumference 479.86m
Number of cells 20
Natural emittance 85.8pm·rad
Natural energy spread 0.61×10−3
Betatron tunes (H/V) 48.19 / 17.19
Natura... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 0 |
88ea21e5-0df5-41cb-a789-1b91ad22fef2 | LPU 38.5 108 3.36 1
Wiggler 100 42 16.00 2
IntheHALFstoragering,theenergyradiatedinthebend-
ingmagnetsbecomescomparabletotheusuallymuchless
energyradiatedinIDs.Consequently,theindependentad-
justmentofIDgapscontrolledbyuserscangeneratelarge
randomvariationsofemittance[4].Severalmethodshave
been developed to suppress th... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 0 |
0611eda6-1e7c-42d3-83da-995b131b44c6 | ness ofvarious emittancevariation suppressiontechniques
is comparatively analyzed.
EFFECT OF INSERTION DEVICES ON
BEAM EMITTANCE
The natural emittance of the electron beam in a storage
ring can be calculated using synchrotron radiation integrals
when it reaches equilibrium between radiation damping and
quantumexcitatio... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 1 |
663d106c-a3dc-44f8-9403-6570dc69fff5 | 3𝜋𝛽𝑥𝜌3
𝐼𝐷+𝛽𝑥𝜆2
𝐼𝐷𝐿𝐼𝐷
15𝜋3𝜌5
𝐼𝐷.(2)
TosuppresstheemittancevariationinducedbyIDs,damp-
ing wigglers in long dispersion-free straight sections can be
usedtocompensate for theenergyloss variationbasedon
theradiationdampingeffect,whichcansignificantlychange
𝐼2while maintaining 𝐼4and𝐼5almost constant. Wh... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 1 |
e0972566-938e-4020-877a-0ad73e38bbc0 | method can be used for the HALF storage ring based on the
quantum excitation effect. When a short wiggler is installed
inthemiddlestraightsectionoftheHALFstoragering,its
gap variations induce a significant change in 𝐼5and relative
small change in 𝐼2and𝐼4, which collectively compensate
for emittance variations by eff... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 1 |
137ad9fe-d126-4e17-93b1-20912605f844 | forapproximately 90%ofIDoperationcases,andthenat-
uralemittancevariationduringthisoperationrangesfrom
72 pm·rad to 84 pm·rad.
Compensation with Leaked Dispersion in Each
Long Straight Sections
InspiredbytheSPring-8-IImethod,weintroducedcon-
trolled dispersion leakage into each long straight section,
and quantified effe... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 1 |
76e89a16-6804-42e1-a237-1f4b03cf6367 | pensation wigglers to suppress the emittance variation. Suc-
cessfulimplementationrequiressynchronousoperationof
both wigglers. The required magnetic field for each wiggler
ranges from 0.28 T to 1.68 T, which is achievable for the
HALF storagering. The primary advantage ofthis method
isthelowcompensationemittance(71 pm... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 1 |
9a0779eb-9704-4edf-afd2-465ec7c92067 | Figure 3: Compensation with variable-gap wigglers in long
dispersion-free straight sections. The green shaded area de-
notes the fluctuation range of beam emittance and energy
spreadinducedbyrandomvariationsoftheIDgaps,andthe
orange shaded area is the available compensation emittance,
the gray area representing the req... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 2 |
4ca731a5-5fa4-475d-86f7-ddfd9d51352e | the maximum magnetic field is lower than the dispersion-
free section case. When the gaps of 2 damping wigglers
located in dispersion-free straight sections are closed, emit-
tance further reduces to 72 pm·radfor the magnetic field
range of 0.67∼1.45 T, as shown in Fig. 4.
Thismethoddemonstratesmultipleadvantagesoverth... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 2 |
8f91afd3-8cbb-4df5-ba9b-8058416353e7 | straight section is a better choice for HALF.
Figure 4: Compensation with one variable-gap wiggler in
amiddlestraightsectionwhenthegapsof2dampingwig-
glers in dispersion-free straight sections are closed. The
green shaded area denotes the fluctuation range of beam
emittance and energy spread induced by random variation... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 2 |
951db9d4-d32d-4930-a34e-d795bf7db4b7 | straight sectionsand leakeddispersion inlong straight sec-
tions. Comparative analysis demonstrates that employing
a short compensation wiggler in a middle straight section
presentssubstantialadvantagesforemittancestabilization
of the HALF lattice.
ACKNOWLEDGEMENTS
ThisworkwassupportedbytheNationalNaturalScience
Founda... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 2 |
be03f114-2357-460e-9cc6-8aa987d42c07 | inProc. IPAC’23, Venice, Italy, May 2023, pp. 1075–1078.
doi:10.18429/JACoW-IPAC2023-MOPM038
[3]Z. Zhao, Y. Xu, and H. Li, “Preliminary design of insertion
devices at Hefei Advanced Light Facility”, inProc. IPAC’23,
Venice, Italy, May 2023, pp. 1247–1249.
doi:10.18429/JACoW-IPAC2023-MOPM115
[4]F.Sannibale,S.C.Leemann,H... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 3 |
c198c05c-1aec-4fa7-a000-26efadfbaa04 | compensation in future synchrotron light sources”,Nucl. In-
strum. Methods Phys. Res. A, vol. 1052, p. 168278, 2023.
doi:10.1016/j.nima.2023.168278
[7]T.Hiraiwa,K.Soutome,andH.Tanaka,“Suppressionofemit-
tancevariationinextremelylowemittancelightsourcestorage
rings”,Phys. Rev. Accel. Beams, vol. 25, p. 040703, 2022.
doi... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP12.pdf | 3 |
18581acb-9c55-4dd5-aff1-76dcd816c37d | MODELING AND OPTIMIZATION OF TRANSVERSE TRAPPED-MODE
IMPEDANCE FOR IN-VACUUM UNDULATORS OF HALF
Haiyan Yao, Xin Huang, Tianlong He∗, Xiaoyu Liu, Weiwei Li, Zhenghe Bai†
National Synchrotron Radiation Laboratory, USTC, Hefei, China
Abstract
The in-vacuum undulator (IVU) exhibits exceptionally
strong trapped-mode impedan... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 0 |
c9f09ccf-ab66-4fdc-89b6-918856c0c9e8 | sition section optimization. Simulation results demonstrate
thatbothstrategieseffectivelyreducetheimpedance,with
thetransitionsectionoptimizationstrategyshowingsuperior
suppression performance.
INTRODUCTION
Modernstorage-ringlightsourcestypicallyemployIVUs,
whichconsistofmagnetarrayswithverynarrowgaps.These
devices can... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 0 |
91833a99-62d8-4175-b4aa-f2625bbc0911 | BESSY II [3], PETRA-IV [4], CLS [5] and HEPS [6] have
conducted relevant studies on the trapped modes of IVU.
The HALF storage ring incorporates one short and one
long IVU with longitudinal lengths of approximately 1.5
meters and 4.2 meters, respectively. This paper models and
simulatestheshortIVUundertwoconfigurations... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 0 |
fcea7234-3bf8-47e5-94a3-bcee7fc73ffe | Fig. 1.
∗htlong@ustc.edu.cn
†baizhe@ustc.edu.cn
Figure 1: Model without pump ports.
Figure 2: Results of wake potential (left) and impedance
(right).
Table1:CharacteristicParametersofthePrimaryTrapped
Modes for the IVU Model Without Pump Ports
𝑓𝑊|𝑓𝐸[MHz] 𝑅/𝑄𝑊|𝑅/𝑄𝐸[kΩ/m] 𝑄𝑊|𝑄𝐸
107.2 | 106.6 154.8 | 154.0 5... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 0 |
d451f2c1-014a-4d1b-ae88-dcb6e145343d | swarm optimization (PSO) algorithm was used to fit the
wakepotentialandextractthecharacteristicparametersof
the trapped modes. A comparison between the wake po-
tential and impedance directly computed by CST and that
obtained via PSO fitting is shown in Fig. 2. Three promi-
nent impedance peaks are observed, with the s... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 0 |
0eae7f88-2f02-4a31-ae01-ed4e8990ae70 | Figure3:Installationschematics:(a)12ferriteblocksand
(b) 20 ferrite blocks.
existinthe 𝑄-values(computedbytheeigenmodesolverare
slightlyhigherthanthosefromthewakefieldsolver).This
differencescanbeprimarilyattributedtothehighsensitivity
of the𝑄-value in the eigenmode solver to the background
material settings: the act... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 1 |
bf463487-7b63-4b17-a140-2e675705f5c9 | MITIGATION STRATEGIES
Ferrite Damping
Ferrite damping has been studied by facilities such as
AustraliaLight Source[1],SPEAR3 [2],andHEPS [6]for
impedance suppression in strong field regions. Based on
this approach,this studydesigned twoferrite configuration
schemesfortheIVUsofHALF:onewith12ferriteblocks
on 6 pairs of s... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 1 |
7f304d9d-a733-4f27-a433-46bc497d6a5e | plitudedecayssignificantlyandrapidly.Correspondingly,the
impedancepeaksarereducedfromapproximately 75MΩ/m
to 1.6MΩ/m and 0.5MΩ/m, respectively.
Transition Section Optimization
Tofurtherreducetheimpedancefundamentally,thispa-
per proposes a three-stage transition optimization design,
consisting of a first tapered transi... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 1 |
d8e8e303-a553-4111-8435-80ad2753dace | tion. The impedance values for transition optimization is
scaled by a factor of 10.
Figure 6 shows the wake potential and impedance of the
optimized transition section model. This design alters the
trapped-modefrequencies.Althoughnewmodesemerge,the
impedanceofallmodesremainssignificantlylowerthanthat
oftheoriginaldesig... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 1 |
19e9a20b-b7e5-4099-a820-a98c30ad666f | value. This result aligns with the findings in Ref. [6], where
the quality factors remained largely unchanged while the
𝑅/𝑄valuesdecreasedduetotheinterruptionoftheresonant
structure of the field distribution.
MODEL WITH PUMP PORTS
To better approximate realistic conditions, this study con-
siders a detailed structura... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 1 |
6a2486b8-7675-445e-8991-24f111b5f693 | Table2:CharacteristicParametersofthePrimaryTrapped
Modes for the Optimized Transition Section Model
𝑓[MHz] 𝑅𝑠[MΩ/m] 𝑅/𝑄⊥[kΩ/m] 𝑄
139.2 0.6 5.6 105.3
240.9 0.8 5.5 147.8
350.6 0.7 4.1 180.1
459.8 0.6 1.6 380.3
581.9 0.5 1.1 437.5
705.2 0.3 0.8 372.2
Figure 7: Model with pump ports.
Table3:CharacteristicParameterso... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 2 |
2e2994b4-d350-4a72-84ef-f3522d06efc6 | ferriteblocks,andthemodelwithoptimizedtransitionsec-
tions. Compared with the initial model, the ferrite damping
effectivelysuppressestheimpedancepeaksnear 179MHz,
221MHz, and297MHz. However, it provides only limited
suppressionofthetrapped-modepeakat 60MHz.Incontrast,
the transition-section optimization significantly ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 2 |
f789148b-3df7-4904-b6ad-94fcea1186cf | withpumpports.Severaldistincttrapped-modeimpedance
peakswereobservedintheverticaldirectioninbothmodels,
withimpedancevaluessubstantiallyexceedingthethreshold
Figure 8: Results of wake potential (left) and impedance
(right).Theimpedancevaluesfortransitionoptimizationare
scaled by a factor of 10.
determined by synchrotro... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 2 |
c4dae44e-6139-4efc-aa47-43ddfe536a44 | thereby providing a more effective solution for overall IVU
impedance suppression and beam stability assurance.
ACKNOWLEDGEMENTS
This work was supported by National Natural Science
FoundationofChina(No.12375324and12105284),andthe
Fundamental Research Funds for the Central Universities
(No. WK2310000127).
REFERENCES
[1]... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 2 |
f1483ff6-c9b4-4ec5-b4ab-079db8b3f420 | doi:1/zero.alt4.11/zero.alt43/PhysRevAccelBeams.22./zero.alt45/zero.alt47/zero.alt42
[3]P.Volz,S.Grimmer,M.Huck,A.Meseck, etal.,“Goubau-line
set up for bench testing impedance of in-vacuum undulator
components”, in Proc. IPAC’21 , Campinas, Brazil, May 2021,
pp. 3883–3885.
doi:1/zero.alt4.18429/JACoW-IPAC2/zero.alt421-... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 2 |
c72677a7-b755-4825-9b90-6c2921bad82a | [6]N. Wanget al., “Impedance characterization and optimization
oftheHighEnergyPhotonSourcein-vacuumundulator”, Phys.
Rev.Accel.Beams , vol. 28, no. 9, p. 094401, 2025.
doi:1/zero.alt4.11/zero.alt43/PhysRevAccelBeams.28./zero.alt4944/zero.alt41 | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP21.pdf | 2 |
610be3ca-5a8b-469e-9948-0419061c9acc | EXPONENTIAL SUM FITTING OF THE LONG-RANGE TRANSVERSE
RESISTIVE-WALL WAKEFIELD
Xin Huang, Haiyan Yao, Tianlong He∗, Weiwei Li, Xiaoyu Liu, Zhenghe Bai, Hongliang Xu†
National Synchrotron Radiation Laboratory, USTC, Hefei, China
Abstract
In high-intensity storage rings, long-range transverse
resistive-wall (RW) wakefield... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 0 |
4dd83f8d-9c63-4af6-a1d3-98bec433da96 | GPU-based parallel implementation, thereby significantly
enhancingcomputationalefficiency.Thisworkdemonstrates
the dependence of the fitting performance on the number of
exponential functions and the fitting interval.
INTRODUCTION
When a charged beam passes through a vacuum chamber
withfiniteconductivity,itinteractswit... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 0 |
dc2f8abb-f006-44a0-a4ca-a957f905fa05 | turn-by-turn centroid histories, which consumes substantial
memory and leads to low computational efficiency.
To address this issue, a wakefield approximation method
known as resonator fitting can be employed. For instance,
intheMUSIC code,M.Migliorati etal.successfullyfitted
thelongitudinalRWimpedanceoftheCERNProtonSy... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 0 |
b76881bf-0386-402c-859d-3fc5b6997224 | 𝜋𝜎,𝐿is the vacuum cham-
ber length, 𝑏is the chamber radius, 𝑍0is the free space
∗htlong@ustc.edu.cn
†hlxu@ustc.edu.cnimpedance, 𝑐is the speed of light, and 𝜎is the chamber
material conductivity.
The long-range transverse RW wakefield is fitted using a
sum of exponentials and is defined as follows:
1
√𝜏≈ ∑
𝑘𝐴�... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 0 |
75e1cf74-e35b-4828-9e78-e203ac1b9dbf | In the following section, we introduce two algorithms for
calculating the fitting coefficients: one based on the Parti-
cle Swarm Optimization (PSO) and the other, an analytical
algorithm.
PSO-Based Algorithm
Determiningasetofcoefficients [𝐴1,𝛼1,𝐴2,𝛼2,…]satis-
fyingEq. (2)canbetranslatedintoasingle-objective,multi-... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 0 |
752407da-271b-4b5a-88d0-43f4f5c80996 | andParticleSwarmOptimization(PSO)[11,12].Incompar-
isontoGAandSA,PSOoffersdistinctadvantages,including
feweradjustableparameters,conceptualsimplicity,andease
of implementation. Considering both its convergence speed
and capability to locate the global optimum, we prioritize
the use of PSO for the fitting procedure in t... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 0 |
0a2fe803-cddb-4167-83d9-f29787b65f07 | for a maximum of 4000 iterations. Parameter bounds, de-
termined through preliminary scanning, were set to 𝐴𝑘∈
[0,4.72×104]and𝛼𝑘∈ [1×103,5×1010].
Analytical Algorithm
Thisalgorithm,proposedbyW.McLean[13],enablesthe
direct computation of weights and decay factors for given
intervals and exponents, offering high comp... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 1 |
7430670a-ee6e-4a43-aca6-610e3cbd43e4 | where𝑀and𝑁are natural numbers satisfying 𝑁 +𝑀 +1
equal to the number of functions, 𝛿𝑥is the step size used
inthediscretizedintegral.Thecorrespondingweightsand
decay factors are given by:
𝐴𝑘=𝛿𝑥
𝑏𝛽Γ(𝛽)𝑒𝛽(𝑘𝛿𝑥−𝑒−𝑘𝛿𝑥)(1+𝑒−𝑘𝛿𝑥),(8)
and
𝛼𝑘=1
𝑏𝑒𝑘𝛿𝑥−𝑒−𝑘𝛿𝑥, (9)
whereΓ(𝑧)is gamma function. Ow... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 1 |
265ead0b-e45a-4be9-a794-0652d7a9e6c8 | considered. This is justified because the wakefieldstrength
decays over time; beyond a certain number of turns, it be-
comes negligible. Neglectingthese distantwakefields does
not compromise the accuracy of the results but significantly
improves computational efficiency. The fitting performance
can be evaluated using t... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 1 |
adebf65f-d589-48da-bae0-ed75587f02d7 | toarevolutionperiodof 1.6µs.Thefittingwasperformed
overtheinterval [1/800,50] usingasetof9fittingfunctions.
As shown in Fig. 1(a), the relative error within the fitting
(a)
(b)
Figure 1: Comparison of PSO-based and analytical fitting
using a ten-exponential model: (a) results for 1/800 to 50
turns; (b) results extended... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 1 |
e9654411-3360-4e78-9922-2e5f055c5e12 | Figure 2 compares the fitting performance of the PSO-
basedandanalyticalalgorithmsacrossdifferentnumberof
functionandfittingintervals,usingtheweightederrormetric
𝑒𝑊.Asthenumberoffunctionsincreasesandthefittinginter-
(a)
(b)
Figure 2: Fitting performance of the (a) PSO-based and
(b) analytical algorithms with varying ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 2 |
0f50548d-804f-4ada-b083-28b32083cf10 | tors, the number of functions has a far greater impact on the
fittingqualitythanthefittinginterval.ThePSOalgorithm
outperformstheanalyticalmethodwithasmallnumberof
basis functions, while the analytical algorithm becomes su-
perior when more than nine are used. In summary, when
thenumberoffittingfunctionsissetto9,bothal... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 2 |
ff6d62b5-65a8-4dc0-a071-239fdcc6a69d | finite wall thickness, which renders the analytical method
invalid.Undertheseconditions,thePSOalgorithmserves
as a robust alternative. It should be noted, however, that the
convergenceof PSO becomes progressivelymore challeng-
ing as the number of basis functions increases, owing to the
linear growth in the number of d... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 2 |
ad3f7353-d764-4aa8-8e01-d572fe5ddad5 | 4 3.76×1021.56×1052.49×1034.94×106
5 8.36×1028.17×1055.96×1033.33×107
6 1.88×1034.19×1061.31×1031.90×108
7 4.24×1032.13×1072.90×1041.01×109
8 9.57×1031.09×1084.71×1044.84×109
9 2.16×1045.53×1083.43×1041.12×1010
SUMMARY AND OUTLOOK
This study presents a method for approximating the long-
range transverse RW wakefield by... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 2 |
0500cca0-7863-4295-aa73-135f3a42d542 | This work was supported by National Natural Science
FoundationofChina(No.12375324and12105284),andthe
Fundamental Research Funds for the Central Universities
(No. WK2310000127).
REFERENCES
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V.Vaccaro,“Resistivewallimpedanceinellipticalmultilayer
vacuum chambers”... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 2 |
aa2032a0-373b-49ca-8bcb-0db64f3c3803 | [2]N. Mounet, “The LHC transverse coupled-bunch instabil-
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f7230528-5898-452f-8444-d49e0a68cf5f | p. 031001, 2015.
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ulation for longitudinal beam dynamics of arbitrary bu... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 3 |
7a6063a5-d3ea-439f-a5a2-501dfbce7d37 | [10]S.Jajodia,I.Minis,G.Harhalakis,andJ. -M.Proth,“CLASS:
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[11]F. Marini and B. Walczak, “Particle swarm optimi... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 3 |
43be8754-998e-4225-9568-db0807304359 | the 80th birthday of Ian Sloan . Cham, Switzerland: Springer,
2018, pp. 911–930.
doi:1/zero.alt4.1/zero.alt4/zero.alt47/978-3-319-72456-/zero.alt4_4/zero.alt4
[14]W. Foosang, A. Gamelin, M. Tordeux, and P. Alexandre,
“Resistive-wall instability evaluation along the ramp in the
SOLEIL II booster”, J. Phys.: Conf. Ser. ,... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP22.pdf | 3 |
d8ff34c2-d331-4ceb-9c07-c2e6fa773e10 | STUDY OF BUNCH LENGTHENING WITH
HARMONIC CAVITIES FOR HLS-III
Wenshu Liang, Tianlong He∗, Weiwei Li, Xiaoyu Liu, Zhenghe Bai†, Qing Luo‡
National Synchrotron Radiation Laboratory, USTC, Hefei, China
Abstract
NSRL recently proposed a future plan to further upgrade
the HLS to an EUV diffraction-limited storage ring, name... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP24.pdf | 0 |
ac8b90b3-995f-4b36-a4ac-f61c65438c6c | the selection of RF frequencies and the design of harmonic
cavity parameters for HLS-III.
INTRODUCTION
The HLS-III upgrade proposal of HLS-II aims to achieve
loweremittanceandhigherbeambrightness.Keydesignpa-
rameters of HLS-III are summarized in Table 1, including a
beamenergyof 800MeV,acircumferenceofapproximately
66... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP24.pdf | 0 |
a43c16bf-ee3e-458c-bfe4-b46c8bf595b1 | Number of cells 4
Natural emittance 2.82nm ⋅rad
Momentum compaction factor 6.74×10−3
Natural energy spread 4.99×10−4
Natural damping times (x/y/z) 16.3 / 23.6 / 15.1ms
Energy loss per turn 20keV
Thispaperpresentsatheoreticalanalysisofbunchlength-
ening with harmonic cavities in HLS-III. By solving the
Haïssinskiequatio... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP24.pdf | 0 |
46d5b7dd-586b-44a0-a5a9-c7d867506993 | risk of coupled-bunch instabilities; the 500MHz option rep-
resents a mature, commercially available technology with
well-dampedHOMs,aligningwithcurrentstate-of-the-art
practices.
THEORY AND METHOD
For the double-RF system, the total cavity voltage can be
expressed as:
𝑉𝑇(𝜏) = 𝑉1sin(𝜔𝑟𝑓𝜏+𝜑1)+𝑘𝑉1sin(𝑛𝜔𝑟𝑓�... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP24.pdf | 0 |
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