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14e2fa76-ab0b-4fc2-ad70-7786b8b542b3 | are presented in Fig. 10. It is seen that when applied to
minimize𝑓3,rms+𝑤·𝑓4,rms,boththeSCCmethodandthe
DE algorithm achieve comparable final results and the SCC
method still converges faster.
CONCLUSION AND OUTLOOK
This study combines the SCC method with minimization
of RDT fluctuations for DA optimization. In con... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP04.pdf | 2 |
7b3786f0-c342-484d-982a-8d06802d2bf4 | REFERENCES
[1]B.Wei et al.,“Minimizingthefluctuationofresonancedriving
terms in dynamic aperture optimization”, Phys. Rev. Accel.
Beams, vol. 26, p. 084001, Aug. 2023.
doi:10.1103/PhysRevAccelBeams.26.084001
[2]B.Wei,Z.Bai,G,Feng,“Analysisofoff-momentumnonlinear
drivingtermsforenlargingoff-momentumdynamicapertures”,
Ph... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP04.pdf | 3 |
a16ea46b-abf4-4329-8aa8-4708effe61cc | GPU- ACCELERATED SIMULATION OF LONGITUDINAL
SINGLE-BUNCH INSTABILITY IN ELECTRON STOR AGE RINGS
Tianlong He∗, Weiwei Li, Weimin Li, Zhenghe Bai
National Synchrotron Radiation Laboratory, USTC, Hefei, China
Abstract
Longitudinal single-bunch instability driven by high-
frequency impedance is a major challenge for achi... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 0 |
5ec72bfd-8c75-45be-8f64-87d2b86d5349 | onadesktopcomputerequippedwithahigh-performance
GPU,providing anaccessible andcost-effectivealternative
to computingclusters.
INTRODUCTION
Forstorage-ringlightsourcesandelectron-positroncol-
liders,thelongitudinalhigh-frequencydominantimpedance,
e.g.,coherentsynchrotronradiation(CSR)impedanceand
NEG-coatingresistivewal... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 0 |
5a9ee734-f0f2-4c4d-bbf6-14185eb2218e | onthemacro-particletracking,suchasELEGANT[3],its
parallel version PELEGANT [4], MBTRACK [5], and its
Python version MBTRACK2 [6]. This paper focuses on
the tracking method. To improve the accuracy of tracking
simulation, it is commonly necessary to have a sufficient
number of particles and slices to accurately count th... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 0 |
523b501a-5c52-4ecf-a087-94675dc52cc3 | STABLE CODE
TheSTABLEcode[7]isdevelopedspecificallyformulti-
bunch, multi-particle tracking simualtion for longitudinal
beam dynamics. It is implemented in a MATLAB envi-
ronmentwiththeuseofstate-of-the-artGPUacceleration
techniques, which significantly improve the tracking effi-
ciency.
From Multi-Bunch to Single Bunc... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 0 |
e9c632cd-b04d-4c05-8853-9168202f7544 | them to obtain the total bunch distribution. In addition, a
fixed bin width is set by default instead of the number of
bins. Therefore,thebinnumberwillincreaseasthebunch
lengthens. Theremainingoperations,suchasconvolution
ofthebunchdistributionandtheshort-rangewake(orshort-
bunch wake potential), and interpolation to o... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 0 |
a2729934-2650-4d82-a826-a3d88c45bb1a | rms values of bunch length and energy spread used for nor-
malization, which do not necessarily have to be equal to the
naturalrmsvaluesdeterminedbytheequilibriumbetween
radiationdampingandquantumexcitation. Thequantity 𝑞
is updatedsimply withthe followingequation:
𝑞𝑖+1=𝑞𝑖+𝛼𝑐𝑇0𝜎𝛿0
𝜎𝜏0𝑝𝑖, (1)
where 𝛼𝑐is ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 0 |
4b20c439-f2b7-46af-99b4-75b5ec361ef8 | where
𝑝𝑅𝐹=Σ𝑗𝑉𝑗sin(𝜔𝑗𝜎𝜏0𝑞+𝜙𝑗)
𝑝𝑟𝑎𝑑.+𝑞𝑢𝑎𝑛.=−2𝑇0
𝜏𝑧𝑝𝑖+2√︄
𝑇0
𝜏𝑧𝑅, (3)
𝑉𝑗,𝜙𝑗,and 𝜔𝑗refertotheRFvoltageamplitude,phase,and
angular frequency, respectively. 𝜏𝑧is the radiation damping
time. 𝑅isarandomnumberfromthestandardnormaldistri-
bution. Please note that, except for the calculation... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 1 |
8a589089-c007-4729-acfa-db52777c941d | be sped up using the fast Fourier transform. In the case of a
bunchbeingverylongcomparedtothewakefieldvariations,
we utilize the techniques of Gaussian filtering and finer-bin
interpolation to improve the convolution convergence and
accuracy. Compared to these two steps, the first step is
usuallythemosttime-consumingan... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 1 |
cb16995b-12d6-47a8-b99e-53b7c01dda1b | blockusestwothreadstocountthesub-distributionforeach-
columnparticles. Finally,thesumofthesub-distributions
is exactly the total distribution.
Figure1showstheefficiencytestresultsforthebuilt-in
function “histcounts” and the self-made kernel “BinNum-
CalZ”. This test was conducted on a desktop computer
equippedwitha“13t... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 1 |
99895dd4-beb3-44bf-8f53-76739a63ea5e | efficiency by a factor of ∼8 and∼40, respectively.
Overall Tracking Performance
For 10 million particles and more than 4800 bins, it takes
about 5 millisecond to track one turn when using the above-
Figure 1: Efficiency test for binning of particle distribution.
mentioned desktop computer configuration. A tracking sim-... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 1 |
bba7e83a-4f63-40c5-9ae1-823d95f8d9b5 | isunderconstructioninHefei,China,andthestorageringis
scheduledtostartcommissioninginspring2027. Figure2
showsthelatestlongitudinalRWwakepotential (consider-
ing a NEG-coating thickness of 1 μm and a resistivity of
1×10−5Ω·m) according to the current vacuum layout.
Figure 2: Longitudinal RW wake potential of 0.02 mm rms... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 1 |
88c82eee-4e95-4aac-98c4-a6020e1432bd | threshold increases to ∼0.75 mA, demonstrating an approx-
imatelylinearproportionalitybetweentheMWIthreshold
and bunch length.
Figure 4 shows the bunch phase-space distribution
at0.5mAwhen MWI occurs, revealing distinct micro-
bunching structures whose dimensions match the oscilla-
tion period length of the wake potent... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 2 |
71c23057-1755-4c4a-9e40-8c9f83f5a1e5 | The Super Tau-Charm Facility Storage Ring
The STCF is being designed as a symmetric electron-
positron collider in Hefei, China, with a centre-of-mass
energy ranging from 2 to 7 GeV. For a minimum energy
of 1 GeV and a nominal beam current of 1.1 A (1.6 mA
per bunch at 48%filling rate), the STCF storage ring is
likely ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 2 |
c201dc61-e97a-4e00-9671-89e7db9f8943 | These simulations informed the optimization of the wiggler
schemetomitigateCSReffects. Notably,thefulltracking
process—simulating 10 million macroparticles over 40,000
turns—wascompletedin ∼1houracross27bunchcurrent
points, demonstrating high computational efficiency.
Figure6: Bunchenergyspread(blue)andrmslength(red)
a... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 2 |
5ce90d2d-6d1e-46ed-b014-1af6c558e699 | afk/STABLE-SingleBunch .
ACKNOWLEDGEMENTS
This work was supported by National Natural Science
Foundation of China (No. 12375324 and 12105284), and
theFundamentalResearchFundsfortheCentralUniversities
(No. WK2310000127). | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 2 |
6fdb29d0-667d-4ccd-ad90-7ad0e1d8c902 | REFERENCES
[1]R.WarnockandJ.A. Ellison,“Ageneral methodforpropa-
gationofthephasespacedistribution,withapplicationtothe
sawtooth instability”, in Proceedings of 2nd ICFA Advanced
Accelerator Workshop on the Physics of High Brightness
Beams, UCLA, 1999.
[2]P. Schönfeldt, M. Brosi, M. Schwarz, J. L. Steinmann, and
A.-S.M... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 3 |
856ac8ad-258a-4cb5-baa6-cd0aa51b6c55 | [5]G. Skripka, R. Nagaoka, M. Klein, F. Cullinan, and P. F.
Tavares, “Simultaneous computation of intrabunch and in-
terbunch collective beam motions in storage rings”, Nucl.
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[6]A. Gamelin, W. Foosang, and R. Nagaoka, “mbtrack2, a Col-
... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 3 |
b1d1d648-6d4d-4d01-9b87-d780f27a5a35 | Venice, Italy, May 2023, pp. 1075–1078.
doi:10.18429/JACoW-IPAC2023-MOPM038
[9]W. Li, T. He, and Z. Bai, “Terahertz scale microbunching
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coating resistive-wall impedance”, Phys. Rev. Accel. Beams ,
vol. 27, p. 034401, 2024.
doi:10.1103/PhysRevAccelBeams.27.0344... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP05.pdf | 3 |
501cd02e-8e96-4453-9fd0-8b6c73da7634 | PRELIMINARY SCHEME FOR ELECTRON COOLING USING
LONGITUDINAL HOLLOW ELECTR ON BEAM *
X. D. Yang†, He Zhao, Institute of Modern Physics, CAS, Lanzhou, China
Abstract
The intra -beam scattering in high charge state intense
heavy ion beams is a problem worth considering. By con-
trolling the longitudinal distributio... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
96271fe2-3ea6-4c15-bf41-b8177d953b51 | cooling at the center of the ion beam. This paper discusses
the generation, measurement, and related issues of longitu-dinal hollow e lectron beams. Corresponding solutions and
suggestions have been proposed for the problems and chal-lenges that may be encountered in the research. The cool-
ing process of longitudina... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
98ea598f-8e57-4398-a265-ae653f571d34 | ion beam with high charge state. The intra -beam scattering
presents dissimilar influence in the different facilities. It
can be counteracted partially by the synchrotron radiation
damping in the lepton machine. It also can be suppressed by the wiggler. But there is no similar dampin g in the had-
ron machine.
The... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
570c5033-03c4-491d-aa7c-3ea13da35fd3 | taining the optimal performance of the accelerator. In this case, intra- beam scattering becomes the primary cause of
emittance growth in the six -dimensional phase space. Par-
ticles with large amplitudes will escape the bucket and be lost in the ring. As a result, the lifetime of the ion beam in
the storage ring d... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
fac20184-1374-4bb3-874a-9fd8fe3940c9 | high- density beams in heavy ion storage rings, more effec-
tive methods to suppress intra -beam scattering should be
explored and attempted.
Under electron cooling, the distribution of ion beams
quickly deviates from the initial Gaussian type, forming a denser core and a longer tail. The ions standing in the tail... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
a01cda4b-8f95-4ba9-935d-960fc8e98f3a | beam.
The traditional DC electron beam in the electron cooler
was modulated into an electron bunch with different longi-tudinal distributions. The stronger cooling was expected in
the tail of the ion beam and the weaker cooling was per-
formed in the tail of the io n beam. The particle on the out-
side will experie... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
6ca566f2-ca72-49b3-8732-a6a2f5e80a69 | ation of future storage and hig h-energy electron coolers.
MOTIV ATION
From the previous experimental results [2] indicated that
the partially transverse hollow electron beam has an ad-
vantage in beam accumulation. The optimal ratio
Ugrid/Uanode is near 0.2 in the electron gun of electron
cooling device. In thi... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 0 |
543f88d3-74c3-4909-b6b1-bcd33d981854 | • Make the beam bunch contain as many particles as
possible.
• Increase the lifetime of ion beams in the storage ring.
GENERATION SCHEME OF
LONGITUDINAL HOLLOW
ELECTRON BEAM
The high voltage pulse required for the generation of the
longitudinal hollow electron beam can be generated by
three schemes.
The... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
4ade3b3d-f933-42d5-ac86-a1f216644321 | nology . From the output of high- voltage power supplies
with sinusoidal wave, chopper technology will cut only the
required phase range from the output of high voltage. A
voltage output similar to a cosine wave is generat ed. The
voltage varies continuously, resulting in a longitudinal hol-
low electron beam .
Th... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
1ceb7596-0912-4872-ba4f-8e4f5bbd1173 | MEASUREMENT OF LONGITUDINAL
HOLLOW ELECTRON
BEAM PARAMETERS
The waveform of the output voltage of the power supply
will be measured offline by the oscilloscope and high -volt-
age dividers in the test platform. From the results, the pa-rameters such as repetition rate, rising edge, plateau, de-
scending edge, and... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
04149150-c548-43e1-a15f-f96be75b4930 | SYNCHRONIZATION OF ELECTRON
BEAM AND ION BEAM
The basic requirement for electron cooling is that the
electron beam can overlap the ion beam, and in the longi-
tudinal direction, the length of the electron beam bunch should be greater than that of the ion beam bunch. The length of the ion beam bunch will gradually d... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
55e5700f-9444-4fc7-ae05-aef5235e8243 | injection and extraction in the storage ring.
The electron cooling device is equipped with beam po-
sition detectors BPM at both ends, which can measure both
the positions of the electron beam and the ion beam in the
cooling section of the electron cooling device. The BPM at
the entrance can be used to measure the... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
6b79a2fd-4854-4fcf-849e-656629885a47 | from the triggering of the high voltage power supply to the
generation of the control electrode voltage waveform and
the generation of the electron beam pulse waveform should
be measured in advance. In addition, there is a certain dis-tance from the cathode surface of the electron gun to the
entrance of the electro... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
04ff59c7-2ad1-4806-8c5a-306f1231b1af | Through repetitious measurements, the measurement re-
sults are calibrated and mutually verified to determine the time for the ion and electron beam bunches to reach and
leave the electron cooling section, as well as the trigger de-lay time and response time of the high -voltage pulse power
supply. These two paramete... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
a6577cf8-6e35-473a-ae92-c0328c3c11e7 | Beam position detectors are installed at both ends of the
cooling section of the electron cooling device, which can measure the position of both the electron beam bunch and
the ion beam bunch. The positions and angles of the elec- | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 1 |
53b794a8-de90-4ecd-97a1-7fc92dfe1287 | tron beam and ion beam in the cooling section were meas-
ured separately. With the help of correct coils in the elec-
tron cooling device and dipoles in the storage ring, the po-
sitions and angles of the electron beam and ion beam in the cooling section were ad justed respectively. After repeated
measurement and adju... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
ccca8363-c78d-4e24-b621-07dbb45a9808 | In order to reduce the repetition frequency of high- volt-
age output , a half, one fourth, or one eighth of revolution
frequency will be used as output frequency of high -voltage
pulses . The ion beam bunch meets the electron beam bunch
every two, four, or eight revolutions .
By using multiple high- voltage p... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
917a64e9-0465-4194-bde9-d1dc0ae9a7cd | can obtain electron beam bunches of different lengths by
chopping in different phase intervals. However, due to the
same frequency sine wave, the voltage values at different
phases are different, and the maximum output voltage after
chopping is different, resulting in different values of the
electron beam current ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
f6a52a2d-b0e0-4613-886a-3f062c099692 | original, and the beam length becomes shorter.
The above -mentioned frequency conversion method can
generate electron beam bunch of different lengths. As the
ion beam is cooled, the length of the ion beam bunch grad-ually becomes shorter, and the ions at the edge of the ion
beam gradually leave the edge region wit... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
a2d070d2-8fac-476b-9bd0-73c12fc03979 | lengths are switched sequentially.
SIMULATION CALCULATION OF
COOLING PROCESS
A numerical simulation code TRACKIT [4] based on
multi- particle tracking was developed to calculate the
bunched ion beam cooling process, in which the electron
cooling, intra -beam scattering (IBS), ion beam space -
charge field, tr... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
01c81caa-d3d1-4069-b53f-40aacd705099 | dinal uniform distribut ion electron beams .
EXPERIMENTAL STUDY ON
COOLING PROCESS
As mentioned above, the electron gun in the electron
cooling device can provide three kinds of electron beam s.
• Traditional DC electron beam .
• Longitudinal uniform distribut ion electron beam .
• Longitudinal hollow electron... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
e5b88107-3400-4dc8-a89c-6a16e5c134d3 | the ion beam, the lifetime of the ion beam, the length of the ion beam bunch, and the upper limit of the number of ions
were obtained . These results will be compared with the
case of DC electron beam cooling process. The difference
of longitudinal hollow electron beam c ompari ng with the
cooling of longitudina... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
cc435612-5ae5-4776-9116-acdfb206380f | rapid cooling at the center of the ion beam. This method
will become a new attempt, and it is expected to achieve
the expected results in subsequent simulation c alculations
and experimental research. Especially, in high -energy elec-
tron cooling, the electron beam bunch will be generated by | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 2 |
73c3f68c-72e7-4d5f-beeb-aca8eb4927da | the photocathode, and microwave electron gun and accel-
erated by the RF cavity.
REFERENCES
[1] A.V. Fedotov, I. Ben -Zvi, Yu. Eidelman, et al . “IBS for ion
distribution under electron cooling”, in Proc . PAC ’05,
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[2] X.D. Yang, V.V. Parkhomchuk , W.... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 3 |
fb17c94e-5a36-4914-b14c-9389ca5bfbf5 | [5] He Zhao, Lijun Mao, Jiancheng Yang, et al. ,“Electron cool-
ing of a bunched ion beam in a storage ring”, Phys. Rev.
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[6] He Zhao and Lijun Mao, “Longitudinal stacking of ion beams with pulsed electron beam cooling”, Phys. ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP06.pdf | 3 |
52820b0a-3bad-468d-b94c-d56dee7965b2 | beam”, in Proc . IPAC2018 , Vancouver, BC, Canada, Apr. –
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[9] M. W. Bruker, S. Benson, A. Hutton, et al. , “Demonstration
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f642b3e3-0a0c-4087-84ab-b9a11af2ce0a | ing”, Phys. Rev. Accel. Beams , vol. 23, p. 021003,
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934e2806-1fd9-4f7d-86bf-30a59be45222 | LONGITUDINAL COLLECTIVE DYNAMICS IN LASER MODULATORS
OF A STEADY-STATE MICROBUNCHING STORAGE RING BASED ON
THE MACROPARTICLE MODEL
Cheng-Ying Tsai∗, School of Electrical and Electronic Engineering,
Huazhong University of Science and Technology, Wuhan, China
Abstract
The mechanism of the steady-state microbunching
(SSMB... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 0 |
4b2f8fb7-6010-4f13-9c8c-bdba402cd03f | dispersionequationis derived,and a detuning parameter is
introduced to characterize the frequency deviation between
theexternal laserand the resonant undulator radiation, and
solve for the instability growth rates of different multibunch
modes. When the detuning approaches a specific multi-
bunchmodedividedbythenumbero... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 0 |
8da0515b-e91e-4a5b-b3e2-a9eb3787ff46 | is replacement of the RF cavity by a laser modulator for
longitudinal focusing/modulation. The laser modulator can
be implemented by a co-propagating laser along a common
axis with the electron beam in an undulator. To reuse the
laserbeamandaccumulatesufficientintensitywhilerelax-
inglaserrequirements,wecanconfinethela... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 0 |
3a005bb9-ab4f-4fe1-bdbb-96b18c59c565 | progressoflongitudinalcollectiveinstabilitystudiesinlaser
modulatorsofanSSMBstorageringusingthemacroparticle
model. An alternative approach using the beam matrix can
be found in Ref. [ 17–19].
∗Email: jcytsai@hust.edu.cn. This work is supported by the Fundamental
Research Funds for the Central Universities (HUST) under... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 0 |
73d9741b-63e8-4d16-93ff-60863aeead9f | SINGLE-PASS MULTI-BUNCH CASE [ 13]
When a microbunch train traverses the modulator undula-
tor, every individual microbunches emit undulator radiation.
Oneachundulatorperiod, thewigglingmotionofelectron
microbunches make the radiation wake advance over one
resonantwavelength 𝜆𝑟,affectingtheleadingmicrobunches.
Denoti... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 0 |
5d1ae835-bdd3-452d-8788-1302fe4549ca | besolvednumerically. Whenthewakefunctionislinearized,
theset ofequationscanhaveanalyticalsolutions. Herewe
skipthedetailedderivationsandreferinterestedreadersto
Ref.[13]. Herewenotethat,besidestheexternalmodulation
laser,theradiationwakemayprovideadditionallongitudinal
focusing to stabilize the electron beam, i.e., eff... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 1 |
65237deb-4296-4519-bf36-a9ad130cbf73 | circulating microbunches come back to the laser modulator.
theysee the radiation wakeaccumulated on previous turns.
Forthesinglemicrobunchcirculatinginthestoragering,on
the𝑚-th turn, from 𝑛-th to(𝑛+1)-th undulator period, the
macroparticle equation of motion can be formulated as
𝑧(𝑛+1)
𝑚= 𝑧(𝑛)
𝑚−𝜂𝑤𝜆𝑤𝛿(𝑛+... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 1 |
bf9e2516-32f8-4f22-8071-ed20eeaec0ed | from conventional Robinson instability. This is because
the radiation wake in the laser cavity can slip, while the
conventional wake in RF cavity is localized. Such a type of
instability appears similar to the free-electron laser (FEL)
instability. Formore detailed discussions, see Ref.[ 15].
MULTI-BUNCH MULTI-TURN CAS... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 1 |
cf4afda1-33bd-4953-b484-041f34965da4 | Figure 2: Illustration of the relative positions of the mi-
crobunches to the phase space buckets and the undulator
radiation wakes for the case of 𝑁𝑤= 6.
For the case of uniform filling, there will be a total of
𝑁𝑏= 𝐶0/Δ𝐿 = 𝐶0/𝜆𝐿microbunches circulating in the
storage ring with the circumference 𝐶0. We remin... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 1 |
cefe5fea-5117-4d9f-8055-245923e6edec | practicalviewpoint. Thestabilitycanthenbedeterminedby
finding the corresponding dispersion or secular equation of
the following tracking equations for the 𝑛-th microbunch at
the𝑝-th period in the modulator undulator on the 𝑚-th turn
𝑧(𝑝+1)
𝑚,𝑛= 𝑧(𝑝)
𝑚,𝑛−𝜂𝑤𝜆𝑤𝛿(𝑝+1)
𝑚,𝑛
𝛿(𝑝+1)
𝑚,𝑛= 𝛿(𝑝)
𝑚,𝑛+𝑘2... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 1 |
679909ca-7eda-4988-bed0-b72a282ec89c | we define the undulator-averaged phase space coordinates
̄ 𝑧𝑚,𝑛=1
𝑁𝑤𝑁𝑤−1
∑
𝑝=0𝑧(𝑝)
𝑚,𝑛,̄𝛿𝑚,𝑛=1
𝑁𝑤𝑁𝑤−1
∑
𝑝=0𝛿(𝑝)
𝑚,𝑛(6)
afterlinearizingtheabovetrackingequationsforthewake
function, the two sets of equations can be simplified to
̄ 𝑧𝑚+1,𝑛= ̄ 𝑧𝑚,𝑛− ̄ 𝜂𝐶0̄𝛿𝑚,𝑛
̄𝛿𝑚+1,𝑛=𝑘2
𝑠0𝐿𝑤
𝜂𝑤̄... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 2 |
8789d24c-64f2-4625-adcb-468dbe08f182 | tweentheexternallaserandtheresonantundulatorradiation.
The cubic dispersion equation can now be solved numeri-
cally forz. For general dynamical systems exhibiting expo-
nentialgrowthordecaywithtime,weassume z∝ 𝑒−𝑖Ω𝑇0,
and the corresponding growth rate per turn can be evalu-
ated by taking the logarithm, i.e., 𝜏−1=... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 2 |
8e9d94a1-d3ec-4871-800d-d71579208505 | ing,thetotalnumberofmicrobunchesisapproximately 108,
whichindeed increasesbyalmostfiveordersofmagnitude
comparedtoconventionalstoragerings,makingturn-by-turn
tracking of individual microbunches nearly impossible. Fig-
ure3presentsthemulti-bunchgrowthrateperturnasafunc-
tion of the detune parameter 𝜈(left) and the mult... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 2 |
cd1446b3-f635-471a-8843-532f306c61d1 | rates,whilethegrowthratesofmostothermodesnotshown
in the figure approach zero. In the right panel we set the
initialdetuneto +1.064×10−4. Asanticipated,theexcited
mode is𝜇 = 104.
Figure3: Growthrateperturnasafunctionofthefrequency
detune𝜈(left) and the multi-bunch mode index 𝜇(right).
According to the current prelim... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 2 |
03fabc4b-8a01-4e72-bd11-3d4f6406a1c8 | undulatorradiationmayenhancesynchrotronoscillations,
as discussed in Ref. [ 13]. Therefore, the growth rates in-
ferred based on the present calculation may still fall within
an acceptable range. It is also worth noting that this infer-
ence seems consistent with the conclusions reached when
applying an alternative app... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 2 |
f0ad2e41-5c70-494f-bb5a-f9f833a2136e | bythe number of total microbunches,this instabilitymech-
anism tends to amplify that mode. We discuss possible
mitigationeffect of the potential wellon the instabilityand
find that based on the nominal SSMB beam and undula-
torparameters,theundulatorradiationdrivenmulti-bunch
instability remains within an acceptable ra... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 2 |
9f8c9860-f6b0-46f4-8881-9130d32d36be | REFERENCES
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b2ed9ede-bffe-45d8-8d0d-9275ccd321a7 | storageringsbasedonthetransverse-longitudinalcoupling
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radiation interact... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 3 |
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collective dynamics in the laser modulators of a steady-state
microbunchingstoragering: Amacroparticlemodel”, Nucl.
Instrum. Methods Phys. Res... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP07.pdf | 3 |
b17b6c18-ef0d-4022-b05f-e2d574b77fdc | COHERENT kW THz RADIATION FROM AN SSMB STORAGE RING VIA
SELF-SUSTAINED LASER MODULATION∗
Cheng-Ying Tsai†, School of Electrical and Electronic Engineering,
Huazhong University of Science and Technology, Wuhan, China
Abstract
Due to the unique role of terahertz (THz) radiation in
the electromagnetic spectrum, it possess... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 0 |
3e234586-02c2-458c-ada2-a776162d6c0c | laser modulator, as well as radiation damping and quantum
excitation effects in the storage ring. Numerical tracking
resultsdemonstratethe feasibilityof thismechanism.In a
demonstrativecase,weshowthat 1kWcontinuouscoherent
radiationcanbeachievedat 5THzfrequency,correspond-
ingtoelectricfieldstrengthsontheorderofMV/m.Si... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 0 |
fecf664a-bf64-4906-b277-3dd5f5aee9e3 | tunable terahertz radiation, leading to the so-called “THz
gap” [1]. Currently,numerous methods exist forgenerating
THz radiation. In this paper we propose a novel mechanism
capable of generating continuous, high-average-power co-
herentTHzradiation.AsillustratedinFig.1,basedonthe
steady-statemicrobunching(SSMB) mechan... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 0 |
b6133918-5ae4-4079-8629-194450e0e6e8 | themicrobuncheswithfrequency-beatingcomponentwill
emitcoherentradiationatthebeatingfrequencyinthedown-
stream radiator. This innovative storage ring differs from
∗ThisworkissupportedbytheFundamentalResearchFundsfortheCentral
Universities (HUST) under Project No. 2021GCRC006 and National
NaturalScience Foundationof Chin... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 0 |
de7e7bdc-cbf5-4477-9f2b-7ab86946e566 | typicallyrequiredtocompensateforcavitylosses.Thisnovel
schemesignificantlyreducesthedependenceontheexternal
modulation laser bydirectlyutilizing the resonant undulator
radiation generated by the traversing electron beam in the
LM. The proposed schemerequiresthe external laser mod-
ulation only very briefly during the i... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 0 |
fdc39b58-f44e-4399-bf89-b67f42c97411 | THEORETICAL MODEL
Herewesummarizethebasicingredientsofthetheoretical
model. Due to page limit, we refer the interested readers to
Refs. [4–7] for more details.
•The transfer matrix of a laser modulator (LM) is de-
scribed as a thick longitudinal quadrupole, in which
the modulation or chirp strength ℎ = 𝑘𝐿Δℰ
𝛾𝑚𝑐2is... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 0 |
b50c12ba-e660-47a0-9e50-489a8d9fc1a2 | •In the LM cavity, the evolution of modulation power
can be described by 𝑃𝐿,𝑛+1= 𝑅⋅𝑃𝐿,𝑛, where𝑅 < 1is
total mirror reflectivity.
•Thelongitudinaltransportfortheremaininghalfastor-
ageringR1/2isexpressedasthefamiliar 2×2transfer
matrix.Theturn-by-turntrackingforthebeamsigma
matrixΣ𝑛followsΣ𝑛+1= 𝒪𝑛Σ𝑛𝒪𝑇
𝑛w... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 1 |
e15ab2a4-c10e-4d76-b4b2-abb982e6cca0 | and𝐾𝑢,mod, where𝐾𝑢≈ 0.934𝐵0[T]𝜆𝑢[cm]. The choice is
not unique; as shown in Fig. 2(a), we select those marked
by red arrows. The total length of modulator undulators
should not be excessively long to prevent the occurrence
of FEL gain process [9]. The parameters for the radiator
undulatorcanbedeterminedthroughth... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 1 |
1570bc0d-ce94-444d-b20e-79d6723d6dd1 | ThelaserpowerstoredintheLMisusedtoprovidesuf-
ficient energy modulation to stabilize the electron beam
through successive turns in the storage ring. During the first
passage,amodulation laser power ≈500kWisrequiredto
providetheinitialequilibriumenergymodulationstrength
ℎ ≈958m−1; however, once the microbunch is formed,... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 1 |
e36b03f0-5fe9-46cd-990f-1f129e0ac134 | ation
Name Value Unit
Beam energy 𝛾𝑚𝑐2600 MeV
Average bunch current 𝐼𝑏 0.55 A
Initial rms energy spread 𝜎𝛿04.28×10−4
Initial rms bunch length 𝜎𝑧0 0.195 𝜇m
Initial rms beam size 𝜎𝑥 100 𝜇m
Transverse beam emittance 𝜖𝑥 4.8 nm
Laser mod. wavelength 𝜆𝐿 1064 nm
Rayleigh length 𝑧𝑅 0.424 m
Initial energy chi... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 1 |
58f2cad7-db6b-4515-b1ed-d8d96d702c61 | Radiation damping time 𝜏𝑅𝐷 0.125 ms
the following formula [8]
𝑃(𝑛)
rad=𝜋
𝜖0𝑐𝑁𝑢,rad⎛⎜
⎝𝐾2
𝑢,rad
4+2𝐾2
𝑢,rad⎞⎟
⎠[JJ]2𝐹𝐹⟂(𝑆)|𝑏𝑛|2𝐼2
𝑏,(1)
where the relevant physical quantities are now evaluated
at the radiator. Here the bunching factor 𝑏𝑛can be eval-
uated from beam sigma matrix as ∣𝑏𝑛∣ = 𝑒−1
2(... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 1 |
5544a1cc-50b1-42c9-8d18-59a8513cb40d | to the blue lines in Fig. 3 and aligns with the initial
design parameters;
2.With external laser compensation as above, we further
considerthegainprocessfromresonantundulatorra-
diationofthe electronbeam inthe LM.This scenario
corresponds to the red lines in Fig. 3;
3.Withoutexternallaser injection,weconsideronlythe
ga... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 1 |
c3072c67-8a28-4e0a-ab0c-c1f4b003ae32 | theblacklinesinFig.3,representingtheself-sustained
LM scheme.
For scenario 2), since the radiation generated by the elec-
tronbeamoneachpassiscapturedandtrappedwithinthe
cavity, the increasingly powerful modulation laser provides
strongerenergymodulationthanthedesignvalue.Thisin-
cremental mismatch leads to shorter mic... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 2 |
22aac20e-ee5d-4c85-af96-f8859f1fc7a5 | is too small, the cavity loss becomes excessiveand the LM
willnotbeself-sustainable.Thus,forscenario3),thegain
processfromresonantundulatorradiationalonecannotcom-
pensate to restore equilibrium if the reflectivity is too low.
Fortunately, there exists a range of reflectivity values where
a portion of resonant undulato... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 2 |
068c7dc3-d6ea-45bb-b460-95cb64cbcba6 | on different cavity reflectivities at 600MeV. Within the
present laser technology, i.e., 0.7MWto1MWlimit, cor-
responding to 𝑅 ≈ 0.9995 ∼ 0.9996 , approximately 1kW
of continuous coherent radiation at 5THzcan be generated.
Intra-cavity powers exceeding 1MWcan induce thermal
distortionsinenhancementcavitymirrors,affect... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 2 |
cadb7da4-cef5-4f28-b7dd-9c8d551a8762 | beam. The selection of beam current needs to consider both
single-bunch and multi-bunch instabilities. Our previous
analysis [11] suggests that multi-bunch beam breakup insta-
bility is not a significant concern. According to Ref. [12],
space-charge-inducedsingle-bunchtuneshiftisnegligibly
smallandmultibunchspace-charg... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 2 |
a7b4eb44-3a32-44a2-ac38-fa3bd40a81ab | Figure4:Dependenceofthelaserpower 𝑃𝐿intheLM(a)
and that of the radiation power in the radiator (b) on the
average bunch current and the total cavity reflectivity.
SUMMARY AND DISCUSSION
Inthispaperweproposeaschemetogeneratecontinuous
kilowattcoherentTHzradiationbasedonself-sustainedlaser
modulationin an SSMB storager... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 2 |
bdb150cd-b778-4505-968c-f62c6fc26c2c | canproducecontinuous 1kWofcoherentradiationat 5THz.
Sincethisschemeisbasedonfreeelectrons,similarradia-
tionoutputcharacteristicscanbetunedacrossawidecentral
frequencyrangeof1–10THz,renderingitanvaluabletool
for scientific explorations.
It deserves here to emphasize that using macroparticle
modeltoanalyzethemulti-bunch... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 2 |
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[9]K.... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 3 |
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[12]Z. Zhao, N. Wang, H. Xu, and Z. Pan, “Calculations of
space-chargetuneshiftsinstorageringswithextremelyshort
bunches a... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 3 |
ce7616b4-dbac-4d30-a5f0-54b3cd20954c | dynamics in a laser cavity modulator with comparison to
Robinson and high-gain free-electron laser instability”, Phys.
Rev. Accel. Beams , vol. 25, no. 6, p. 064401, 2022.
doi:1/zero.alt4.11/zero.alt43/PhysRevAccelBeams.25./zero.alt4644/zero.alt41
[15]C.-Y.Tsai,“Studyofthelongitudinalmultibunchmultiturn
collective dyna... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP08.pdf | 3 |
f3316203-de6f-4a8d-8e40-ff0775eec973 | QUASI-LINEAR THEORY OF SINGLE-PASS MICROBUNCHING
INSTABILITY
Cheng-Ying Tsai∗, School of Electrical and Electronic Engineering,
Huazhong University of Science and Technology, Wuhan, China
Abstract
The existing theoretical treatment of single-pass mi-
crobunching instability (MBI) typically assumes a coast-
ingbeamandad... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 0 |
edbaa504-f4c8-452a-bfbe-1ea3bab5c79e | equations describing the evolution of the bunching factor
and energy spread, still under the coasting beam approxima-
tionwheredifferentmodulationwavelengthsevolveindepen-
dently. Thisapproachprovidesa morerealisticdescription
of the nonlinear evolution of MBI and offers insight into its
natural saturation mechanism.
I... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 0 |
d1cda3e3-2a6f-4e8b-8f8d-0cad7718b19a | too high, but still a linear theory [ 9–12]. Here in this paper
weformulateaquasi-lineartheory,which,althoughnotin-
cludingIBS/ISR,canleadtosaturationwhentheintrinsic
energy spread increases due to the instability mechanism
itself. Itisfoundthatthequasi-lineartheorygivesasetof
coupled equations for bunching factor and ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 0 |
667026c4-4c80-441e-93c0-142ec3f1cc7f | Research Funds for the Central Universities (HUST) under Project No.
2021GCRC006 and National Natural Science Foundation of China under
projectNo. 12275094.transverse dimensions. We start from the single particle
equations of motion
𝑑𝑧
𝑑𝑠= −𝜂𝛿 = 𝑅′
56𝛿
𝑑𝛿
𝑑𝑠=𝑘2
𝑠0
𝜂𝑧 −4𝜋𝜖0𝑟𝑒𝑐𝑁
𝛾∫∞
−∞𝑑𝑘
2𝜋𝑍‖(�... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 0 |
a97ab11d-e8b9-4c8a-89f3-f51f9c80fa01 | Note that 𝑏∗(𝑘) = 𝑏(−𝑘) and𝑍∗
‖(𝑘) = 𝑍‖(−𝑘).
Figure1: Illustrationofintrinsicenergyspreadincreasein
the longitudinal phase space distribution.
The phase space distribution 𝑓(𝑧,𝛿;𝑠), with normaliza-
tion condition ∬𝑓(𝑧,𝛿) = 𝑁 , follows the Vlasov equation
𝜕𝑓
𝜕𝑠+(𝑑𝑧
𝑑𝑠)𝜕𝑓
𝜕𝑧+(𝑑𝛿
𝑑𝑠)𝜕𝑓
𝜕... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 0 |
5a2e5e05-c449-459e-9206-d142dced1531 | Fig. 1. This treatment is similar to that applied in the quasi-
lineartheoryof FEL[ 14]. Anequivalentintegral equation
of Eq. (4) can be written as
𝑓1(𝑠) = 𝑓1(𝑠 = 0)−∫𝑠
0𝑑𝛿
𝑑𝜏𝜕𝑓0
𝜕𝛿𝜏𝑑𝜏, (5)
which we will solve. Before proceeding, let us define the
bunching function below
ℬ(𝑘,𝛿;𝑠) =1
2𝜋∫∞
−∞𝑓1(𝑧,𝛿... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 1 |
4cbd7572-7f8a-4c86-9a75-4764e691e471 | 𝑚-th moment, denoted by square bracket [𝑚]
𝒱[𝑚](𝑠) = ∫∞
−∞𝑉(𝛿;𝑠)𝛿𝑚𝑑𝛿
𝑏[𝑚](𝑘;𝑠) =2𝜋
𝑁∫∞
−∞ℬ(𝑘,𝛿;𝑠)𝛿𝑚𝑑𝛿.(9)
For𝑚 = 0case, we have
𝒱[0]= ∫∞
−∞𝑉(𝛿;𝑠)𝑑𝛿 = ∫∞
−∞∫∞
−∞𝑓0(𝑧,𝛿;𝑠)𝑑𝑧𝑑𝛿 = 𝑁,
(10)
which indicates the conservation of particles. The usual
bunching factor becomes 𝑏[0](𝑘;𝑠). ... | d:\Daily_ihep\Weekly Progress Report\20260425\110_SAP2025\THP - Poster Session_ THP\THP09.pdf | 1 |
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