In this paper, a study using the Polarization Current Approach (PCA) model is performed to optimize the design of a short bunch length monitor using two dielectric radiators that produce coherent Cherenkov Diffraction Radiation (ChDR). The electromagnetic power emitted from each radiator is measuring a different part of the bunch spectrum using Schottky diodes. For various bunch lengths, the coherent ChDR spectrums are calculated to find the most suitable frequency bands for the detection system. ChDR intensities measured by each detector are estimated for different impact parameters to explore the dependence of bunch length monitor on beam position and angular jitter. It is found that, in the present configuration, the effects of beam position and angular jitter are negligibly small for bunch length measurement

Apsimon, O.

Davut, C.

Karataev, P.

Lefevre, T.

Mazzoni, S.

Xia, G.

English

The University of Manchester - Institutional Repository

The University of Manchester ResearchOptimization Study of Beam Position and Angular JitterIndependent Bunch Length Monitor for Awake Run 2DOI:10.18429/JACoW-IBIC2022-WEP29Document VersionFinal published versionLink to publication record in Manchester Research ExplorerCitation for published version (APA):Davut, C., Xia, G., Apsimon, O., Karataev, P., Mazzoni, S., & Lefevre, T. (2022). Optimization Study of BeamPosition and Angular Jitter Independent Bunch Length Monitor for Awake Run 2. In Journal of AcceleratorConferences Website (pp. 465-468) https://doi.org/10.18429/JACoW-IBIC2022-WEP29Published in:Journal of Accelerator Conferences WebsiteCiting this paperPlease note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscriptor Proof version this may differ from the final Published version. If citing, it is advised that you check and use thepublisher's definitive version.General rightsCopyright and moral rights for the publications made accessible in the Research Explorer are retained by theauthors and/or other copyright owners and it is a condition of accessing publications that users recognise andabide by the legal requirements associated with these rights.Takedown policyIf you believe that this document breaches copyright please refer to the University of Manchester’s TakedownProcedures [http://man.ac.uk/04Y6Bo] or contact uml.scholarlycommunications@manchester.ac.uk providingrelevant details, so we can investigate your claim.Download date:04. Mar. 2023OPTIMIZATION STUDY OF BEAM POSITION AND ANGULAR JITTERINDEPENDENT BUNCH LENGTH MONITOR FOR AWAKE RUN 2C. Davut∗ ,1,2, G. Xia1, University of Manchester, Manchester, UKO. Apsimon1, University of Liverpool, Merseyside, UKP. Karataev, Royal Holloway, University of London, London, UKS. Mazzoni, T. Lefevre, CERN, Geneva, Switzerland1also at Cockcroft Institute, Daresbury, UK2also at CERN, Geneva, SwitzerlandAbstractIn this paper, a study using the Polarization Current Ap-proach (PCA) model is performed to optimize the designof a short bunch length monitor using two dielectric radia-tors that produce coherent Cherenkov Diffraction Radiation(ChDR). The electromagnetic power emitted from each ra-diator is measuring a different part of the bunch spectrumusing Schottky diodes. For various bunch lengths, the coher-ent ChDR spectrums are calculated to find the most suitablefrequency bands for the detection system. ChDR intensitiesmeasured by each detector are estimated for different im-pact parameters to explore the dependence of bunch lengthmonitor on beam position and angular jitter. It is foundthat, in the present configuration, the effects of beam posi-tion and angular jitter are negligibly small for bunch lengthmeasurement.INTRODUCTIONIn recent years, coherent Cherenkov Diffraction radiation(ChDR) has become a suitable candidate for non-invasivelongitudinal bunch profile diagnostics with successful ex-perimental validations [1, 2]. Although, the exact solutionsof the electromagnetic problems are often not known, anddetailed computer simulations require extensive time andresources, the properties of the radiation are often derivedfrom simplified models, that assume specific assumptionson the radiator shape [3].The emission characteristics of ChDR can be calculatedby Polarization Current Approach (PCA) which describessimultaneously generated DR and ChDR as a solution tothe “vacuum” set of macroscopic Maxwell’s equations [4].Among the other theoretical models, PCA introduces somelimitations on the longitudinal size of the radiator whencalculating of the spectral-angular distribution of ChDR thatmakes it a powerful tool to calculate expected radiation yieldand directivity of ChDR cone [5].Considering a relativistic charged particle with energy𝛾 = 1/√1 − 𝛽2 moving rectilinearly at a distance 𝑏 from aprismatic dielectric target, such as in Fig. 1, the particle fieldflattened into a plane perpendicular to its motion having arelation between its components 𝐸⟂ ≫ 𝐸∥ and 𝐻 ≈ 𝐸 for 𝛽 =𝑣/𝑐 ∼ 1. The Fourier component of 𝐸⟂ is spatially restrictedin a circle with a radius which is called the effective field∗ can.davut@manchester.ac.ukradius 𝑙 = 𝛾𝛽𝜆/2𝜋, where 𝜆 is the radiation wavelength.Hence, the following the condition should be satisfied :𝑙 ≳ 𝑏. (1)In this case the dielectric medium will be polarised and thepolarization radiation will be emitted [6].Figure 1: The geometry of ChDR emission by a relativisticcharged particle moving rectilinearly at a distance 𝑏 fromthe bottom surface of a prismatic dielectric target.Therefore the spectral-angular distribution of ChDR canbe calculated by Polarization Current Approach (PCA), asdescribed in [4], in terms of its vertical and horizontal com-ponents with respect to particle trajectory and after the radi-ation is refracted out at the exit surface of the prism.𝑑2𝑊𝑑𝜔𝑑Ω = 𝑆𝑒 (𝜔) =𝑑2𝑊⟂𝑑𝜔𝑑Ω +𝑑2𝑊‖𝑑𝜔𝑑Ω.(2)The total radiation intensity generated by an electronbunch can be described by𝑆(𝜔) = 𝑆𝑒(𝜔) [𝑁 + 𝑁(𝑁 − 1)] 𝐹(𝜔), (3)where 𝑆(𝜔) is the experimentally measured spectrum, 𝑆𝑒(𝜔)is the theoretically calculated single electron spectrum, Nis the number of electrons within the bunch and 𝐹(𝜔) isthe longitudinal bunch form factor [7]. As an importantfeature of the radiation spectrum, the domination of thelongitudinal bunch form factor on the radiation spectrumindicates how far the radiation intensity extends in the fre-quency range. The amplitude of the longitudinal form factor11th Int. Beam Instrum. Conf. IBIC2022, Kraków, Poland JACoW PublishingISBN: 978-3-95450-241-7 ISSN: 2673-5350 doi:10.18429/JACoW-IBIC2022-WEP2905 Longitudinal Diagnostics and SynchronizationWEP29465ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIcan be calculated as a modulus squared of a Fourier trans-form applied to the longitudinal charge distribution 𝜌(𝑧)within the bunch [8],𝐹 (𝜔) = ∣∫∞0𝜌 (𝑧) exp (𝑖𝜔𝑐 𝑧) 𝑑𝑧∣2(4)and can be written in the following form for a bunch withGaussian distribution,𝐹 (𝜔) = exp (−𝜔2𝜎2𝑧𝑐2) = exp(−𝑘2𝜎2𝑧 ), (5)where 𝑘 = 𝜔/𝑐 = 2𝜋/𝜆 is the wave number. Finally, ne-glecting the contribution from incoherent emission, we canwrite𝑆 (𝜔) = 𝑁2 𝑆𝑒 (𝜔) 𝐹 (𝜔) . (6)CALCULATION METHODThe measurement concept of the longitudinal electronbunch length monitor consists of three Alumina radiatorsplaced on only one side of the electron bunch (see Fig. 2).Figure 2: The geometry of ChDR emission by a relativisticcharged particle moving rectilinearly at a distance 𝑏 fromthe bottom surface of a prismatic dielectric target.Two Schottky detectors having two different frequencyranges, is used to measure the ChDR from the first two ra-diators. Coherent ChDR spectral responses are measuredby these two detectors and the longitudinal charge distribu-tion of the bunch can be eliminated by by using a similarapproach with [1].𝑆1 (𝜔1)𝑆2 (𝜔2)=𝑆𝑒1 (𝜔1) 𝑒𝑥𝑝(−𝑘21𝜎2𝑧 )𝑆𝑒2 (𝜔2) 𝑒𝑥𝑝(−𝑘22𝜎2𝑧 ). (7)Thus, RMS bunch length can be calculated by,𝜎𝑧,𝑟𝑚𝑠 = √∣1𝑘22 − 𝑘21ln (𝑆1 (𝜔1) 𝑆𝑒2 (𝜔2)𝑆2 (𝜔2) 𝑆𝑒1 (𝜔1))∣. (8)In order to calculate the ChDR radiation spectrum and in-tensity captured at the corresponding horn antenna aperture,the coordinate system in PCA equations is transformed intocartesian as depicted in Fig. 3. As 𝜌 being the radius vectormagnitude,sin 𝜃𝑥 =𝑥𝜌 = sin 𝜃 sin 𝜑sin 𝜃𝑦 =𝑦𝜌 = sin 𝜃 cos 𝜑.(9)Figure 3: Transformation of coordinate system.Thus, coherent ChDR spectrum can be calculated by𝑑𝑊𝑑𝜔 = 𝑁2 𝑒𝑥𝑝(−𝑘2𝜎2𝑧 ) ∫Δ𝜃𝑥2−Δ𝜃𝑥2∫𝜃𝐶ℎ𝐷𝑅+Δ𝜃𝑦2𝜃𝐶ℎ𝐷𝑅−Δ𝜃𝑦2𝑑2𝑊𝑑𝜔𝑑Ω𝑑𝜃𝑥 𝑑𝜃𝑦.(10)Hence ChDR intensity, 𝑆 (𝜔), can be found by integratingEq. (10) over each corresponding detector horn aperturewith their frequency detection ranges.PCA ANALYSISSince RMS bunch length is calculated by taking ChDRintensity ratios of detectors to be determined, it is impor-tant to find the most suitable frequency range of Schottkydetectors operates in such a way that one should be usedas normalization detector which measures nearly the sameChDR intensity independent from the bunch length whilethe other one should be sensitive to the bunch length. Forthat purpose, a variety of Schottky diode detectors and cor-responding pyramidal and diagonal horn antennas availablefrom Millitech [9] and Virginia Diodes [10] considered todetermine the most suitable frequency bands of detectors tobe used for this specific calculation method by using sim-ulation parameters including the AWAKE Run 2 electronbunch parameters [11] in Table 1.Table 1: Simulation ParametersParameter ValueBunch Energy, E 150 MeVBunch Length, 𝜎𝑧 200 fsBunch Size, 𝜎𝑟 5.25 �mPosition Jitter < 𝜎𝑟Impact Parameter, b 15 mmDielectric constant, 𝜀𝐴𝑙𝑢𝑚𝑖𝑛𝑎 9.5Radiator Angle, 𝜙 19 �Radiator Length, a 16.28 mmAs coherent ChDR spectrum extend up to THz rangefor such a short electron bunch length, the diffraction ef-fects dominate in lower frequencies while the dominationof the bunch form factor begins at higher frequencies of thespectrum.These two effects lead us to have the advantageto choose the Schottky diodes to be used with different pur-poses considering the aim of the RMS bunch length calcula-11th Int. Beam Instrum. Conf. IBIC2022, Kraków, Poland JACoW PublishingISBN: 978-3-95450-241-7 ISSN: 2673-5350 doi:10.18429/JACoW-IBIC2022-WEP29WEP29ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI466 05 Longitudinal Diagnostics and Synchronizationtion method. ChDR spectrum and intensity of each selectedSchottky detector are shown in Fig. 4. According to the PCAsimulations,the detectors which operate between 60-90 GHzand between 400-600 GHz are selected as normalization andsensitivity detector, respectively.Figure 4: ChDR spectral responses calculated by using the-oretical PCA model considering frequency ranges of eachselected detector and its corresponding horn aperture.Beam position and angular jitter is investigated with theselected Schottky detectors and results shown in Figs. 5 and6, respectively. Although beam position jitter for AWAKERun 2 is specified as less than 𝜎𝑟, ChDR intensity capturedby each detector is calculated for ±1 mm to check the inten-sity ratio in wider range. It is found that the ±1 mm beamposition jitter causes 6% change in ChDR intensity ratio ofthe detectors while it is 0.03% in the range of ±𝜎𝑟 as shownin Fig. 5.Figure 5: Impact parameter scan.Following the same principle, angular jitter is also cal-culated in a wider range for a conventional accelerator,±1 mrad, and the change in the ChDR intensity ratio isfound 0.9% as shown in Fig. 6.Figure 6: Angular jitter scan.By having less than 1% sensitivity to beam position andangular jitter we can clearly say that the RMS bunch lengthcalculation is independent from these effects.The goal of RMS bunch length calculation method is notonly being insensitive to the beam position and angular jitterbut also being highly sensitive to any change in the bunchlength simultaneously. Thus, bunch length sensitivity of theChDR intensity ratio is calculated in the range of ±10 fs.Figure 7 shows ChDR intensity for each selected detectorand the intensity ratios in that range. It is found that ±1 fschange in the bunch length causes 5% change in the ChDRintensity ratio.Figure 7: Bunch length sensitivity scan.CONCLUSION AND FUTURE PLANSThe determination of the Schottky diodes and most suit-able frequency ranges to be used for the detection of theChDR was made by using PCA investigation of ChDR spec-trum and intensity among a variety of Schottky diodes fromMillitech and Virginia diodes. The dependence of ChDRintensity ratio to the beam position and angular jitter besidesbunch length sensitivity of the calculation method was in-venstigated. It was found that RMS bunch length calculationis independent of beam position and angular jitter by having< 1% change in the CHDR intensity ratio while having 5%for ±1 fs bunch length change.The commissioning of the bunch length monitor has beenstarted and tests are on going in the CLEAR facility at CERN.Comprehensive analysis and the details will be published ina journal in the future.11th Int. Beam Instrum. Conf. IBIC2022, Kraków, Poland JACoW PublishingISBN: 978-3-95450-241-7 ISSN: 2673-5350 doi:10.18429/JACoW-IBIC2022-WEP2905 Longitudinal Diagnostics and SynchronizationWEP29467ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIACKNOWLEDGEMENTSC. Davut is supported by the Turkish Ministry of NationalEducation, Republic of Turkey through the PostgraduateStudy Abroad Program. The authors would like to acknowl-edge the support from the Cockcroft Institute Core Grantand the STFC AWAKE Run 2 Grant ST/T001917/1.REFERENCES[1] A. Curcio et al., “Noninvasive bunch length measurementsexploiting cherenkov diffraction radiation”, Phys. Rev. Accel.Beams, vol. 23, no. 2, p. 022802, 2020.doi:10.1103/PhysRevAccelBeams.23.022802[2] K. Fedorov et al., “Development of longitudinal beam profilemonitor based on coherent transition radiation effect for claraaccelerator”, J. Instrum., vol. 15, no. 06, p. C06008, 2020.doi:10.1088/1748-0221/15/06/C06008[3] K. Łasocha et al., “Experimental Verification of Several The-oretical Models for ChDR Description”, in Proc. IPAC’22,Bangkok, Thailand, Jun. 2022, pp. 2420–2423.doi:10.18429/JACoW-IPAC2022-THOYGD1[4] M. V. Shevelev and A. S. Konkov, “Peculiarities of the gen-eration of vavilov-cherenkov radiation induced by a chargedparticle moving past a dielectric target”, J. Exp. Theor. Phys.,vol. 118, no. 4, pp. 501–511, 2014.doi:10.1134/S1063776114030182[5] C. Davut, O. Apsimon, P. Karataev, T. Lefèvre, S. Maz-zoni, and G. X. Xia, “Analytical and Numerical Character-ization of Cherenkov Diffraction Radiation as a Longitudi-nal Electron Bunch Profile Monitor for AWAKE Run 2”, inProc. IPAC’21, Campinas, Brazil, May 2021, pp. 4355–4358.doi:10.18429/JACoW-IPAC2021-THPAB284[6] M. L. Ter-Mikaelian, High energy electromagnetic processesin condensed media, Wiley-Interscience, 1972.[7] J. S. Nodvick and D. S. Saxon, “Suppression of coherentradiation by electrons in a synchrotron”, Phys. Rev., vol. 96,no. 1, p. 180, 1954. doi:10.1103/PhysRev.96.180[8] A. P. Potylitsyn, M. I. Ryazanov, M. N. Strikhanov, andA. A. Tishchenko, “Coherent radiation generated by bunchesof charged particles”, in Diffraction Radiation from Relativis-tic Particles, Berlin, Germany: Springer, 2010, pp. 197–220.doi:10.1007/978-3-642-12513-3_7[9] Smiths Interconnect,https://www.smithsinterconnect.com[10] Virginia Diodes, https://www.vadiodes.com/en/products/detectors[11] P. Muggli and for the AWAKE Collaboration, “Physics to planAWAKE Run 2”, J. Phys.: Conf. Ser., vol. 1596, p. 012008,2020. doi:10.1088/1742-6596/1596/1/01200811th Int. Beam Instrum. Conf. IBIC2022, Kraków, Poland JACoW PublishingISBN: 978-3-95450-241-7 ISSN: 2673-5350 doi:10.18429/JACoW-IBIC2022-WEP29WEP29ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI468 05 Longitudinal Diagnostics and Synchronization

Optimization Study of Beam Position and Angular Jitter Independent Bunch Length Monitor for Awake Run 2

Davut, Can

Apsimon, Oznur

Karataev, Pavel

Lefèvre, Thibaut

Mazzoni, Stefano

Xia, Guoxing

CERN Document Server

https://pure.manchester.ac.uk/ws/files/246939704/wep29_4.pdf

Optimization Study of Beam Position and Angular Jitter Independent Bunch Length Monitor for Awake Run 2

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