Two parallel corrugated plates will be installed at the KIT storage ring KARA (KArlsruhe Research Accelerator). This impedance manipulation structure will be used to study and eventually control the beam dynamics and the emitted coherent synchrotron radiation (CSR). In this contribution, we present the results obtained with the Vlasov-Fokker-Planck solver Inovesa showing the impedance impact of different corrugated structures on the bunch and its emitted CSR power

Brosi, M.

Maier, S.

Mochihashi, A.

Müller, A-S.

Nasse, M. J.

Schreiber, P.

Schwarz, M.

English

KITopen

SIMULATION OF THE EFFECT OF CORRUGATED STRUCTURES ONTHE LONGITUDINAL BEAM DYNAMICS AT KARAS. Maier∗, M. Brosi† , A. Mochihashi, M. J. Nasse, P. Schreiber, M. Schwarz,A.-S. Müller, Karlsruhe Institute of Technology, Karlsruhe, GermanyAbstractTwo parallel corrugated plates will be installed at theKIT storage ring KARA (KArlsruhe Research Accelerator).This impedance manipulation structure will be used to studyand eventually control the beam dynamics and the emittedcoherent synchrotron radiation (CSR). In this contribution,we present the influence of the parameters of the structureon its impedance and the results obtained with the Vlasov-Fokker-Planck solver Inovesa showing the impedance impactof different corrugated structures on the CSR power.INTRODUCTIONIn contrast to incoherent radiation, CSR scales quadrati-cally with the number of particles and therefore enhancesthe photon flux by several orders of magnitudes. As theemission is coherent for wavelengths larger than the bunchlength, high electron density and short bunches are neces-sary to extend CSR to higher frequencies and to increase theintensity of the radiation. In such short bunch regimes com-plex nonlinear phenomena can occur due to the interactionbetween the passing bunch and its emitted CSR. This resultsin dynamic instabilities and bunch deformations like theso-called microbunching instability [1]. This instability cancause longitudinal substructures on the bunches generatingintense THz radiation.At KIT, we are developing and designing a versatileimpedance chamber for the KARA storage ring to studythe microbunching instability by manipulating the wakefieldand thereby affecting the longitudinal beam dynamics ofthe electrons. The additional impedance and the resultingwakefield change will be generated by two horizontal paral-lel plates with periodic rectangular corrugations. AlthoughBane et al. [2, 3] showed that narrow-band THz pulses canbe generated by installing such structure into a linear ac-celerator, to our knowledge such a structure has never beeninstalled into a storage ring, where the electrons pass thestructure multiple times. In Fig. 1, a schematic drawing withthe characteristic parameters periodic length 𝐿, corrugationdepth ℎ and corrugation width 𝑔, as well as the plate distance2𝑏 is given. The theoretical longitudinal impedance 𝑍 ∥ forparallel corrugated plates is given by Ng et al. [4] under theassumptions 𝐿 ≲ ℎ ≪ 𝑏 as𝑍 ∥𝐿 =𝑍vac.𝜋𝑏2[𝜋𝑘res𝛿 (𝑘2 − 𝑘2res) + 𝑖 ⋅ P.V. (𝑘𝑘2 − 𝑘2res)](1)with the resonance wave number 𝑘res = √ 2𝐿𝑏𝑔ℎ , wave number∗ sebastian.maier@kit.edu† Now at MAX IV Laboratory, Lund, Swedenzy2bghLFigure 1: The corrugated plates in cross section with the rel-evant geometric parameters are shown. The electron bunchis indicated in blue.𝑘 = 𝜔𝑐 , the vacuum impedance 𝑍vac., the 𝛿-distribution, andprincipal value P.V.(x).Previous impedance simulations with CST Studio [5] haveshown how the parameters of the structure influence theimpedance and that the results are in good agreement withthe theoretical prediction [6]. The impedance can be de-scribed by the resonator model [7], which is characterizedby the three parameters resonance frequency 𝑓res, the shuntimpedance 𝑍0, and the quality factor 𝑄.The resonance frequency of the investigated impedanceis in the range between 50 GHz and 200 GHz, where a frac-tion of the CSR impedance is shielded by the beam pipeand therefore an additional impedance with 𝑍0=1 kΩ has asignificant contribution to the total impedance of the KARAstorage ring.SIMULATIONFor the beam dynamics simulations Inovesa [8], anin-house developed Vlasov-Fokker-Planck solver, is used,which describes the micro-bunching instability at the KARAstorage ring [9] very well. For the results presented in thiscontribution, the settings were chosen so that they are com-parable to the KARA short-bunch operation mode with syn-chrotron frequency 𝑓sync = 9.44 kHz and the accelerationvoltage 𝑉RF = 1.048 MV at a beam energy of 𝐸 = 1.3 GeV.For modeling the storage ring impedance the dominatingCSR parallel plate impedance is used [10], which alreadyhas proven to govern the microbunching instability [9,11] forKARA. The additional impedance of the corrugated plates ismodelled by the resonator model with its parameters 𝑓res, 𝑍0,𝑄. The impedance simulation for the corrugated structurehas shown [6], that a quality factor 𝑄 = 3 and a shuntimpedance 𝑍0 = 1 k𝛺 are suitable for a structure lengthof 20 cm, which is the maximum space available along thebeampipe in KARA. As long as it is not explicitly mentioned,these values are used for the Inovesa simulations.Above the threshold current 𝐼thr of the microbunchinginstability the first fluctuations of the CSR intensity occur.Therefore, the behaviour of the standard deviation (STD) ofthe CSR emission as function of the bunch current indicates13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS006MC5: Beam Dynamics and EM FieldsD04: Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsWEPOMS0062241ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI80 100 120 140 160 180 20002040Impedance resonance frequency fres [GHz]Fluctuationpower[ a.u.]Ibelow =221 µA80 100 120 140 160 180 200Impedance resonance frequency fres [GHz]Iabove =228 µAFigure 2: Fluctuation power at the bursting frequency 𝑓burst for additional corrugation impedances with different resonancefrequencies 𝑓res and fixed shunt impedance 𝑍0 = 1 k𝛺 and quality factor 𝑄 = 3 at a beam current below (left) and above(right) the unperturbed bursting threshold. The red dashed line indicates the intensity without the additional impedance.the threshold current, because it increases drastically abovethe instability threshold, so a kink at the threshold current isvisible [12]. However, certain additional impedances changethe beam dynamics in such a way, that the bursting thresholdcannot be determined properly by this method. Alternatively,since the fluctuation power at the bursting frequency - themain frequency in the intensity fluctuations of the CSR dur-ing the microbunching instability - is drastically reduced inamplitude below the threshold current, this parameter, whichis closely related to the STD of the CSR intensity, can beused to determine the threshold current. For the case con-sidered here both methods come to the same results for thethreshold current (𝐼thr = 226 µA) and the bursting frequencyat the threshold (𝑓burst = 34.6 kHz) for the simulation settingwithout additional impedance.IMPEDANCE SCANFor the design of the corrugated structure it is of greatinterest how the microbunching instability is affected by anadditional impedance. For this purpose two currents, oneslightly above (𝐼above = 228 µA) and one below (𝐼below =221 µA) the unperturbed threshold current, have been cho-sen to simulate the beam dynamics and the temporal de-velopment of the emitted radiation intensity for differentadditional corrugation impedances with varying resonancefrequencies. The Fourier transform of the simulated emit-ted CSR shows the fluctuation frequency of the radiationand therefore points out the dominant frequencies of the mi-crobunching. In Fig. 2, the fluctuation power at the burstingfrequency corresponding to the maximum intensity is dis-played as a function of the additional impedance resonancefrequency for the two above-mentioned currents.For 𝐼below = 221 µA, i.e., below the unperturbed thresholdcurrent, there is no significant emitted CSR power withoutan additional impedance (red dashed line). However, certainimpedances lead to a high power fluctuation that is compa-rable to or even higher than the fluctuation power directlyabove the unperturbed threshold but without an additionalimpedance. This is the case for an impedance resonancefrequency in a range from 85 GHz to 160 GHz. Here, thebursting threshold is reduced to a value below 𝐼below, causingthe instability to still occur at 𝐼below. In contrast, a higheror smaller resonance frequency does not seem to affect theemitted CSR power and therefore does not reduce the thresh-old current below 𝐼below. For 𝐼above = 228 µA, i.e., abovethe unperturbed threshold current, the fluctuation power isamplified for 𝑓res < 130 GHz, where the maximum increaseis at about 𝑓res = 100 GHz and results in more than dou-bling of the fluctuation power in comparison with no addi-tional impedance. Here, higher resonance frequencies leadto a reduction and above 𝑓res = 180 GHz even to a suppres-sion of the fluctuation power, which means that the burstingthreshold current is increased above 𝐼above by these addedimpedances.THRESHOLD CURRENT & BURSTINGFREQUENCYFor a more detailed investigation, a current scan has beensimulated for two corrugation impedances. The ones cho-sen, are the impedance that produces the maximum intensitybelow and above the threshold (𝑓res = 110 GHz) and theimpedance with the lowest 𝑓res to increase the threshold cur-rent above 𝐼above (𝑓res = 180 GHz). The Fourier transformof the emitted CSR power as a function of time is shownfor a certain current range in the spectrograms in Fig. 3,in which the finger-like structure indicates the dynamics ofTable 1: Corrugation parameters for an additional impedancewith the shunt impedance 𝑍0=1 kΩ and the quality factor𝑄 = 3𝑓res = 110 GHz 𝑓res = 180 GHzcorrugation depth ℎ 130 µm 60 µmperiodic length 𝐿 80 µm 40 µmcorrugation width 𝑔 40 µm 20 µm13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS006WEPOMS006ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI2242MC5: Beam Dynamics and EM FieldsD04: Beam Coupling Impedance - Theory, Simulations, Measurements, Code Developments25 35 45200250300Frequency [kHz]Bunchcurrent[ µA]with corrugatedstructure fres=110 GHz25 35 45Frequency [kHz]no corrugatedstructure25 35 45Frequency [kHz]with corrugatedstructure fres=180 GHz10−610−410−2100102Fluctuationpower[ a.u.]Figure 3: Color-coded power of the emission fluctuations for different bunch currents as a function of the fluctuationfrequency around the bursting frequency 𝑓burst without and with additional corrugation impedances for two resonancefrequencies 𝑓res.The shunt impedance and quality factor of the impedance were fixed at 𝑍0 = 1 k𝛺 and quality factor 𝑄 = 3,respectively. The horizontal white dashed line marks the start of the fluctuations due to the micro-bunching instability andthe vertical one the corresponding bursting frequency for the case with no corrugated structure (middle).the microbunching instability directly above the thresholdcurrent [11]. It can be seen, that the general shape of thefinger and hence the bursting behavior of the microbunchingis not substantially changed due to adding an impedancewith 𝑍0 = 1 k𝛺. Nevertheless, the characteristic param-eters of the bursting can be changed, notably the thresh-old current and the bursting frequency. In the spectrogramwith the additional impedance of a corrugated structure with𝑓res = 110 GHz it can be verified that the threshold currentis reduced by 16 µA (7.1 %), whereas the bursting frequencyof the fingertip stays unchanged.In contrast, an additional impedance with 𝑓res = 180 GHzcauses a slight increase of the bursting threshold by 3 µA(1.3 %). However, this additional impedance also increasesthe bursting frequency by about 1.9 kHz, so that the lon-gitudinal beam dynamics caused by the the instability areslightly modified. In Fig. 4 the threshold current and thebursting frequency at the fingertip are shown as a function180200220Thresholdcur-rentI thr[ µA]0 1000 2000 3000 4000 5000354045Shunt impedance Z0 [Ω]Burstingfrequencyf burst[ kHz]fres=110 GHzfres=180 GHzFigure 4: Bursting threshold and frequency for differentshunt impedances 𝑍0. An additional impedance with a reso-nance frequency 𝑓res = 110 GHz (red) decreases the thresh-old current, whereas 𝑓res = 180 GHz (blue) increases thebursting frequency.of the shunt impedance 𝑍0 of the additional corrugationimpedance for the two different resonance frequencies con-sidered in Fig. 3. It can be seen, that for each plot one of theparameters scales nearly linearly with the shunt impedance,whereas the respective other parameter does not significantlychange.SUMMARY & OUTLOOKIt is planned to install a corrugated structure into theKARA storage ring to study and manipulate the microbunch-ing instability. Longitudinal beam dynamics and radiationemission simulations with the Vlasov-Fokker-Planck solverInovesa showed that the resonance frequency of the addi-tional impedance is the decisive parameter that determineshow the instability is influenced, while the shunt impedanceaffects the intensity of the influence. By choosing the res-onance frequency correctly, it is possible to either reducethe threshold current and therefore emit intense THz radia-tion at even lower bunch currents or to change the dominantfluctuation frequency of the microbunching.As a next step, beam dynamics simulations with differentmachine settings will be carried out for understanding howthe impedance affects the beam dynamics for different ma-chine settings. Furthermore, we will design and fabricatethe corrugated structures and the whole impedance manipu-lation chamber for the KARA storage ring.ACKNOWLEDGEMENTSH.J. Cha is acknowledged for helpful discussions. Thiswork is supported by the DFG project 431704792 in theANR-DFG collaboration project ULTRASYNC. S. Maieracknowledges the support by the Doctoral School „KarlsruheSchool of Elementary and Astroparticle Physics: Scienceand Technology“ (KSETA).13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS006MC5: Beam Dynamics and EM FieldsD04: Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsWEPOMS0062243ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIREFERENCES[1] A.-S. Müller et al., “Far Infrared Coherent Synchrotron EdgeRadiation at ANKA”, in Proc. PAC’05, Knoxville, TN, USA,May 2005, paper RPAE038, pp. 2518-2520.[2] K. L. F. Bane, G. Stupakov, “Terahertz radiation from a pipewith small corrugations”, Nuclear Instruments and Methodsin Physics Research A, vol. 677, pp. 67-73, 2012.[3] K. L. F. Bane et al., “Measurement of terahertz radiationgenerated using a metallic, corrugated pipe”, Nuclear Instru-ments and Methods in Physics Research A, vol. 844, pp. 121-128, 2017.[4] K. Y. Ng et al.,“Explicit expressions of impedances and wakefunctions”, Fermi National Accelerator Lab (FNAL), Batavia,IL (United States), 2010.[5] CST Studio Suite, Dassault Systèmes, https://www.cst.com[6] S. Maier, M. Brosi, A. Mochihashi, A.-S. Müller, M. J. Nasse,and M. Schwarz, “Impedance Studies of a Corrugated Pipe forKARA”, in Proc. IPAC’21, Campinas, Brazil, May 2021, pp.2039–2042. doi:10.18429/JACoW-IPAC2021-TUPAB251[7] K. Y. Ng,“Impedances of bellow corrugations”, Fermi Na-tional Accelerator Lab. (FNAL), Batavia, IL, USA, 1987.[8] P. Schönfeldt et al., Inovesa, 2017. doi:10.5821/zenodo.597356[9] P. Schönfeldt et al.,“Parallelized Vlasov-Fokker-Planck solverfor desktop personal computers”, Phys. Rev. Accel. Beams,2017. doi:10.1103/PhysRevAccelBeams.20.030704[10] J. B. Murphy, R. L. Gluckstern, and S. Krinsky, “Longitudinalwakefield for an electron moving on a circular orbit”, Part.Accel., vol. 57, pp. 9-64, 1997. https://cds.cern.ch/record/1120287/[11] M. Brosi et al., “Fast Mapping of Terahertz Bursting Thresh-old and Characteristics at Synchrotron Light Sources”, Phys.Rev. Accel. Beams, vol. 19, p. 110701, 2016. doi:10.1103/PhysRevAccelBeams.19.110701[12] M. Brosi et al., “Studies of the Micro-Bunching Instability inMulti-Bunch Operation at the ANKA Storage Ring”, in Proc.IPAC’17, Copenhagen, Denmark, May 2017, pp. 3645–3648.doi:10.18429/JACoW-IPAC2017-THOBA113th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS006WEPOMS006ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI2244MC5: Beam Dynamics and EM FieldsD04: Beam Coupling Impedance - Theory, Simulations, Measurements, Code Developments

Simulation of the Effect of Corrugated Structures on the Longitudinal Beam Dynamics at KARA

https://publikationen.bibliothek.kit.edu/1000149536/149124397

Simulation of the Effect of Corrugated Structures on the Longitudinal Beam Dynamics at KARA

Abstract

Similar works

Full text

Available Versions

KITopen