During the operation of an electron synchrotron with short electron bunches, the beam dynamics are influenced by the occurrence of the micro-bunching instability. This collective instability is caused by the self-interaction of a short electron bunch with its own emitted coherent synchrotron radiation (CSR). Above a certain threshold bunch current dynamic micro-structures start to occur on the longitudinal phase space density. The resulting dynamics depend on various parameters and were previously investigated in relation to, amongst others, the momentum compaction factor and the acceleration voltage. In this contribution, the influence of the energy of the electrons on the dynamics of the micro-bunching instability is studied based on measurements at the KIT storage ring KARA (Karlsruhe Research Accelerator)

Brosi, Miriam

Müller, Anke-Susanne

Schreiber, Patrick

Schuh, Marcel

English

KITopen

INFLUENCE OF DIFFERENT BEAM ENERGIES ON THEMICRO-BUNCHING INSTABILITYM. Brosi∗, P. Schreiber, M. Schuh, A.-S. Müller,Karlsruhe Institute of Technology, Karlsruhe, GermanyAbstractDuring the operation of an electron synchrotron with shortelectron bunches the beam dynamics are influenced by theoccurrence of the micro-bunching instability. This collectiveinstability is caused by the self-interaction of a short electronbunch with its own emitted coherent synchrotron radiation(CSR). Above a certain threshold bunch current dynamicmicro-structures start to occur on the longitudinal phasespace density. The resulting dynamics depend on variousparameters and were previously investigated in relation toamongst others the momentum compaction factor and theacceleration voltage. In this contribution, the influence ofthe energy of the electrons on the dynamics of the micro-bunching instability is studied based on measurements at theKIT storage ring KARA (Karlsruhe Research Accelerator).BEAM DYNAMICSThe micro-bunching instability is not the type of instabil-ity which directly leads to total beam loss. More accurately,the micro-bunching instability leads to dynamic changesand deformation of the charge density in the longitudinalphase space, which deteriorates the beam properties. Thesedynamics are caused by the self-interaction of the bunchwith its own emitted CSR. If a bunch is short enough toemit CSR in wavelengths shorter than the waveguide cut-off of the vacuum pipe, the resulting wake-potential actsback on the bunch and causes a change in the energy distri-bution. The resulting change in the energy distribution istransferred into a change of the longitudinal charge distribu-tion via synchrotron motion. The occurring deformation inthe longitudinal bunch profile then causes coherent emissionin even higher frequencies which drives the deformationfurther. In the end, this leads to the formation of dynamicsubstructures on the charge distribution in the longitudinalphase space rotating with the synchrotron motion.Depending on the exact parameters, especially the bunchcurrent, this dynamic takes different forms. Below the insta-bility threshold, at low bunch currents, the bunch profile isdeformed but stays constant over time (“potential well distor-tion”). For a certain bunch current, the instability threshold,the bunch profile starts to change periodically as substruc-tures form and rotate in the phase space. At bunch currentssignificantly above the threshold the dynamic changes again.Now a cycle develops. Substructures start to gain in intensityand grow driven by the wake-potential. Until at one point thefilamentation of the substructures in the phase space takesover and they are washed out which leads to an increase ofthe size in phase space and therefore of the bunch length.∗ miriam.brosi@kit.eduThis significantly reduces the driving wake-potential. Thecharge distribution now damps down and the bunch lengthshrinks again until the bunch length is short enough so thatthe corresponding CSR emission causes a stronger wake-potential again and the cycle starts anew. In the followingsuch a cycle will be referred to as burst, as it corresponds toone outburst in the emitted CSR power which is an easy tomeasure quantity and indicator for the dynamics.The characteristics of the micro-bunching instability, likethe threshold current or the repetition rate of the bursts de-pend on multiple beam parameters. Some of which areinfluenced by the beam energy. So in the following, theinfluence of the beam energy on the micro-bunching insta-bility is studied based on measurements at a beam energy of1.3 GeV as well as 0.9 GeV.MEASUREMENTIn its role as test-facility KARA provides the flexibilityto systematically study the influence of different operationparameters on the micro-bunching instability [1, 2]. Pre-vious studies [3, 4] focused, for example, on the influenceof the momentum compaction factor 𝛼c or the accelerationvoltage 𝑉RF, as both parameters influence the bunch lengthas well as the restoring force in the longitudinal direction.The beam energy also has a big influence on the longitudi-nal dynamics as it directly changes the radiation dampingtime and therefore the natural energy spread and the natu-ral bunch length. First measurements of the influence ofthe longitudinal damping time where conducted by using aCLIC damping ring wiggler prototype [5] to change the syn-chrotron radiation losses. The results show a change in therepetition rate of the burst while the threshold current andinstability frequency directly above the threshold remainedunchanged [6].KARA is a ramping machine with an injection energyof 0.5 GeV and provides besides the standard operation at2.5 GeV also a short bunch operation mode at 1.3 GeV. Tostudy the influence of the energy an additional short bunchoperation mode was established at 0.9 GeV. The transversetunes were chosen close to the ones of the 1.3 GeV shortbunch mode. Optics at several different values of 𝛼c wereimplemented.To observe the dynamics of the micro-bunching instability,the emitted CSR was measured with a quasi-optical broad-band Schottky barrier diode detector [7]. The detector signalwas read out with KAPTURE a fast data acquisition systemwhich allows a continuous turn-by-turn and bunch-by-bunchread-out [8].12th Int. Particle Acc. Conf. IPAC2021, Campinas, SP, Brazil JACoW PublishingISBN: 978-3-95450-214-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2021-WEPAB246MC5: Beam Dynamics and EM FieldsD06 Coherent and Incoherent Instabilities - Measurements and CountermeasuresWEPAB2463209ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2021).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIAs the dynamic of the instability strongly depends on thebunch current and KARA, as ramping machine, does not pro-vide top-up operation, the emitted CSR power was measuredfor each setting over a bunch current decay. The fluctuationfrequencies of the measured CSR power give direct insightinto the time scales of the dynamics of the instability. Thesefluctuation frequencies are typically displayed in form of aspectrogram as a function of the bunch current as shown inFig. 1.RESULTSThe measurements in Fig. 1a and Fig. 1b were taken atsimilar values of 𝛼c and 𝑉RF which results due to the dif-ference in energy in a different bunch length. Contrary tothat, the measurements in Fig. 1a and Fig. 1c where takenat a similar natural bunch length (which was achieved byoperating at different values of 𝛼c and 𝑉RF for the differentenergies).In all three spectrograms the same characteristic struc-tures can be seen but their positions and exact shapesdiffer. A finger-like structure is visible which decreasesin frequency with decreasing bunch current and ends ina narrow frequency line at the instability threshold (of-ten referred to as initial instability mode/frequency). Thethreshold current below which nearly no fluctuations areobserved1 differ quite drastically between the measure-ment at 1.3 GeV (≈ 0.159 mA) and the measurements at0.9 GeV (≈ 0.040 mA and ≈ 0.055 mA).Nevertheless, the measured thresholds fit quite well to theprediction in [9]. This can be seen in Fig. 2. The represen-tation in the dimensionless parameters2 Π and 𝑆CSR showthat they coincide with the predicted linear dependence ofthe threshold (𝑆CSR)th = 0.5 + 0.12 Π. Even the additionalarea of instability due to the weak instability occurring forsettings with even shorter natural bunch length coincides for0.9 GeV and 1.3 GeV.The repetition rate of the burst is only visible as bright areaat the left edge of the spectrograms in Fig. 1 as the frequencyis much lower than the rest of the dynamics. It is therefore inthe following referred to as low bursting frequency. Figure 3shows the low bursting frequency extracted as a function ofbunch current for several measurements at different values ofΠ for 1.3 GeV (Fig. 3a) and 0.9 GeV (Fig. 3b). For both ener-gies a similar behavior is visible. The low bursting frequencyis roughly constant at higher bunch currents but varies forlower bunch currents. Noteworthy is that the absolut valuesof the frequency are systematically lower in the 0.9 GeVmeasurements, for the typical value at higher bunch cur-rents (∼90 Hz vs. ∼270 Hz) as well as for the span at lowercurrents ((∼60 Hz to ∼300 Hz) vs. (∼180 Hz to ∼900 Hz)).There is an approximate factor of 3 between the frequen-cies at 0.9 GeV and 1.3 GeV. This coincides with the in-1 With an exception for the measurement in Fig. 1b where directly belowthe threshold at ≈ 0.04 mA another instability (the weak instability [4,9])starts.2 Π = 𝜎z,0 𝜌1/2ℎ3/2, 𝑆CSR =𝐼n 𝜌1/3𝜎4/3z,0with 𝐼n =𝜎z,0𝐼b𝛼c𝛾𝜎2𝛿𝐼A, see [4](a) 1.3 GeV, 𝛼 = 4.8 ⋅ 10−4, 𝑉RF = 1500 kV→ 𝜎z,0 = 3.3 ps(b) 0.9 GeV, 𝛼 = 5.1 ⋅ 10−4, 𝑉RF = 1500 kV→ 𝜎z,0 = 1.9 ps(c) 0.9 GeV, 𝛼 = 3.6 ⋅ 10−4, 𝑉RF = 300 kV→ 𝜎z,0 = 3.6 psFigure 1: Spectrograms showing the fluctuation frequenciesin the measured CSR power in the THz frequency range asa function of bunch current. (a) and (b) show measurementsat similar settings of 𝛼c and 𝑉RF but different beam ener-gies (1.3 GeVand 0.9 GeV) resulting in a different naturalbunch length 𝜎z,0. The measurement in (c) was also takenat 0.9 GeV but with a natural bunch length similar to themeasurements in (a).verse change in radiation damping time 𝜏 from 31.7 ms (at0.9 GeV) to 10.4 ms (at 1.3 GeV). So, for 0.9 GeV where theradiation damping is slower the repetition rate of the burst islower. The direction of this change fits well to the dynamicsduring one burst as described in the beginning. The observedfactor of 1/𝜏 is only a rough approximation over the total ofall measurements shown in Fig. 3. When comparing singlemeasurements with similar settings at different energies thisfactor would probably vary. Especially, since dependingon the analysis objective, similarity could mean differentcombinations of settings and therefore yield different results.12th Int. Particle Acc. Conf. IPAC2021, Campinas, SP, Brazil JACoW PublishingISBN: 978-3-95450-214-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2021-WEPAB246WEPAB246ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2021).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI3210MC5: Beam Dynamics and EM FieldsD06 Coherent and Incoherent Instabilities - Measurements and CountermeasuresFigure 2: The measured instability thresholds as well as theprediction by [9] are shown using the dimensionless shield-ing parameter Π and 𝑆CSR. The measured thresholds forboth beam energies agree with the prediction and show boththe additional region of instability (weak instability) [4, 9] atlower values of Π (≈ shorter natural bunch length).(a) 1.3 GeV(b) 0.9 GeVFigure 3: The low bursting frequency corresponds to therepetition rate of the outburst during the micro-bunchinginstability. It is shown for measurements at different valuesof Π as a function of the bunch current. (a) For a beam en-ergy of 1.3 GeV the frequency spans approx. from 180 GHzto 900 GHz. (b) While for 0.9 GHz the frequency spansapprox. from 60 GHz to 300 GHz. For both energies themeasurements show a wider span for higher values of Πwhich corresponds to settings with a longer natural bunchlength.Also, it needs to be checked if the observed factor of 1/𝜏 isconsistent over different energies by conducting additionalmeasurements at further values of the beam energy.In [6, 10] a simplified model for the temporal develop-ment of the bunch length during a burst was established. Itassumes that the duration of a burst consists of two parts. Inthe first (Δ𝑡rise) the bunch length increases due to the sub-structures increasing and filamenting out. And in the second(Δ𝑡shrink) the bunch length is damped down as the drivingwake potential is small due to the now smoother distribution.For a small enough wake potential, this can be assumed asan exponential decay with the longitudinal damping timefrom the maximal blown-up bunch length 𝜎z,max down to-wards the natural bunch length 𝜎z,0. The decay stops at aminimal bunch length 𝜎z,min as soon as the wake potentialbecomes non-negligible due to the now shorter bunch lengthand drives the formation of new substructures. The 1/𝜏dependency observed in the measurements is not directlyobvious from that model. While the damping time is a lin-ear factor in Δ𝑡shrink the beam energy also changed 𝜎z,0 andprobably 𝜎z,min/max as well as Δ𝑡rise.Therefore, the next steps will be to further investigate theinfluence of the energy, e.g. by measurements at additionalenergies and employing a VFP solver. Adjusting the simplemodel described above and figuring out the energy depen-dence of the different terms to fit the simple model to themeasurements could provide an insight into the driving partsbehind the dynamics. It could, for example, strengthen theunderstanding of why at one point the substructures are notdriven further but start to filament out so that the charge dis-tribution in phase space is damped down to a small enoughbunch length to start a new burst again.CONCLUSIONThe micro-bunching instability is a longitudinal, coherentinstability caused by the self-interaction of a bunch with itsown emitted coherent synchrotron radiation. A complex dy-namic enfolds in the charge distribution in the longitudinalphase space with the formation of dynamic substructuresleading to changes in the bunch profile and length. In com-parison of measurements taken at 0.9 GeV and 1.3 GeV sig-nificant changes in the dynamics could be observed due tothe difference in beam energy. The observed decrease in thethreshold current fits well to the predictions. Additionally achange of the low bursting frequency (the repetition rate ofthe burst during the instability) by an approximate factor of1/𝜏 was observed.REFERENCES[1] A.-S. Müller et al., “Far Infrared Coherent Synchrotron EdgeRadiation at ANKA”, in Proc. 21st Particle Accelerator Conf.(PAC’05), Knoxville, TN, USA, May 2005, paper RPAE038,pp. 2518-2520.[2] M. Klein et al., “Modeling the Low-Alpha-Mode at ANKAwith the Accelerator Toolbox”, in Proc. 24th Particle Acceler-12th Int. Particle Acc. Conf. IPAC2021, Campinas, SP, Brazil JACoW PublishingISBN: 978-3-95450-214-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2021-WEPAB246MC5: Beam Dynamics and EM FieldsD06 Coherent and Incoherent Instabilities - Measurements and CountermeasuresWEPAB2463211ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2021).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIator Conf. (PAC’11), New York, NY, USA, Mar.-Apr. 2011,paper WEP005, pp. 1510–1512.[3] M. Brosi et al., “Fast mapping of terahertz bursting thresholdsand characteristics at synchrotron light sources”, Phys. Rev.Accel. Beams, vol. 19, p. 110701, Nov. 2016.doi:10.1103/PhysRevAccelBeams.19.110701[4] M. Brosi et al., “Systematic studies of the microbunching in-stability at very low bunch charges”, Phys. Rev. Accel. Beams,vol. 22, p. 020701, Feb. 2019.doi:10.1103/PhysRevAccelBeams.22.020701[5] A. Bernhard et al., “A CLIC Damping Wiggler Pro-totype at ANKA: Commissioning and Preparations fora Beam Dynamics Experimental Program”, in Proc.7th Int. Particle Accelerator Conf. (IPAC’16), Busan,Korea, May 2016, pp. 2412–2415. doi:10.18429/JACoW-IPAC2016-WEPMW002[6] M. Brosi et al., “Studies of the Micro-Bunching Instability inthe Presence of a Damping Wiggler”, in Proc. 9th Int. ParticleAccelerator Conf. (IPAC’18), Vancouver, Canada, Apr.-May2018, pp. 3273–3276.doi:10.18429/JACoW-IPAC2018-THPAK029[7] ACST GmbH, http://www.acst.de/.[8] M. Caselle et al., “An ultra-fast data acquisition system forcoherent synchrotron radiation with terahertz detectors”, J. In-strum., vol. 9, p. C01024, Jan. 2014.doi:10.1088/1748-0221/9/01/C01024[9] K. L. F. Bane, Y. Cai, and G. Stupakov, “Threshold studiesof the microwave instability in electron storage rings”, Phys.Rev. ST Accel. Beams, vol. 13, p. 104402, Oct. 2010.doi:10.1103/PhysRevSTAB.13.104402[10] M. Brosi, “In-Depth Analysis of the Micro-Bunching Char-acteristics in Single and Multi-Bunch Operation at KARA”,Ph.D. thesis, Phys. Dept., Karlsruher Institut für Technologie,Karlsruhe, Germany, 2020.doi:10.5445/IR/1000120018.12th Int. Particle Acc. Conf. IPAC2021, Campinas, SP, Brazil JACoW PublishingISBN: 978-3-95450-214-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2021-WEPAB246WEPAB246ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2021).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI3212MC5: Beam Dynamics and EM FieldsD06 Coherent and Incoherent Instabilities - Measurements and Countermeasures

Influence of Different Beam Energies on the Micro-Bunching Instability

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Influence of Different Beam Energies on the Micro-Bunching Instability

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