Borysenko, A.

Hertle, E.

Hiller, N.

Judin, V.

Müller, A.S.

Naknaimueang, S.

Schuh, M.

Schwarz, M.

Schönfeldt, P.

Steinmann, J.L.

Müller, A. S.

Steinmann, J. L.

KITopen

AbstractThe ANKA electron storage ring of the Karlsruhe Insti-tute of Technology (KIT, Germany) is regularly operated inlow-alpha mode to produce short bunches for the generationof coherent synchrotron radiation (CSR). This paper evalu-ates systematic bunch length measurements taken in low-αcoperation of the ANKA storage ring. Above the burstingthreshold not only the emission of CSR occurs in bursts,but also a continuous fluctuation of the bunch’s length isobserved. The measurements were carried out using con-current multi-turn (using a streak camera, SC) as well assingle-shot (using electro-optical spectral decoding, EOSD)methods. Furthermore, we compare information obtainedon the fluctuation to simulations.INTRODUCTIONFor bunch charges above a threshold that depends on beamoptics and RF voltage, bursts of CSR are observable. Thesedefine the so-called bursting instability. Bunch lengtheningis a well known feature of this instability, but measurementshave also shown oscillations of the bunch length that had thesame periodicity as bursts measured at the same time [1].There are two challenges one faces when trying to resolvefluctuations of the bunch length in low-αc operation. First ofall, the bunch length goes down to a few picoseconds, so oneneeds methods that are sensitive enough to resolve the lengthto sub-ps-accuracy, to be able to see fluctuations. EOSD aswell as a SC can fulfill this. Secondly, the bunch length andlongitudinal oscillation might have about the same magni-tude. So one needs measurements that are not disturbed bythe synchrotron oscillation. To meet these requirements, wehad to operate the SC to resolve the synchrotron frequency.Doing this, the turn-by-turn fluctuation cannot be resolveddirectly, so we also did a cross check simulating SC images.Furthermore we compare our results to a simulation of thephysics in longitudinal phase space based on the Vlasov-Fokker-Planck equation.Table 1: ANKA Machine SettingsCircumference 110.4mf s 7.7 kHzVRF 4 × 450 kVEnergy 1.3GeVFilling pattern single bunchCurrent range 0.065mA < I < 2.0mABursting Threshold Ith ≈ 0.07mA∗ patrik.schoenfeldt@kit.eduSince all measurements mentioned in this paper werecarried out with one single bunch inside the ANKA storagering, interaction between different bunches does not have tobe taken into account. The most important parameters usedare shown in Table 1.FLUCTUATION OF BUNCH LENGTHSimulationFor the simulation of SC images (MSCI, Mock StreakCamera Images) we use bunch length and synchrotron fre-quency as input, and add realistic noise. The parameterizedaverage bunch length isl¯ (Ib ) =q√(l0)q +(k × I3/7b)q(1)with the bunch current Ib , the natural bunch length l0 and theempirical fit parameters q and k. Since incoherent light isused for the SC, the number of photons hitting the screen isscaled proportional to Ib . This already allows investigationof statistical influences. As an additional input parameter,here we used the main bursting frequency, as measured usingfast THz detectors [2] (see Fig. 1). For the length fluctuationan amplitude of 10% has been assumed. The simulatedimages are subjected to the same analyzes chain as the actualmeasurements. 150 200 250 300 350 400 450 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1Bursting Frequency / HzBunch Current / mAFigure 1: Main frequency at which radiation bursts occurplotted over bunch current. Actual measurement points havebeen connected to guide the eye. Note that the frequenciesare a lot lower than the synchrotron frequency (7.7 kHz),which has to be resolved using the SC. This data is used asinput parameter to create MSCI.This simulation gives an impression of the fluctuation ofbunch length that would be measured using the SC. For thebunch length the simulation on the one hand verifies thatboth sources of noise do not have a big impact on the mea-surements in the current range we present in this paper. OnFLUCTUATION OF BUNCH LENGTH IN BURSTING CSR:MEASUREMENT AND SIMULATIONP. Schönfeldt∗, A. Borysenko, E. Hertle, N. Hiller, V. Judin, A.-S. Müller,S. Naknaimueang, M. Schuh, M. Schwarz, J.L. SteinmannKarlsruhe Institute of Technology, Karlsruhe, GermanyProceedings of IPAC2014, Dresden, Germany MOPRO06802 Synchrotron Light Sources and FELsA05 Synchrotron Radiation FacilitiesISBN 978-3-95450-132-8237 Copyright©2014CC-BY-3.0andbytherespectiveauthors 0 5 10 15 20 25 0  0.2  0.4  0.6  0.8  1Bunch Length / psBunch Current / mASCMSCIEOSDVFPS 0.1 1 10 0  0.2  0.4  0.6  0.8  1Fluctuation / psBunch Current / mAFigure 2: The upper plot shows bunch length (FWHM), the lower plot the fluctuation of bunch length obtained by all usedmethods. All results agree well. For the fluctuation (lower plot) on the other hand, there are some differences between themethods. The increase in measured fluctuation for low currents obtained using EOSD can be explained by the decreasedshot-to-shot accuracy with decreasing electrical field. The MSCI approach which folds bunch length, the SC’s time range,and the frequencies of the bursts reproduces the fluctuation directly obtained using the SC very well.the other hand it gives evidence that the bursting frequencyindeed has an impact on the measured fluctuation of bunchlengths. The results are shown in Fig. 2 and will be discussedin the results section.The Vlasov-Fokker-Planck Solver (VFPS) used for the sec-ond simulation was originally implemented by M. Klein [3].A brief explanation can be found in [4]. As for the MSCIsome input parameters are derived from measurement data.The momentum compaction factor αc and the slip factor ηare calculatedαc ≈ −η ≈f 2s × 2pi × E/efrev × V˙RF(2)with the revolution frequency frev , the time derivative ofthe RF voltage V˙RF ≈ fRF × VRF,1 = 500MHz × 450 kV,and the beam energy E. The energy spread σE has beenderived from the natural bunch length σz,0 usingσE =σz,0 × 2pi f sηc. (3)The accuracy of the VFPS data is limited by computationtime as well as by the accuracy of the input parameters,particularly by l0 ≈ σz,0 × 2.35 = (6.50 ± .06 ± .24) ps.Especially for long bunch lengths, a large mesh has to beused. So only a limited number of synchrotron periods canbe simulated in reasonable computation time, which meansthat statistics for the fluctuation is not optimal. Currentlythe number of simulated bursts is N = 50. 9.5 10 10.5 11 0  2  4  6  8  10 0 5 10Bunch Length / psTHz Power /a.u.Time / msFigure 3: Example for a solution of the Vlasov-Fokker-Planck equation. At the time the bunch length (RMS× 2.35,blue, left axis) starts to increase, the CSR (red, right axis)is bursting. When the CSR intensity drops, the bunches toshortens again.The qualitative result that correlates bursting CSR withfluctuations in the bunch length – as seen in Fig. 3 – agreesMOPRO068 Proceedings of IPAC2014, Dresden, GermanyISBN 978-3-95450-132-8238Copyright©2014CC-BY-3.0andbytherespectiveauthors02 Synchrotron Light Sources and FELsA05 Synchrotron Radiation Facilitieswell with the expectations: The bunch length is correlatedto the emitted CSR power, both quantities fluctuate at thesame frequency. While the frequency itself deviates fromthe measurements by a factor of about 2.5 (see also [4]), thepattern of the THz power looks similar to measured intensityfluctuations.As for the MSCI, the results for the average bunch lengthas well as for the length fluctuation are shown in Fig. 2 andwill be discussed in the results section.MeasurementsTo measure bunch length and longitudinal profile wemainly use two methods. The used SC, a HamamatsuC5680, has dual sweep which allows to record a bunch’sprofile continuously over time. Since we are interested inaccurate measurements for short bunches, the amplitudeof the synchrotron oscillation has to be taken into account.Hence the (slow) time axis has to be chosen in a way thatthe synchrotron oscillation is clearly visible. We then areable to deduct it and get an (averaged) bunch profile fromthe projection onto SC the position (fast time) axis. Ac-cording to benchmarks using MSCI for constant bunchlengths this method gives an accuracy which is better than∆lSC < 0.3 ps.Additionally we do near field measurements using electrooptical spectral decoding [5] to obtain the electron bunches’profile in a single pass-by. The statistical uncertainty of thismethod is limited by the field strength, thus can vary shot byshot depending on the distance between beam and electro-optical crystal. Furthermore there is a timing-dependent biaswhich in the worst case adds a deviation of up to one third(peak to peak) for bunch length. Thus the uncertainty for asingle shot is ∆lEO = 10%.Discussion and ResultsAll measurement results (as well as simulation results)are shown and compared in Fig. 2. Note that the (average)bunch length l¯ obtained with both measurement methodsagrees well (upper plot), but the standard deviation of thedistributionsσl =√1N − 1ΣNi(l¯ − li)2(4)(lower plot) show significant differences. For the valuesobtained by EOSD, there is an increase for currents below0.3mA, which can be explained by a very low signal to noiseratio. For any other case (real) fluctuation of the actual lengthgive an important contribution to σl . The fact that streakcamera measurements show lower values for the fluctuationcan be explained by the averaging that even plays a role forslow burst: The slow time axis was set to 1ms, the fastestfluctuation always happens with f s = 7.7 kHz (cf. Fig. 3).All results obtained for the bunch length (see upper plotin Fig. 2) match very well. There is a slight tendency that theEOSD’s average length is smaller than the one obtained bythe SC. A possible explanation is that the single SC lengthsare deducted from bunch profiles averaged over 1ms.For the fluctuation of bunch length (see lower plot inFig. 2) the MSCI using bursting frequencies as input param-eters match the real SC measurements almost perfectly. TheVFPS data also agrees within the uncertainty estimation. Asone would expect, the fluctuation decreases when the currentis near the bursting threshold. The EOSD measurements forthe lower currents (Ib < 0.3mA) are influenced by a badshot-to-shot accuracy. For the higher currents the EOSDresults are larger but in the same range as the ones obtainedusing the SC. This feature is expected because of the aver-aging in every SC image. Also note that the change in thefluctuation obtained by SC is mainly caused by the changingbursting frequency: While over a wide current range thebunch length changes proportional to I3/7, the measuredfluctuation changes exponentially.CONCLUSION AND OUTLOOKThis paper has presented both simulations and systematicmeasurements of the length of bunches above the burstingthreshold. It has been shown that the bunch length fluctuateswith the main frequencies of the THz bursts. Since at theSC the bursting frequency plays a big role when measuringlength fluctuations, even a simple model for the amplitudegives sufficient results. Optimizations at the EOSD setupand continued work on the VFPS will help to also find amore accurate model for the fluctuation amplitude.ACKNOWLEDGMENTSWe would like to acknowledge the ANKA infrared groupfor allowing access to the IR1 and IR2 beam lines.Work supported by the Initiative and Networking Fund ofthe Helmholtz Association (Grand No. VH-NG-320), theGerman Federal Ministry of Education and Research (GrantNo. 05K10VKC and 05K13VKA) and by the HelmholtzInternational Research School for Teratronics (HIRST).REFERENCES[1] Y.-R. E. Tan et al. “Low Alpha Configuration For GeneratingShort Bunches”, PAC 2009, TH6PFP009.[2] Advanced Compound Semiconductor Technologies GmbH,Merckstr. 25, D-64283 Darmstadt, Germany; www.acst.de[3] M.Klein “Optics Calculations and Simulations of LongitudinalBeam Dynamics for the Low-alpha Mode at ANKA”, VerlagDr. Hut, München.[4] V. Judin et al. “Bursting Patterns of Coherent Synchrotron Ra-diation in the ANKA Storage Ring”, IPAC 2013, WEPEA011.[5] N. Hiller et al. “Status of Single-Shot EOSD Measurement atANKA”, IPAC 2014, WEOBB02.Proceedings of IPAC2014, Dresden, Germany MOPRO06802 Synchrotron Light Sources and FELsA05 Synchrotron Radiation FacilitiesISBN 978-3-95450-132-8239 Copyright©2014CC-BY-3.0andbytherespectiveauthors

Fluctuation of bunch length in bursting CSR: Measurement and simulation

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Fluctuation of bunch length in bursting CSR: Measurement and simulation

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