BESSY VSR, a scheme where 1.7 ps and 15 ps long  bunches  rms  can be stored simultaneously in the BESSY II  storage ring has recently been proposed [1]. The strong  longitudinal bunch focusing is achieved by superconducting  high gradient RF cavities. If the bunch fill pattern exhibits a  significant inhomogeneity, e.g. due to gaps, transient beam  loading causes a distortion of the longitudinal phase space  which is different for each bunch. The result are variations  along the fill pattern in synchronous phase, synchrotron fre   quency and bunch shape. This paper presents investigations  of transient beam loading and depicts the consequences on  bunch length, phase stability and longitudinal multi bunch  oscillations for the projected setup of BESSY VS

Goslawski, P.

Jankowiak, A.

Neumann, A.

Ries, M.

Ruprecht, M.

Weis, T.

Wüstefeld, G.

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INFLUENCE OF TRANSIENT BEAM LOADING ON THELONGITUDINAL BEAM DYNAMICS AT BESSY VSR∗M. Ruprecht†, P. Goslawski, A. Jankowiak, A. Neumann, M. Ries, G. Wüstefeld,HZB, Berlin, GermanyT. Weis, TU Dortmund University, Dortmund, GermanyAbstractBESSY VSR, a scheme where 1.7 ps and 15 ps longbunches (rms) can be stored simultaneously in the BESSY IIstorage ring has recently been proposed [1]. The stronglongitudinal bunch focusing is achieved by superconductinghigh gradient RF cavities. If the bunch fill pattern exhibits asignificant inhomogeneity, e.g. due to gaps, transient beamloading causes a distortion of the longitudinal phase spacewhich is different for each bunch. The result are variationsalong the fill pattern in synchronous phase, synchrotron fre-quency and bunch shape. This paper presents investigationsof transient beam loading and depicts the consequences onbunch length, phase stability and longitudinal multi-bunchoscillations for the projected setup of BESSY VSR.INTRODUCTIONThe upgrade proposal BESSY VSR [2] is based on theidea that the superposition of the voltage of two differenthigher harmonic cavity systems will allow to store shortand long bunches simultaneously. In order to separate thesynchrotron radiation from single bunches by means of amechanical chopper, they need to be placed in the centerof gaps in the bunch fill pattern. Therefore, the fill patternis proposed to have two 100 ns gaps as depicted in Fig. 2,which gives rise to potentially strong transient beam loading.TRACKING CODEA tracking code written in C++ has been developed whichuses one macro-particle per bunch for the calculations pre-sented here. The cavity-bunch interaction is calculated bymeans of phasor addition and active cavities are controlledby a feedback loop which does not act within a revolution butacts quickly from one revolution to another. This simplifiedmethod is sufficient to evaluate the effects of beam dynamicsdiscussed in this paper. Related studies, with a focus on RFcontrol are given in [3].Experimental Verification at BESSY IITransient beam loading can readily be observed atBESSY II as it is typically operated with a 200 ns gap inthe fill pattern and the 1.5GHz Landau cavities set to bunchlengthening mode. Figure 1 shows an example of measure-ments at BESSY II compared to simulations performed withthe tracking code used in this paper. Both, the data of thesynchronous phase position of each bunch, measured in ps∗ Work supported by German Bundesministerium für Bildung undForschung, partly under contract 05K13PEB, and Land Berlin.† martin.ruprecht@helmholtz-berlin.dewith respect to the nominal equidistant bucket reference,and the individual synchrotron frequencies was taken by thediagnostics of bunch-by-bunch feedback systems [4].The agreement of simulation and measurement can beconsidered satisfying. Despite some deviation, all majorfeatures, such as magnitude of phase transient, magnitudeand shape of the synchrotron frequencies are predicted bythe simulation. The deviations are expected to stem fromuncertainties from both the measurements and the input pa-rameters to the simulation, such as quality factors Q, theshunt impedances Rcs and the tuning settings. Investigationstowards identification and improving the accuracy are ongo-ing.0123456current / mA6040200204060position / ps0 50 100 150 200 250 300 350 400bunch number5.05.56.06.5f s / kHzsimulationmeasurementFigure 1: Comparison between simulation and measure-ments of synchronous phase position of each bunch (center),measured in ps w.r.t. the nominal equidistant bucket refer-ence, and synchrotron frequency (bottom) at BESSY II fora given fill pattern (top). Error bars show a statistical erroronly.BESSY VSR SETUPIn BESSY VSR, the storage ring will be equipped withfour 5-cell SC cavities, two at 1.5GHz and two at 1.75GHz.In this simulation, the normalized shunt impedance1 is setto Rcs/Q = 250Ω per cavity. In order to accelerate theapproach of the equilibrium state in this simulation, thequality factor of the cavities is set to Q = 4 × 105 and theradiation damping time to τ = 4 × 10−4 s. The 1.5GHzand 1.75GHz system are tuned to ∆ f = −11.3 kHz and∆ f = 15.3 kHz respectively to compensate for the average1 Given in circuit definition: Rcs = V2acc/(2Pdiss) with Vacc the maximumeffective accelerating voltage and Pdiss the dissipated power.Proceedings of IPAC2015, Richmond, VA, USA MOPWA0225: Beam Dynamics and EM FieldsD07 - High Intensity Circular Machines - Space Charge, HalosISBN 978-3-95450-168-7141 Copyright©2015CC-BY-3.0andbytherespectiveauthorsbeam loading. However, as the generator power is not limitedin this simulation, precise tuning is not necessary. The NC500MHz system has a combined shunt impedance of Rcs =12.4MΩ and Q = 26700 and is tuned to ∆ f = −45 kHz.The target values for the feedback controlled cavities are setto 1.5MV, 20MV and 17.5MV, for the 500MHz system,the 1.5GHz system and the 1.75GHz system respectively.Those numbers are an outcome from an optimization thatmaximizes the average bunch length of the long bunch whileensuring that there is no net energy transfer between the1.5GHz and 1.75GHz systems. The numbers are valid onlyfor the BESSY VSR baseline fill pattern shown in Fig. 2.The energy loss due to incoherent synchrotron radiationper turn is set to 178 keV for the long bunches. Short bunchesloose additional energy by coherent synchrotron radiation.The total synchrotron radiation loss for the single short bunchis set to 689 keV and for the short bunches in the train to603 keV [2]. Additional parameters can be found in Table 1.Table 1: Basic Machine ParametersParameter ValueEnergy E 1.7 GeVMomentum compaction factor α 7.1 · 10−4Total beam current I 300 mARevolution period 800 nsLongitudinal radiation damping time τz 8 msRESULTSThe variation of the relative deviation of the voltage am-plitude and the phase of all three cavity systems is shown inFig. 2 center and bottom.42024∆V / Vnominal / 10−3500 MHz1.5 GHz1.75 GHz0 100 200 300 400 500 600 700 800t / ns2.01.51.00.50.00.5phase / ◦ 500 MHz1.5 GHz1.75 GHz0.11.010.0current / mA shortlongFigure 2: Simulation of transient beam loading inBESSY VSR with the baseline fill pattern (top). The timevariation of the relative deviation of the voltage amplitude(center) and the phase (bottom) are shown for all three cavitysystems.All cavities are of high quality factor and operated atrather high fields close to zero-crossing where beam loadingprimarily acts as a phase shift. Therefore, the variations ofthe relative voltage are small, see Fig. 2 center.For the same reason, the variation in phase are more pro-nounced and relate directly to the bunch charges of the fillpattern, i.e. each bunch adds a certain value to the phase,proportional to its charge. Empty buckets cause a phaseshift in opposite direction given by the detuning which is setto compensate the average beam loading. Furthermore, forthe 1.75GHz system, the sign depends on the bucket type,long or short, because of the 180° phase difference. Still,the variation in phase is below 0.5° for all SC cavities.Synchronous Phase and Bunch ShapeThe variation in phase and amplitude of the involved cav-ity systems mean that the time-behavior of the total voltageis different at each bucket position. For even buckets (shortbunches), where all contributions sum up with the same signto achieve a high gradient, the relative effect is expected tobe small. At the buckets of the long bunches however, thecontributions of the SC cavities are supposed to cancel eachother, thus relative variations are amplified. The majority ofthe current is placed in long bunches which cause the cavityphases to shift in opposite directions for the 1.5GHz and the1.75GHz system.Figure 3 depicts the time-behavior of the total voltagein the vicinity of the nominal bucket positions for threeselected bunches. The constant synchrotron radiation losshas been subtracted so that the synchronous phase positionis to be found at V = 0. It can be seen in Fig. 3, that small50 0 50t / ps0.40.20.00.20.4V / MVbunch 51500 MHz 1.5 GHz 1.75 GHz Sum position50 0 50t / psbunch 13350 0 50t / psbunch 399Figure 3: Time-behavior of the individual contributionsand the total voltage in the vicinity of the nominal bucketposition for three selected bunches. Black circles indicatethe synchronous phase positions.changes in the phases of the SC cavity systems are enoughto significantly shift the zero-crossing of the total voltage,i.e. the synchronous phase position. In turn, the slope of thetotal voltage is different for each bunch which changes itssynchrotron frequency and bunch length.The synchrotron phase position, the synchrotron fre-quency fs and the normalized zero-current bunch lengthis shown in Fig. 4. A peak-to-peak phase transient of approx.80 ps is visible for the long bunches while the short bunchesare barely affected by the transient beam loading. The syn-chrotron frequency and analogously the bunch length showa variation of a factor of about two and exhibit their extremaapproximately in the center of the bunch trains.Touschek LifetimeThe over-all beam lifetime at BESSY VSR will be Tou-schek dominated. Despite their high electron density, henceMOPWA022 Proceedings of IPAC2015, Richmond, VA, USAISBN 978-3-95450-168-7142Copyright©2015CC-BY-3.0andbytherespectiveauthors5: Beam Dynamics and EM FieldsD07 - High Intensity Circular Machines - Space Charge, Halos6040200204060position / ps shortlong020406080f s / kHzshortlong0 50 100 150 200 250 300 350 400bunch number0.00.51.01.5σ0/σ0,BESSYII shortlongFigure 4: Simulated synchronous phase position (top), syn-chrotron frequency (center) and zero-current bunch lengthscaled to the nominal BESSY II value of 10 ps (bottom) forthe BESSY VSR baseline fill pattern shown in Fig. 2.poor lifetime, the electron loss rate of the short bunches isexpected to be manageable as their total current is ratherlow. As the number of long bunches halves in BESSY VSRcompared to BESSY II, the bunch charge doubles and anelongated long bunch would be desirable.Unfortunately, these simulations show that the effect oftransient beam loading prevents a significant average elon-gation of the long bunches. While decreasing the amplitudeof the 1.5GHz cavity system or increasing the amplitude ofthe 1.75GHz cavity system increases the bunch length fora small number of long bunches, the majority of bunchesbecomes shortened, consequently lowering the Touscheklifetime, see Fig. 5. The elongation of a single long bunchis limited by the non-linear behavior of the potential, result-ing in a bunch no longer than approximately 2.5 times thenominal BESSY II value and has been taken into account inthe averaging in Fig. 5 right panel.17.0 17.5 18.0voltage 1.75 GHz / MV050100150200250300350400bunch0.500.751.001.251.501.752.002.252.5017.0 17.5 18.0voltage 1.75 GHz / MV0.70.80.91.01.1σ0/σ0,BESSYIIFigure 5: Scaled bunch lengths (color code) vs. voltageof the 1.75GHz cavity system for all bunches (left) andaveraged over all bunches (right).Landau DampingSignificant progress in the development of higher ordermode damped SC cavities has been made [5]. Yet the issueof higher order mode driven coupled bunch instabilities inBESSY VSR, as discussed in [6], may continue to be achallenge and the question whether a mitigation by meansof Landau damping is possible remains of interest.The Landau damping for an arbitrary, discrete distribu-tion can be evaluated by means of a dispersion relation [7,Eq. 2.12, Eq. 2.18], d(ω) = Iωr Z , where the dispersionfunction d contains all machine parameters, the fs distribu-tion and the (radiation) damping time τ.In Fig. 6 right panel, d is drawn at the threshold for thegiven fs distribution (left panel) and for comparison for acase with constant fs. Both cases assume τ = 8ms.The damping performances can be read out from the ra-dius of the IωrZ-circle intersecting with d. In this case,Landau damping increases the damping performance by afactor of 14.7 compared to radiation damping. This is about50% more than the present bunch-by-bunch feedback perfor-mance of BESSY II [4] and could intentionally be furtherincreased by small changes in the tuning of the SC cavitysystems. However, the latter comes along with a reductionof the Touschek lifetime.5 6 7 8 9 10 11fs / kHz0510152025bunchesRMS: 1.341 kHz10-2 10-1 100Re(d) / (MV GHz)0.30.20.10.00.10.20.3Im(d) / (MV GHz)threshold with fs spreadIωrZ-circle with fs spreadthreshold no fs spreadIωrZ-circle no fs spreadFigure 6: Left: Distribution of the synchrotron frequency ofthe long bunches. Right: Complex plane of the dispersionfunction at the instability threshold (solid lines) and IωrZ-circles (dashed lines) indicating the maximum current.CONCLUSIONSThe calculations in this paper have shown that transientbeam loading is significant in BESSY VSR. It poses a limiton the maximum achievable elongation of the long buncheswhich limits their Touschek lifetime. On the other hand, ifnecessary, transient beam loading could be used to obtainLandau damping to mitigate coupled bunch instabilities,however, only as a trade-off to lifetime.REFERENCES[1] G. Wüstefeld et al., IPAC 11, San Sebastián, Spain, p. 2936.[2] A. Jankowiak, J. Knobloch, P. Goslawski, N. Neumann, edi-tors, “BESSY VSR – Technical Design Study”, Helmholtz-Zentrum Berlin, 2015, to be published.[3] A. Neumann et al., IPAC 15, MOPHA010, these proceedings.[4] A. Schälicke et al., IPAC 14, Dresden, Germany, p. 1733.[5] A. Vélez et al., IPAC 15, WEPMA013, these proceedings.[6] M. Ruprecht et al., IPAC 14, Dresden, Germany, p. 1659.[7] Olaf Naumann, “Landau Damping of Longitudinal Multi-Bunch Instabilities in Electron Storage Rings”, PhD Thesis,Technische Universität Berlin, 1999.Proceedings of IPAC2015, Richmond, VA, USA MOPWA0225: Beam Dynamics and EM FieldsD07 - High Intensity Circular Machines - Space Charge, HalosISBN 978-3-95450-168-7143 Copyright©2015CC-BY-3.0andbytherespectiveauthors

Influence of Transient Beam Loading on the Longitudinal Beam Dynamics at BESSY VSR

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Influence of Transient Beam Loading on the Longitudinal Beam Dynamics at BESSY VSR

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