Observation of Vertical Betatron Sideband due to Electron Clouds in the KEKB LER ∗ J. W. Flanagan, K. Ohmi, H. Fukuma, S. Hiramatsu, and M. Tobiyama High Energy Accelerator Research Organization (KEK) E. Perevedentsev Budker Institute of Nuclear Physics (Dated: February 2, 2008) 5 Theeffectsofelectroncloudsonpositively-chargedbeamshavebeenanactiveareaofresearchin 0 recentyearsatparticleacceleratorsaroundtheworld. Transversebeam-sizeblow-upduetoelectron 0 clouds has been observed in some machines, and is considered to be a major limiting factor in the 2 development of higher-current, higher-luminosity electron-positron colliders. The leading proposed n mechanism for beam blow-up is the excitation of a fast head-tail instability due to short-range a wakes within the electron cloud. We present here observations of betatron oscillation sidebands in J bunch-by-bunch spectra that may provide direct evidence of such head-tail motion in a positron 9 beam. 1 ] The development of clouds of electrons in positively- h charged-beamstoragerings has been observedat several p - machines,includingtheKEKBLowEnergyRing(LER), c a3.5GeVpositronstorageringwhichispartoftheKEK c a B-Factory. Observations at the KEKB LER of betatron . tune shifts along a bunch train via gated tune meter [1], s c and of transverse bunch size along the train via high- si speed gated camera [2] and streak camera [3], show a y characteristicincreaseoftransversetuneshiftsandbeam h size starting near the head of the train, reaching satura- p tion at some point along the train. Simulations of elec- [ tron cloud density due to photo-electrons being drawn 3 towards the positron beam have shown a similar build v up of cloud density along the train, reaching saturation FIG.1: Two-dimensionalplotofverticalbunchspectrumver- 9 at some point [4, 5]. Electrons from the cloud have also sus bunch number. The horizontal axis is fractional tune, 4 from 0.5 on theleft edge to 0.7 on the right edge. The verti- 1 been measured directly via electrode [6]. Solenoids have cal axis is bunch number in the train, from 1 on the bottom 7 beenwoundaroundapproximately95%ofthedriftspace edge to 100 on the top edge. The bunches in the train are 0 in the LER, with a maximum field at the center of the spaced 4 RF buckets (about 8 ns) apart. The bright, curved 4 beam pipe of 45 Gauss [7]. The beam size blow-up has line on the left is the vertical betatron tune, made visible by 0 / been observedto occur above a threshold averagebunch reducingthebunch-by-bunchfeedbackgainby6dBfromthe s current of ∼ 0.35 mA/bunch at 4-rf bucket spacing be- level usually used for stable operation. The line on the right c i tween bunches with the solenoids off; this threshold is is thesideband. s raised when the solenoids are powered on[8]. The beam y h blow-uphasbeenfoundtoreducethe specific luminosity The sideband peak first appears near the bunch- p of the affected bunches [8]. current threshold of beam blow-up – the sidebands can- : v Oneproposedmechanismforthebeamblow-updueto notbe seenwhenthe averagebunchcurrentis below the i X the presence of electron clouds is a strong head-tail in- beam-blow-upthreshold,andcanbeseenwhentheaver- r stability caused by wake fields created by the passage of age bunch currentis over the threshold. In addition, the a thebunchparticlesthroughthecloud[9]. Attemptshave presenceofthesidebandisaffectedbytheelectron-cloud- been made to observe this head-tail motion directly via suppression solenoids; for example, it has been observed streak camera [3], but have been unsuccessful, possibly to appear in bunches at 1 mA per bunch and a 4-bucket due to a lack of sufficient light intensity. A vertical side- spacing only when the solenoidsare turned off, and does band peak has been reported for a proton beam at the not appear when the solenoids are turned on. These be- CERNSPSwhichcouldbeanindicationofhead-tailmo- haviorscannotbe explainedby ordinaryhead-tail mech- tion[10],thoughnoclearsignaturehasyetbeenreported anisms; we conclude that the sidebands, like the beam at a positron machine. We report here on observations blow-up, are caused by the presence of electron clouds. of a sideband peak, above the betatron tune, which may Observationsweremadeusingsignalstakenfromapair provide direct evidence of such a coupled-mode spectral of Beam Position Monitor (BPM) electrodes, which are peak in a positron beam. mounted on the beam pipe, and measure 6 mm in di- 2 1000 0.055 2µm 10 0 10 0.100 .010101 0.5 a) F 0.e52edba 0c.5k4 Ga i0n.5:6 HiF g0.rh5a8ctio n0.6al Tu 0n.6e2 0.64 0.66 0.68 0.7 Tune Difference 00 ..0000..34005545 a) Sideband-Betatron Peak SepSSayyrnnaccthhirrooonttrrsoonn TTuunnee == 00..00224364 2m 1 1000 b) Feedback Gain: Low 0.03 0 20 B 40unch Numb e60r 80 100 µ 1 0.1 0.004 0.01 e 0.003 b) Change in Peak Seps. for Change in Synch. Tune 0.5 0.52 0.54 0.56 0F.r5a8ctio 0n.a6l T u0n.6e2 0.64 0.66 0.68 0.7 enc 0.002 1 100000 c) Feedback Off Differ 0.00 01 2m 10 e -0.001 µ 0 .11 Tun-0.002 0.01 -0.003 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0 20 40 60 80 100 Fractional Tune Bunch Number FIG. 2: Averaged spectra of all bunches with the feedback FIG. 3: Effect of changing synchrotron tune on the separa- gain a) high, b)lowand c)set tozero. Theverticalbetatron tion between sideband peak and betatron peak. In a), the peak is visible at 0.588, and the sideband peak can be seen sideband-betatronpeakseparationisplottedalongthebunch around 0.64. train for νs = 0.0246 (solid lines) and νs = 0.0234 (dashed lines). Inb),thedifferencebetweenthetwocurvesisplotted. Statistical 1-sigma error bars are shown. ameter. The difference signal from two electrodes on opposite sides of the beam pipe is detected at 2.032 GHz (=4 × f ), and recorded by the Bunch Oscilla- Thehorizontalscaleisinunitsoffractionaltune,andthe RF 2 tion Recorder (BOR), which is a diagnostic tool in the vertical scale is in units of µm . The vertical betatron bunch-by-bunch feedback system [11, 12]. The BOR it- tune can be seen as a broad, low peak at a fractional self consists of an 8-bit digitizer front-end, with a 20- tune of approximately 0.58-0.59. To the right of it can MByte memory, which is capable of storing one beam be seen the sideband peak at approximately 0.64. The centroidpositionmeasurementperbunchforall5120RF broad, pedestal-like tail to the left of the peak is due to buckets in the ring over 4096 turns. the projection of a succession of narrow peaks, one for eachbunch, which havelower tunes nearthe headof the DataweretakenattheLERon24June2004,insingle- train. beam mode (no colliding bunches in the HER) and with the majority of the solenoids turned off. The fill pattern The vertical gain of the feedback system was lowered consistedoffourtrainsofbunches,spacedevenlyaround by 6 dB, to the point where the beam started to be- the ring. Each train consisted of 100 bunches, spaced 4 come slightly unstable, as seenin oscilloscopetracesand RF buckets (≈ 8 ns) apart. In Figure 1, the spectrum as reflected in a reduced lifetime for the beam. Under for each bunch is plotted, with fractional tune on the these conditions, the verticalbetatron peak becomes en- horizontal axis and bunch number on the vertical axis. hanced, as shown in Fig. 2b, howeverthe sideband peak The betatron tune (made visible by lowering the gain amplitude is virtually unchanged. of the bunch-by-bunch feedback system) is seen as the Finally,thefeedbackwasturnedoffentirely. TheBOR left curved line. The betatron tune is seen to shift suc- was set to record the 4096 turns immediately following cessively higher as one moves from the head of the train the feedback being turned off. As seen in Fig. 2c, the towardsthetail,saturatingataroundthe40thbunch. To betatron peak grows enormously, but the sideband peak the rightoftheν peak isthe sidebandpeak,whichlike- heightisagainessentiallyunchanged. Thisindicatesthat y wise shifts along the train, until saturating a little after this peakdoesnotrespondto dipolekicksfromthe feed- the ν peak. In experiments that have been performed back system. The estimated amplitude of the motion at y over the past year, it has been observed that changing this peak is approximately 1.6 µm,or half of one percent the vertical betatron tune causes the sideband peak to oftheverticalbeamsizeof320µmatthepickuplocation. shift by an equal amount, and in the same direction as Experimentsweredonewithchangingthesynchrotron that of the betatron tune. Changing the horizontal tune tune. In one set of measurements, the RF voltage was has no effect on this sideband. reduced, which lowered the synchrotron tune by 0.0012. Figure 2a shows the observed bunch spectra with the The position of the sideband relative to the vertical be- feedback gain set at the nominal value for physics run- tatrontune for both values ofν areshowninFigure 3a; s ning,−9.45dB.Inthis plot,the Fourierpowerspectrum the sidebands are visible starting from the fifth bunch of each bunch in the ring is calculated individually, then in the train. The difference between the two curves is the power spectra of all bunches are averaged together. shown in Figure 3b. The average of the peak separation 3 100 a) Single Bunch Time Series (BPM signal) 50 W m µ 0 -50 0 0.5 1 1.5 2 0 500 1000 1500 2000 2500 3000 3500 4000 −z/σz Turn Number 210 nits) 200 b) Single Bunch Time Series (PMT signal) FIG. 5: Model focusing wake. The horizontal axis is longitu- u 190 dinal position normalized to thebunch length. arb 180 y ( 170 sit 160 0.1 en 150 nt 140 I 0 500 1000 1500 2000 2500 3000 3500 4000 0.05 Turn Number e n FIG. 4: Example time series of single bunches taken via a) u 0 BPM and b) PMT. Different bunchesare shown for each de- T tector; the data were taken within one minute of each other. A burst-like behavior is visible in the BPM signal. A fast −0.05 ramp-up behavior with a similar rise-time as the BPM burst isseen inthePMTsignal, followed byagradualramp-down. 0 2 4 6 8 10 over all bunches is not statistically different from zero. cR/Q [m- 2 ] ×106 ObservationshavealsobeenmadeusingthesameBOR memory recorder, but using a fast photo-multiplier tube FIG. 6: Examplemode spectrum for model focusing wake at (PMT) as input device instead of a BPM electrode. A νs=0.022 (dashed lines) and νs=0.024 (solid lines). Hamamatsu H6780 PMT, was set up to record the light intensity from a focused image of the beam using syn- chrotron radiation. The image was partially obscured in nate. During the bursts of violent dipole motion, the the verticaldirection, leaving only the upper edge of the beam size increases by a further ≈ 5% from its already image visible. The spectra obtained via PMT wereiden- blown-up state. After it blows up, the dipole motion is tical to those obtained from the BPM electrode, though temporarilyabsent,as the emittance of the beamdamps with a lower signal-to-noise ratio. The amplitude of the down. peak seen by PMT can only be crudely estimated, but One possible interpretation for this sideband is that agreesroughlywiththatseenbytheBPMelectrode. One feature that the PMT can detect that the BPM cannot is changes in the beam size. Sideband Peak Height Along Train The time-series data of the BPM, shown in Fig. 4a, 20 reveala burst-liketime structureto the sidebandoscilla- tions. The sideband peak is present as a low level oscil- 2) lation that suddenly grows and damps in a burst lasting µm 15 ∼500 turns (5 ms). A break down of the data into 512- ht ( g turn slices shows that the sideband peak is seen most ei H strongly during the burst, and disappears entirely just k 10 a e after the burst. P d n In the PMT data, as seen in Fig. 4b, a similar a b e 5 500-turn-durationphenomenonisobservablewhereinthe d Si light level (beam size) increases over the course of 500 turns, then slowly damps afterwards, over the course of Synchrotron Tune = 0.0237 Synchrotron Tune = 0.0203 ∼ 1500 turns. A slice-by-slice breakdown of such events 0 10 20 30 40 50 60 70 80 90 100 Bunch Number reveals that the sideband peak is a maximum during the ramp-up, and disappears momentarily just after the FIG. 7: Peak heights of maximum-amplitude frequency bins burst. in sideband region of bunch spectrum, plotted for the first Thetwosetsofobservationssuggestthatintheblown- 100 bunchesin thetrain, for two valuesof νs. Error bars are up state, a series of bursts and quiescent periods alter- 1-sigma statistical error bars. 4 it is a signature of mode-coupling due to the head-tail frequencybinintheregionofthesidebandwasfoundfor instabilitypredictedbyOhmi,ZimmermannandPereve- each bunch in the train, and the peak heights of those dentsev [13]. A notable feature of the side band is that maximum bins were averaged together within each set. it occurs on the upper side of the betatron peak, which The average peak heights, and 1-sigma statistical error suggests that the effective wake function in the region bars at each synchrotron tune are plotted as a function of the tail of the bunch is a focusing wake. A possi- of bunch number along the train in Fig. 7. As can be ble mechanism for producing such a wake is a pinch- seen, the development of the sideband peak height oc- ing effect on the electron cloud. Simulations of wakes cursearlierinthe trainatthe lowersynchrotrontune, in that change from defocusing to focusing with distance agreement with expectation. along the bunch have been found in simulations using Simulations and linear theory also indicate that for a the KEKB parameters [13, 14]. given cloud density, larger beam sizes should be more When the synchrotron tune is changed, the average stable due to a weaker beam-cloud interaction [13]. The separation between the sideband peak and the betatron burst-like activity of the blown-up beam may be the peak does not change significantly. In the case of strong result of the beam size varying around some threshold head-tail instability, the coupled mode frequency does value, as the bunch alternates between states of emit- notnecessarilydependstronglyonν . Asanillustration, tance growth due to the instability occurring when the s mode spectra were generated using a toy model with an beam size is below the threshold, and the beam size airbag charge distribution and a simple effective wake, damping down once over the threshold. shown in Fig. 5, which uses a resonator-like wake W, Abetatronsidebandpeakhas beenfoundinthe verti- increasing along (−z) to represent the enhancement of caltune spectrum of positronbunches in the presence of the wake near the tail of the bunch due to pinching of beam-size blow-up due to electron clouds. The sideband the electron cloud: peak is on the upper side of the betatron peak in terms of fractional tune, first appears early in the bunch train, and the separation between this peak and the betatron R z W(z)=c e−αz/csinωR , (1) tune peak increases going along the train, until it satu- Q c rates at a certain point. The best explanation for it is where α = ω /4, and ω = 2π ×40 GHz. (Note: the thatitisasignatureofthe head-tailinstability hypothe- R R oscillationfrequencyofcloudelectronsascalculatedfrom sizedtoexplaintransversebeamblow-upduetoelectron theLERbeamsizeandpositronchargedensityis∼2π× clouds. The presence ofthis sidebandpeak also provides 43 GHz.) a sensitive diagnostic for the presence of electron clouds. Plots of mode spectra as a function of effective R/Q The authors wouldlike to thank ProfessorK.Oide for are shown in Fig. 6 for synchrotron tunes of 0.022 and hissupportofthiswork,andDrs. Y.Funakoshi,T.Ieiri, 0.024. As can be seen, the tune of the coupled mode H. Ikeda, H. Koiso, M. Masuzawa and A. Valishev for in the region far above the coupling threshold does not many fruitful discussions. changesignificantlywiththesynchrotrontune. However, the coupling point between the l = +1 mode (ν +ν ) y s andthe l=+2mode(ν +2ν )shifts to the right. Since y s the electron cloud density increases along the leading ∗ john.fl[email protected] bunches of the train, this change in the threshold would [1] T. Ieiri et al., Phys. Rev. STAB 5, 094402 (2002). lead one to expect the position of the first bunch to ex- [2] J.W.Flanaganetal.,ProceedingsofEPAC2000p.1119 hibitthesidebandshouldshiftasthesynchrotrontuneis (2000). changed. Toinvestigatethisbehaviornearthethreshold, [3] H. Fukuma et al., Proceedings of 30th Ad- data originally taken on 23 December 2003 at two dif- vanced ICFA Beam Dynamics Workshop on ferent values of the synchrotron tune were re-examined. High Luminosity e+e- Colliders http://www- conf.slac.stanford.edu/icfa03/papers/WGB04.PDF The LER was in single beam mode, with all solenoids (2003). off. The bunches were stored at a four-bucket spacing, [4] K.Ohmi, Phys. Rev. Lett. 75, 1526 (1995). at a bunch current of 0.52 mA/bunch. Due to the lower [5] F. Zimmermann, CERN-SL-Note-2000-004 AP (2000). bunch current, the growth of the sideband peak is more [6] Y. Ohnishi et al., Proceedings of HEAC01 gradual in this data set than it is in the July 2004 data http://conference.kek.jp/heacc2001/, P1hlf19 set. (Due to a high feedback gain, the betatron peak is (2001). not pronounced enough to measure.) One set, of four [7] H. Fukuma et al., AIP Conference Proceedings 62, 357 (2002). measurements, was taken at an RF voltage of 8 MV, [8] H. Fukuma et al., Proceedings of HEAC01 andthe otherset, ofthree measurements,wastakenat6 http://conference.kek.jp/heacc2001/, P1hlf10 MV. The synchrotrontunes ofthe twosets, asmeasured (2001). from the synchrotron peak visible in the spectra, were [9] K. Ohmi and F. Zimmermann, Phys. Rev. Lett. 85, 0.0237 and 0.0203, respectively. The maximum-height 3821 (2000). 5 [10] G. Arduini et al., Proceedings of 012801 (2000). ECLOUD04 http://mafurman.lbl.gov/ [13] K. Ohmi, F. Zimmermann, and E. Perevedentsev,Phys. 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