Arduini, Gianluigi

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OBSERVATIONS IN THE SPS: BEAM EMITTANCE, INSTABILITIESG. Arduini, CERN, Geneva, SwitzerlandAbstractThe build-up of electron cloud observed for the LHCbeam in the SPS might induce instabilities and thereforeemittance blow-up and losses. The results of beamobservations performed in the SPS are presented.1  PRELIMINARY OBSERVATIONSDuring the machine development studies performed onthe injection and acceleration of the LHC beam in theSPS strong distortions of the signal provided by the pick-ups driving the damper were observed for batchintensities Ibatch >  2-3 x 1012 p. This phenomenon could besuppressed by the application of a solenoidal magneticfield at the pick-up location [1]. Furthermore significantincrements of the vacuum pressure were correlated to thepresence of the LHC beam for Ibatch >  4 x 1012 p [2]. Theseobservations were soon correlated to the build-up of anelectron cloud induced by the LHC beam as aconsequence of its bunch spacing.The machine studies also evidenced the need of strongnegative octupole radial strength1 in order to get a decentinjection efficiency for Ibatch > 4 x 1012 p even withdampers ON and with the pick-up solenoidal magneticfield to guarantee proper signals for the dampers.Furthermore an important emittance blow-up wasobserved during injection and acceleration.In order to get a better understanding of the aboveobservations profile and beam oscillation measurementshave been performed for the LHC beam.2  PROFILE MEASUREMENTSProfile measurements were performed by means of arotational wire scanner read by a photomultiplier withgated reading. The gate, 350 ns long, repeats every turnwith a constant delay with respect to the revolutionfrequency of the beam so that a given part of the batchcan be measured. The observation slice can be movedalong the batch by modifying the delay of the gate withrespect to the revolution frequency. In order to verify thetime constant of the read-out electronics a measurementof the profile peak height was performed as a function ofthe gate delay for a beam of given intensity. The result isshown in Fig. 1 and shows that the time constant is of theorder of a few hundreds of ns.                                                          1 This implies a positive detuning with amplitude, i.e. anincrease of the horizontal tune with the amplitude of oscillation.  0500100015002000250030003500400045000 1000 2000 3000 4000 5000 6000GATE DELAY [ns]PEAK HEIGHT [a.u.] Figure 1: Measurement of the time constant for the read-out electronics of the wire scanner.The wire scanner is located in a dispersive region (DH=2.9 m, DV= 0 m). The measurements were performed withthe TSTLHC beam [3][4], with one horizontal and onevertical damper ON, low positive chromaticity(('Q/Q)/('p/p) < 0.02) and strong negative radialoctupole component.  The results of the profilemeasurements at 4 different positions in the batch (i.e. 4different gate delays) and for different batch intensitiesare shown for the horizontal plane a few ms (Fig. 2) and600 ms after injection (Fig. 3). The data for the verticalplane are presented in Fig. 4 and 5. 0246810121500 2000 2500 3000 3500 4000POSITION IN THE BATCH [ns]4σ2 /β [10−6 m]2.5 4.5 5.5 6.5 Figure 2: Horizontal profile measurement along the batcha few ms after injection for different Ibatch (expressed in1012 p).For Ibatch >  4 x 1012 p the tail of the batch is affected byan important blow-up both in the horizontal and vertical123Chamonix Xplanes. In the horizontal plane the blow-up mainly occursat injection. In the vertical plane it continues all throughthe injection plateau as can be clearly seen consideringthe ratio between the beam size after 600 ms and that atinjection for the horizontal (Fig. 6) and vertical plane(Fig. 7). 0246810121500 2000 2500 3000 3500 4000POSITION IN THE BATCH [ns]4σ2 /β [10−6 m]2.5 4.5 5.5 6.5 Figure 3: Horizontal profile measurement along the batch600 ms after injection for different Ibatch (expressed in 1012p). 0.20.40.60.811.21.41.61500 2000 2500 3000 3500 4000POSITION IN THE BATCH [ns]4σ2 /β [10−6 m]2.5 4.5 5.5 6.5 Figure 4: Vertical profile measurement along the batch afew ms after injection for different Ibatch (expressed in 1012p). 0.20.40.60.811.21.41.61500 2000 2500 3000 3500 4000POSITION IN THE BATCH [ns]4σ2 /β [10−6 m]2.5 4.55.5 6.5 Figure 5: Vertical profile measurement along the batch600 ms after injection for different Ibatch (expressed in 1012p). 0.50.60.70.80.911.11.21.31.41.51500 2000 2500 3000 3500 4000POSITION IN THE BATCH [ns]HORIZONTAL BLOW-UP2.5 4.5 5.5 6.5 Figure 6: Beam blow-up in the horizontal plane duringthe injection plateau. 0.811.21.41.61.821500 2000 2500 3000 3500 4000POSITION IN THE BATCH [ns]VERTICAL BLOW-UP2.5 4.55.5 6.5 Figure 7: Beam blow-up in the vertical plane during theinjection plateau. 3  BEAM OSCILLATIONMEASUREMENTSIn order to understand the source of the blow-up of thetail of the batch the oscillations of the batch have beenmeasured. As for the profile measurements the beamposition measurement has been gated and six differentgate delay could be selected allowing to see six differentslices of the batch at the same turn. 1024 consecutiveturns could be acquired at every cycle. Measurementswere initially performed with an electrostatic pick-upread by a FET amplifier. This set-up is similar to thedamper pick-ups and indeed the signals it provided alsoshowed an important baseline distortion. A secondattempt was conducted by using couplers equipped by a200 MHz receiver having a 2 MHz bandwidth. In thatcase no disturbance of the signal was observed.The beam oscillations were observed at 6 consecutiveslices, each 400 ns long. In this paper slice 1 correspondsto the head of the batch and slice 6 corresponds to the tailof the batch. The measurements were performed with theTSTLHC beam [3][4] with Ibatch ~ 4 x 1012 p. Twohorizontal dampers and a vertical one were active and nooctupolar component was introduced, the chromaticityChamonix X124was small and positive (< 0.02). The chosen beamintensity offers the following advantages:x losses at injection are small, even withoutoctupoles;x the machine has a linear behaviour andinterpretation of the measurements is easier;x the machine is operated above the threshold for theonset of the beam induced electron cloud.The results of the measurements for the horizontalplane are shown in Fig. 8. A rapidly growing oscillationis affecting mainly the tail of the batch just after injection.It saturates and then it is damped. The dampingmechanism is not clear: injection losses are small at thisintensity, no significant detuning with amplitude ispresent. Possible damping mechanisms are the horizontalblow-up of the beam and/or the action of the damper. Thefrequency of the oscillation corresponds to the horizontaltune as can be observed from the Fourier analysis of thedata in Fig. 9. 090180270360450540630720810900990-40000-30000-20000-10000010000200003000040000BEAM POSITION [a.u.]TURN NUMBER1 2 3 4 5 6 Figure 8: Horizontal beam oscillations for six consecutiveslices of the batch at injection. 0.5000.5460.5920.6380.6840.7290.7750.8210.8670.9130.95902000004000006000008000001000000AMPLITUDE [a.u.]TUNE1 2 3 4 5 6 Figure 9: Fourier analysis of the horizontal beamoscillations at injection. The scale of the amplitudes hasbeen artificially compressed to show the fine structure ofthe spectrum.  The growth rate of the oscillation has been estimatedfor the different slices of the batch by fitting anexponentially growing (damped) sinusoidal function tothe data. The results are shown in Fig. 10. While the headof the batch undergoes a damped oscillation the rest ofthe batch gets unstable. The growth time is getting shorterand shorter going from the head to the tail of the batchand saturates to about 25 turns in the second half of thebatch. -80-60-40-2002040600 1 2 3 4 5 6 7SLICE NUMBERGROWTH TIME [turns] Figure 10: Growth time of the horizontal instabilityobserved at injection vs. position in the batch.  The Fourier analysis (Fig. 9) evidenced the presence ofseveral peaks of smaller amplitude with respect to thatcorresponding to the horizontal tune and to the harmonicsof the synchrotron frequency (the monitor is located in adispersive region). These peaks are more and moreintense as one moves from the head to the tail of thebatch. The frequencies of the peaks of the Fourier spectraand their evolution along the batch are shown in Fig. 11(harmonics of the synchrotron frequency excluded). 0.50.550.60.650.70.750.80.850.90.9510 1 2 3 4 5 6 7SLICE NUMBERPEAK POSITION Figure 11: Position of the peaks of the Fourier spectrumof the oscillations observed at injection vs. position alongthe batch.  An interesting feature of these peaks is that they areequidistant. A more detailed analysis shows that theappearance of these peaks is typical of an exponentiallygrowing sinusoidal function that saturates at a giventhreshold. Fig. 12 shows the Fourier spectrum of anexponentially growing sinusoidal function oscillatingwith a tune 0.637 (corresponding to the measuredhorizontal tune) and a growth time of 22.7 turns (as125Chamonix Xmeasured for the tail of the batch) for two differentsaturation levels. The secondary peaks can be easilyindividuated.  0.0E+002.0E+064.0E+066.0E+068.0E+061.0E+071.2E+071.4E+071.6E+071.8E+072.0E+070.5 0.6 0.7 0.8 0.9 1TUNEAMPLITUDE [a.u.]Saturation=32768Saturation=20000 Figure 12: Fourier spectrum of an exponentially growingsinusoidal function for two saturation levels. The tune ofthe oscillation is 0.637 and the growth time is 22.7 turns.  Another interesting feature of the measured data is thedependence of the horizontal tune on the position alongthe batch. The horizontal tune increases slightly from thehead to the tail of the batch as can be observed in Fig. 13which is simply a copy of Fig. 11 but with an expandedvertical scale. This could explain why a negative radialoctupolar component is needed to stabilise the beam; infact the detuning with amplitude induced by the octupolesenforces the tune spread observed from the head to thetail of the batch as the tail is oscillating at largeramplitudes.  0.620.6250.630.6350.640.6450.650 1 2 3 4 5 6 7SLICE NUMBERPEAK POSITION Figure 13: Horizontal tune vs. position along the batch.  Measurements performed after 30 ms (Fig. 14) and 500ms (Fig. 15) after injection show that the oscillation iscreeping from the tail into the head of the batch and thandisappears. 090180270360450540630720810900990-40000-30000-20000-10000010000200003000040000BEAM POSITION [a.u.]TURN NUMBER1 2 3 4 5 6 Figure 14: Horizontal oscillation 30 ms after injection fordifferent slices of the batch. 090180270360450540630720810900990-40000-30000-20000-10000010000200003000040000BEAM POSITION [a.u.]TURN NUMBER1 2 3 4 5 6 Figure 15: Horizontal oscillation 500 ms after injectionfor different slices of the batch.  Similar measurements were performed in the verticalplane. These show a strong damping of the injectionoscillations (Fig. 16) followed by a residual oscillationlasting for hundreds of ms (Fig. 17). The Fourier analysisof the data shows that the half-integer is the dominatingfrequency (Fig. 18-19). 090180270360450540630720810900990-8000-6000-4000-200002000400060008000BEAM POSITION [a.u.]TURN NUMBER1 2 3 4 5 6 Figure 16: Vertical oscillation at injection for differentslices of the batch.   Chamonix X126 This behaviour points to a non-optimum tuning of thevertical damper as the line on the half integer can beexplained by an excessive gain of the feedback loop. 090180270360450540630720810900990-8000-6000-4000-200002000400060008000BEAM POSITION [a.u.]TURN NUMBER1 2 3 4 5 6 Figure 17: Vertical oscillations 500 ms after injection fordifferent slices of the batch. 0.5000.5500.6000.6490.6990.7490.7990.8490.8980.9480.998050000010000001500000AMPLITUDE [a.u.]TUNE1 2 3 4 5 6 Figure 18: Fourier spectra of the vertical oscillation atinjection for different slices of the batch. 0.5000.5500.6000.6490.6990.7490.7990.8490.8980.9480.998050000010000001500000AMPLITUDE [a.u.]TUNE1 2 3 4 5 6 Figure 19: Fourier spectra of the vertical oscillation 500ms after injection for different slices of the batch.  Some measurements (at higher intensity  - Ibatch = 6 x1012 p of which 5-5.5 x 1012 p were injected - and withstrong negative radial octupolar component), wereperformed after having switched off the vertical damperto confirm the above hypothesis. These do not show anymore the residual oscillation already 30 ms after injection(Fig. 20) and the line on the half-integer disappearscompletely already at injection (Fig. 21). 090180270360450540630720810900990-8000-6000-4000-200002000400060008000BEAM POSITION [a.u.]TURN NUMBER1 2 3 4 5 6 Figure 20: Vertical oscillations 30 ms after injection fordifferent slices of the batch. Vertical dampers OFF. 0.5000.5470.5940.6410.6880.7340.7810.8280.8750.9220.969050000010000001500000AMPLITUDE [a.u.]TUNE1 2 3 4 5 6 Figure 21: Fourier spectra of the vertical oscillation atinjection for different slices of the batch. Verticaldampers OFF.  A part from the half integer line those corresponding tothe horizontal (qH= 0.637) and vertical (qV=0.602) tunesare also visible (see Fig. 18-19). The horizontal tune peakdominates at injection but its amplitude decreases withtime faster than that of the vertical tune. This can beobserved in Fig. 22 where the spectral power in twointervals centred on qH and qV is considered as a functionof the time elapsed from injection. The spectral power considered for each point is thesum of the spectral powers of the six slices constitutingthe batch. The reason for the appearance of such strongoscillations in the vertical plane at the frequencycorresponding to the horizontal tune is not clear as thebetatronic coupling was corrected to less than 0.005(closest-tune approach) before the measurement. The beam oscillation measurements confirm the resultof the beam profile measurements, presented in Section 2,showing that the tail of the batch blows-up horizontallymainly at injection while the vertical size suffers of acontinuous blow-up all through the injection plateau. Thisis consistent with the evolution of the spectral power of127Chamonix Xthe oscillation along the batch as a function of the timeelapsed from injection (Fig. 23  - horizontal plane andFig. 24 - vertical plane). These figures show that atinjection the tail of the batch is unstable mainlyhorizontally. This instability whose strength saturates inthe second half of the batch creeps into the head of thebatch after a few ms and then decays so that after 500 msvertical oscillations, mainly of the tail of the batch,dominate. 1.E+071.E+081.E+091.E+101.E+111.E+121.E+130 100 200 300 400 500 600TIME AFTER INJECTION [ms]SPECTRAL POWER0.585-0.6150.615-0.645 Figure 22: Spectral power vs. time for the tune intervals0.585-0.615 and 0.615-0.645. 1.E+091.E+101.E+111.E+121.E+131.E+141.E+150 1 2 3 4 5 6 7SLICE NUMBERSPECTRAL POWERInj 30 ms 500 ms Figure 23: Spectral power along the batch vs. time frominjection (horizontal plane). 1.E+091.E+101.E+111.E+121.E+131.E+141.E+150 1 2 3 4 5 6 7SLICE NUMBERSPECTRAL POWERInj 30 ms 500 ms Figure 24: Spectral power along the batch vs. timefrom injection (vertical plane).  In Fig. 23 and 24 the spectral power has beenintegrated between 0.5 and 0.95 to exclude thecontribution of the synchrotron frequency and itsharmonics which are not relevant for this context.4  OTHER OBSERVATIONS In occasion of other machine development sessionsperformed with the TSTLHC beam additionalobservations were performed:x For Ibatch = 6 x 1012 p losses were observed in thelast third of the batch during a few minutes afterinjection. These losses might occur at highintensity as a consequence of the blow-up of thetail of the batch observed horizontally andvertically [5].x Vertical oscillations in the range 400 to 800 MHzwere observed by means of a vertical wide-bandpick-up. These occurred at injection and thenslowly disappeared [5]. 5  CONCLUSIONS A series of measurements were performed with theTSTLHC beam to understand its behaviour at injectionand individuate possible correlation with the onset of theelectron cloud. An important blow-up of the tail of thebatch has been evidenced in both planes. In the horizontalplane this occurs just after injection. In the vertical planea continuous blow-up has been observed all through theinjection plateau. While the behaviour in the vertical plane is very likelydue to a non-optimum adjustment of the gain of thetransverse feedback the blow-up in the horizontal plane isdue to a strong instability developing just after injection.Its growth time decreases along the batch (going from thehead to the tail) and saturates at about 23 turns in the lasthalf of the batch. The amplitude of the oscillations alsosaturates and than decreases after about 100 turns. Thismight be the result of the blow-up of the beam or to theaction of the transverse feedback. After a few ms theinstability creep towards the head of the batch and thendies.  At injection the energy transfer from the horizontalto the vertical plane dominates the vertical activity. Thecoupling mechanism is not clear as the betatroniccoupling was minimised (closest tune approach < 0.005)before the experiment took place. No clear correlation with the electron cloud build-uphas for the moment been found. Possible qualitativearguments in favour of an instability induced by theelectron cloud are:x Similar threshold for the onset of the instabilityand for the electron cloud.x Stronger effect in the horizontal planex Increase of the growth rate of the instability alongthe batch (from the head to the tail) and saturationin the second half of it.Chamonix X128x Observation of high frequency (single bunch)activity. ACKNOWLEDGEMENTS I would like to thank G. Ferioli and L. Jensen for therapid implementation of the hardware and softwareneeded for the measurement of the beam profile andbeam oscillation along the batch, K. Cornelis, T.Linnecar, F. Ruggiero and F. Zimmermann for interestingdiscussions before and during the workshop. REFERENCES[1] W. Höfle, "Observation of the electron cloud effecton pick-up signals in the SPS", these Proceedings.[2] J. M. Jimenez, "Electron Cloud: SPS vacuumobservations with LHC type beams", theseProceedings.[3] D. Manglunki, "The CPS, Status and prospects fornext year", these Proceedings.[4] G. Arduini,  "Schedule and Priorities for 2000", theseProceedings.[5] T. Linnecar, private communication.129Chamonix X

Observations in the SPS: beam emittance, instabilities

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