Radio Frequency noise induced bunch lengthening can strongly affect the Large Hadron Collider performance through luminosity reduction, particle loss, and other effects. Models and theoretical formalisms demonstrating the dependence of the LHC longitudinal bunch length on the RF station noise spectral content have been presented*,**. Initial measurements validated these studies and determined the performance limiting RF components. For the existing LHC LLRF implementation the bunch length increases with a rate of 1 mm/hr, which is higher than the intrabeam scattering diffusion and leads to a 27% bunch length increase over a 20 hour store. This work presents measurements from the LHC that better quantify the relationship between the RF noise and longitudinal emittance blowup. Noise was injected at specific frequency bands and with varying amplitudes at the LHC accelerating cavities. The experiments presented in this paper confirmed the predicted effects on the LHC bunch length due to both the noise around the synchrotron frequency resonance and the noise in other frequency bands aliased down to the synchrotron frequency by the periodic beam sampling of the accelerating voltage

Baudrenghien, P.

Butterworth, A.

Fox, J.D.

Mastoridis, T.

Molendijk, J.

Rivetta, C.

English

Mastoridis, T

Fox, J D

Rivetta, C H

Baudrenghien, P

Butterworth, A C

Molendijk, J C

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Studies of RF Noise Induced Bunch Lengthening at the LHC

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STUDIES OF RF NOISE INDUCED BUNCH LENGTHENINGAT THE LHC∗T. Mastorides† , C. Rivetta, J.D. Fox, SLAC, Stanford, CA 94309, USAP. Baudrenghien, A. Butterworth, J. Molendijk, CERN, Geneva, SwitzerlandAbstractRadio Frequency (RF) noise induced bunch lengtheningcan strongly affect the Large Hadron Collider (LHC) per-formance through luminosity reduction, particle loss, andother effects. This work presents measurements from theLHC that better quantify the relationship between the RFnoise and longitudinal emittance blowup and identify theperformance limiting RF components. The experimentspresented in this paper confirmed the predicted effects onthe LHC bunch length growth.BEAM DIFFUSION WITH RF NOISEFollowing [1] and [2], the bunch length growth rate canbe estimated bydσ2τdt=dσ2φω2RF dt=ω2s2πω2RFSφ(fs) (1)= 2στdστdtwhere ωRF is the RF angular frequency, ωs = 2πfsis the angular synchrotron frequency, and Sφ(f) is thephase noise spectral density experienced by the beam (inrad2/Hz).Since the beam is a very high Q resonator at the syn-chrotron frequency fs, the beam sampled powerPn is dom-inated by the noise power spectral density around kf rev ±mfs where frev is the revolution frequency, k an integer,and m is the azimuthal mode number (m = 1 for dipolemodes, m = 2 for quadrupole modes etc). In this work wefocus on m = 1, since this mode dominates the diffusionof the bunch core, with the LHC bunch length (250-375 ps)small compared to the bucket width of 675 ps.LHC MEASUREMENTSDedicated measurements with protons [3] and ions wereconducted to better quantify the relationship between thesampled noise power and the bunch length, and also to bet-ter understand the effect of the BPL.ProtonsIn this study, the Beam Phase Loop (BPL)1 gain was var-ied which had a significant effect on the noise power spec-∗Work supported by the U.S. Department of Energy under contract #DE-AC02-76SF00515 and the US LHC Accelerator Research Program(LARP).† themis@slac.stanford.edu1The Beam Phase Loop (BPL) is a narrow bandwidth loop that actson the VCXO to damp out barycentric longitudinal motion around thesynchronous phase. As such, it damps out longitudinal motion aroundtral density around fs (k = 0), and consequently the noisepower sampled by the beam. The wideband spectral den-sity for RF station 6 of Beam 2 (RF station 6B2) is shownin Fig. 1, as a function of the BPL gain.100 101 102 103 104 105 106 107−180−160−140−120−100−80−60−40Frequency (Hz)Noise (dBc/Hz)  G = 1125G = 281G=140G=20G=5G=0Figure 1: RF station 6B2 noise spectral density with BPLgain.Figure 2 shows the effect of the BPL gain settings on thelongitudinal bunch length for Beam 2.0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000100105110115120125130135140145150Time (s)Bunch Length (ps)  DataG = 1125G = 281G=140G=0G=20G=5Figure 2: Beam 2 Bunch Length with time.The growth rate of the longitudinal bunch length can beapproximated from these figures. Using Eq. 1, and the mea-sured accelerating voltage noise spectrum it is then possibleto compute the estimated bunch length growth rate for eachsetting and compare with the measured growth rates. Re-sults are presented in Table 1 for Beam 2 (results for Beam1 are omitted due to space limitations). One can see thethe synchronous phase, motion driven by noise in the RF system or othermechanisms.Proceedings of 2011 Particle Accelerator Conference, New York, NY, USA MOODS3 Beam Dynamics and EM Fields Dynamics 04: Instabilities 91 Table 1: Bunch Growth Rate Dependence on BPL Gain andNoise Power for B2BPL gain Estimated Measureddσ2τ/dt dσ2τ/dt dστ/dt(ps2/hr) (ps2/hr) (ps/hr)0 19000 22500 915 12800 12900 4720 5500 2800 8140 2900 1200 5281 1250 800 41125 1000 800 3clear correlation between the scaled bunch length as esti-mated by Eq. 1 and the longitudinal emittance growth. Asexpected, the agreement is better for higher noise levels,since at those points the Intra-Beam Scattering (IBS) con-tributions are insignificant and there is less uncertainty inthe bunch length growth estimation.IonsThrough these initial measurements, it was evident thatthe growth rate of the bunch length is strongly related tothe accelerating voltage phase noise power spectral den-sity around fs + kfrev, as predicted in [4]. For a morequantitative and accurate study, a technique was developedto inject noise of controllable amplitude in a narrow bandaround the synchrotron sidebands of a set revolution har-monic (k = 1 for these measurements). Measurementswere then conducted in November 2010 using ions at 3.5ZTeV, with four equidistant non-colliding bunches of 7 10 9intensity per ring. The initial bunch length was approxi-mately 160 ps for both beams. The total RF voltage was setto 12 MV. The bunch emittance was blown up transverselyto reduce IBS.Noise was injected in one RF cavity per ring for thismeasurement, with a bandwidth of 10 Hz from f s − 10 tofs. The injected noise power level was varied during thismeasurement. Figure 3 shows the power spectral densityof the various levels of injected noise around frev + fs andFigure 4 shows the resulting bunch length growth for Beam1, with linear fits for each noise level.The bunch length growth in ps/hr can be determinedby the slope of the linear fit. Of course, the accuracy ofthese estimates are limited by the length of each time seg-ment and the granularity of the BQM measurements. Table2 shows the results for both beams (the negative numbersin the end are due to substantial beam loss). In the earlystages of this measurement (up to the first -76 dBc/Hz levelin bold), the bunch is short enough that the growth is dom-inated by IBS. This background level of about 40 ps/hris present until the bunch grows sharply from 210 ps to240 ps and is mostly attributed to IBS. As the bunch growslonger, the background growth (from IBS plus the nomi-nal RF noise) drops to about 20 ps/hr. It is also evident−100 −80 −60 −40 −20 0 20 40 60 80 100−130−120−110−100−90−80−70Frequency (Hz)Injected Noise 10log(rad2/Hz)  −70 dBc/Hz−76 dBc/Hz−82 dBc/Hz−85 dBc/Hz−88 dBc/Hz−94 dBc/Hz−100 dBc/HzFigure 3: Levels of injected noise around frev + fs. Hori-zontal axis shifted by frf + frev.0 2000 4000 6000 8000 10000 12000150200250300350400Bunch Length (ps)Time (s)Figure 4: Beam 1 bunch length growththat the threshold for the injected noise is between -82 and-85 dBc/Hz; since in the former case there is no noticeablechange from the background level, whereas in the latterthere is a measurable increase in the bunch length growthrate.The estimated growth from Eq. 1 is shown for all thenoise levels higher than or comparable to the noise thresh-old. There is good agreement with the measurements. Thereported values are dστ/dt rather than dσ2τ /dt, so there isan additional dependence to σ.LHC RF NOISE THRESHOLDSince the bunch length growth rate dσ/dt is approxi-mately proportional to the RF noise power, it is possibleto estimate a noise threshold to reach a growth rate of 2.5ps/hr (or equivalently a 4σ growth rate of 10 ps/hr). Thisrate achieves an acceptable lifetime and is comparable tothe IBS growth.MOODS3 Proceedings of 2011 Particle Accelerator Conference, New York, NY, USA Beam Dynamics and EM Fields Dynamics 04: Instabilities 92 Table 2: Bunch Length Growth as a Function of the PowerSpectral Density (PSD) of the Injected Noise – Referred toa Single Sideband (SSB)PSD B1 dστ/dt B2 dστ/dt Estimated(dBc/Hz) (ps/hr) (ps/hr) (ps/hr)background 60 72-100 45 40-94 44 34-88 42 39-82 41 68 40-76 119 128 150background 19 30-82 45 49 35background 23 20-85 21 26 20background 20 6-76 119 140 125background 12 16-76 at 3fs 35 -6-70 352 580 380-450background -1 1-70 at 3fs -49 -52At the time of the proton measurements the noise injec-tion capability was not implemented. As a result, the high-est RF noise level for the proton data occurred when theBPL was off, with a SSB noise PSD of approximately -85 dBc/Hz at the fundamental band (k = 0). In this case,the fundamental band is dominating, so we do not needto include the other contributions at fs + kfrev. A bunchlength growth rate of about 100 ps/hr was measured withthis configuration. Therefore, to achieve 2.5 ps/hr the SSBnoise power spectral density should be approximately -101dBc/Hz. This noise threshold is per cavity and assumesuncorrelated noise sources [5].During the ion measurements, the injected noise poweris larger than the nominal RF station noise, so that thebunch length growth rate dσ/dt is approximately propor-tional to the injected noise power, if the the noise is sig-nificantly large to be the dominant contribution over IBS.For this reason and since the beam loss is not too high toaffect the accuracy of the estimate, the SSB PSD level of-76 dBc/Hz is used for the noise threshold estimate. Atthat noise level, the growth rate was estimated to about 130ps/hr. Scaling to 2.5 ps/hr, we get a threshold of approxi-mately -93 dBc/Hz for a single cavity (SSB). The thresh-old adjusted for all 8 RF cavities is then -102 dBc/Hz. Notsurprisingly, the estimates for protons or ions are in closeagreement.The cumulative PSD from the double synchrotron side-bands around each of the 30 revolution harmonics betweenfrev and the end of the closed loop cavity bandwidth (ap-proximately 300 kHz) is approximately -110 dBc/Hz ac-cording to the LHC measurements. With the BPL on, thenoise contribution at the fs is reduced below this level.Therefore, the LHC RF noise is about 9 dB lower than thenoise level for 2.5 ps/hr growth rate, assuming the 2010LLRF configuration.CONCLUSIONSDedicated measurements were conducted in the LHC togain insight in the effect of RF noise to the longitudinalbeam diffusion. It was evident that the growth rate of thebunch length is strongly related to the accelerating voltagephase noise power spectral density around fs + kfrev, aspredicted in [4]. The noise threshold for 2.5 ps/hr growthwas estimated to -101 dBc/Hz (SSB flat noise spectral den-sity from fs to the edge of the closed loop bandwidth). A9 dB margin is achieved with the current RF configurationand the BPL on.With this formalism it is now possible to estimate theeffect of different operational and technical RF configura-tions on the LHC beam diffusion. This formalism couldalso be useful for the design of future RF systems and thebudgeting of the allowed noise.ACKNOWLEDGMENTSThe authors would like to thank the CERN BE-RF groupfor the help and support in all phases of this project. Weare grateful to E. Shaposhnikova for her insight and guid-ance during the beam diffusion measurements. The authorswould also like to thank J. Tuckmantel at CERN for all hisinspiring work on beam diffusion effects. Conversationswith R. Ruth at SLAC were very helpful for the devel-opment of the single bunch longitudinal beam emittancegrowth formalism. The US-LARP program and SLACAARD group have greatly supported this work.REFERENCES[1] D. Boussard, CERN 84-15, 1984, p. 283.[2] J. Steimel et. al., “Effects of RF Noise on Longitudinal Emit-tance Growth in the Tevatron”, Proc. PAC 2003, May 12-162003, Portland, OR.[3] T. Mastorides et. al., “LHC Beam Diffusion Dependence onRF Noise: Models and Measurements”, Proc. IPAC 2010, 23-28 May 2010, Kyoto, Japan.[4] T. Mastorides et. al., “RF system models for the CERN LargeHadron Collider with Application to Longitudinal Dynam-ics”, Phys. Rev. ST Accel. Beams 13, 102801 (2010).[5] T. Mastorides, et. al., RF Noise Effects on Large Hadron Col-lider Beam Diffusion, in preparation for submission to Phys.Rev. ST Accel. Beams.Proceedings of 2011 Particle Accelerator Conference, New York, NY, USA MOODS3 Beam Dynamics and EM Fields Dynamics 04: Instabilities 93 

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Studies of RF Noise Induced Bunch Lengthening at the LHC

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