The longitudinal coupling impedance of the CERN PS has been studied in the past years in order to better understand collective effects which could produce beam intensity limitations for the LHC Injectors Upgrade project. By measuring the incoherent quadrupole synchrotron frequency vs beam intensity, the inductive impedance was evaluated and compared with the impedance model obtained by taking into account the contribution of the most important machine devices. In this paper, we present the results of the measurements performed during a dedicated campaign, of the real part of the longitudinal coupling impedance by means of the synchronous phase shift vs beam intensity. The phase shift has been measured by using two different techniques: in one case, we injected in the machine two bunches, one used as a reference with constant intensity, and the second one changing its intensity; in the second case, more conventional, we measured the bunch position with respect to the RF signal of the 40 MHz cavities. The obtained dependence
of the synchrotron phase with intensity is then related to the loss factor and the resistive coupling impedance, which is compared to the real part of the PS impedance model

BIANCACCI, NICOLÒ

Damerau, H.

MIGLIORATI, Mauro

PERSICHELLI, SERENA

Sterbini, G.

VENTURA, LETIZIA

English

BIANCACCI, NICOLÒ

Archivio della ricerca- Università di Roma La Sapienza

MEASUREMENTS OF THE CERN PS LONGITUDINAL RESISTIVECOUPLING IMPEDANCEM. Migliorati∗1, S. Persichelli, L. Ventura, University of Rome La Sapienza and INFN-Roma1, ItalyN. Biancacci, H. Damerau, G. Sterbini, CERN, Geneva, Switzerland1also at CERN, Geneva, SwitzerlandAbstractThe longitudinal coupling impedance of the CERN PShas been studied in the past years in order to better under-stand collective effects which could produce beam intensitylimitations for the LHC Injectors Upgrade project. By mea-suring the incoherent quadrupole synchrotron frequency vsbeam intensity, the inductive impedance was evaluated andcompared with the impedance model obtained by takinginto account the contribution of the most important machinedevices. In this paper, we present the results of the measure-ments performed during a dedicated campaign, of the realpart of the longitudinal coupling impedance by means ofthe synchronous phase shift vs beam intensity. The phaseshift has been measured by using two different techniques:in one case, we injected in the machine two bunches, oneused as a reference with constant intensity, and the secondone changing its intensity; in the second case, more conven-tional, we measured the bunch position with respect to theRF signal of the 40 MHz cavities. The obtained dependenceof the synchrotron phase with intensity is then related to theloss factor and the resistive coupling impedance, which iscompared to the real part of the PS impedance model.INTRODUCTIONFirst estimations of the coupling impedance in the CERNProton Synchrotron (PS) date back to the late 1970s [1]. Fur-ther measurement campaigns were performed over the years,and, in 2012 [2], the more recent results of the inductive com-ponent of the longitudinal broadband coupling impedance(Z (p)) were obtained by measuring the quadrupolar beamtransfer function and deducing the zero amplitude syn-chrotron frequency as a function of bunch intensity. The re-sults of the measurements gave Im[Z (p)]/p = 18.2±1.2Ω,with p = ω/ω0. In addition to the measurements, longitudi-nal and transverse impedance models have been developedby taking into account important contributions of the rele-vant components of the PS [3,4]. The calculated total broadband longitudinal impedance at the frequency of the bunchspectrum cutoff was in good agreement with the measuredeffective impedance of the PS. The imaginary part of thelongitudinal impedance has been measured again in 2015after the first long shutdown, during which a whole seriesof renovation work has been carried out in the framework ofthe LHC Injectors Upgrade project [5]. In Fig. 1 the resultsof the measurements are shown, confirming the results of2012.∗ mauro.migliorati@uniroma1.it0 0.002 0.004 0.006 0.008 0.01 0.012X (1/+)1.751.81.851.91.9522.05f 2s/f s0data from 2015 campaignIm[Z(p)/p]=19.5535'3.99 OhmFigure 1: Quadrupole frequency shift vs bunch intensityobtained in the 2015 campaign of measurements. HereX = 12eNpVRFh cosφs0ω20τ3b, where e is the electron charge, Npthe bunch population, VRF the RF peak voltage, h the har-monic number, φs0 the unperturbed synchronous phase, ω0the angular revolution frequency, τb the total bunch length.In addition to the imaginary part of the couplingimpedance, a dedicated campaign of measurements has beenperformed to determine its real part. We have measured thesynchronous phase shift as a function of bunch intensity [6]by using two different techniques. The results, discussedin this paper, are compared with respect to the impedancemodel, and some considerations on observed discrepanciesbetween the model and the measurements are also presented.MEASUREMENT SETUPThe measurements of the synchronous phase shift as afunction of bunch intensity were performed at a fixed mo-mentum of 26 GeV/c, corresponding to the extraction energyof LHC-type beam in the PS, and with a single-harmonicRF system at 40 MHz (h=84). Two bunches, one with fixedintensity with a population of about Np = 2 × 1011, andthe other one with varying intensity up to Np = 3.5 × 1011protons were injected from the PS Booster in the PS with analmost constant longitudinal emittance into two diametricopposite buckets, and accelerated on the 16th harmonic ofthe revolution frequency up to a momentum of 26 GeV/c.On the flat top, the bunches were first synchronized to afixed revolution frequency of f0 = 476.82 kHz, allowingto pulse a higher-harmonic RF cavity at 40 MHz. At round150 ms before extraction, the bunches were handed overfrom h = 16 to h = 84. This rebucketing to the 40 MHzRF system was completed 140 ms before extraction. AsideMOPOR014 Proceedings of IPAC2016, Busan, KoreaISBN 978-3-95450-147-2626Copyright©2016CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code Developmentsfrom a 5 ms time window for longitudinal emittance andcurrent measurements, about 130 ms were left under station-ary conditions to perform the beam measurements. Duringthat time, the bunches were held with a constant 40 MHzRF voltage. The beam signal from a wall current monitorpick-up was used to measure the synchronous phase shiftwith two methods and with two different devices. In onecase we sent the signal directly into one channel of a 14 bit400 MS/s digitizer. In this way we could record the signalof the two bunches and measure directly the time distancebetween the two. In addition to this measurement, we alsoused a second channel to get the signal from the 40 MHzcavity as a reference, so that the distance between the refer-ence and one bunch could also be used to measure the phaseshift vs beam current. The digitizer has a relatively poorsampling rate with a maximum value of 400MS/s, but a longacquisition time with about 64 MS, allowing about 160 msof total acquisition. We also used an oscilloscope with amaximum sampling rate of 2.5 GS/s over a 4 ms. Also withthe oscilloscope we measured the distance between the twobunches and with respect to the 40 MHz cavity. A sketch ofthe measurement setup is shown in Fig. 2pick-up 40 MHz cavityFigure 2: Sketch of the phase shift measurement setup.DATA ANALYSISAn example of the pick up signal measured with the oscil-loscope over a few turns is shown in Fig. 3, with two differentintensity bunches circulating. Figure 4 shows a zoom of asingle bunch.0 1 2 3 4 5 6 7 8 9 10−0.500.511.522.5time [µs]arb.units1 turn Figure 3: Pick up signal measured over 10 µs.The same information can be obtained with the Digitizerwith a longer time interval. In order to obtain the distanceFigure 4: Oscilloscope output showing the bunch distribu-tion and the Gaussian fit.between two bunches, we fitted any distribution with a Gaus-sian curve. Even if the shape is asymmetric, the differencein the centres of mass between the two curves is negligible.We then averaged all the centres of mass for the entire timerange, obtaining a time distance between two bunches orbetween one bunch and the 40 MHz signal. As a final resultof the analysis we obtained a time as a function of bunchintensity. We made measurements with two different RFpeak voltages, 50 and 100 kV. In Fig. 5, we summarize theresults for 100 kV. The slope of the linear fit, ∆t/∆Np , canbe related to the loss factor. Indeed, in order to compensatethe energy loss per turn due to the interaction of the bunchwith the real part of the impedance, the RF system has toprovide some extra energy that, in the linear approximationof the synchrotron oscillations, is given by [7]∆E = hω0∆teVRF cos φs0 =e2NpT0∞∑p=−∞Re[Z (pω0)]λ2 (pω0) (1)where ∆t is the time shift for a given bunch intensity, T0 therevolution time, Re [Z (ω)] the real part of the longitudinalimpedance, λ(ω) the single bunch spectrum.Since the loss factor is related to the real part of theimpedance bykl =1T0∞∑p=−∞Re[Z (pω0)]λ2 (pω0) (2)we getkl = hω0VRF cos φs0∆teNp(3)By taking into account both the measurements performedwith the Digitizer and the oscilloscope, we obtained a timeshift of about (0.088 ±0.012) ns/1011 particles at 100 kV,which gives a loss factor of (0.138 ± 0.019) V/pC. With themeasurements at 50 kV, from the previous equation, oneshould expect a time shift twice higher, since the loss factorshould not depend on the total voltage if the longitudinal dis-tribution remains constant. Our measurements gave insteada factor of about 3 higher.Proceedings of IPAC2016, Busan, Korea MOPOR01405 Beam Dynamics and Electromagnetic FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsISBN 978-3-95450-147-2627 Copyright©2016CC-BY-3.0andbytherespectiveauthors0.5 1 1.5 2 2.5 3 3.5Np [1011]00.050.10.150.20.250.30.35t [ns]2 bunches, digitizer2 bunches, oscilloscope40 MHz, digitizer40 MHz oscilloscopey =(0.088'0.012)x-0.041'0.027Figure 5: Time shift versus bunch population obtained witha peak voltage of 100 kV.IMPEDANCE MODELThe real part of the impedance model was obtained in2012 by taking into account the contribution of kickers andRF cavities. From the definition of loss factor given by Eq. 2,the model gives kl = 0.044 V/pC, a factor of about 3 lowerthan the measured one. The loss factor is very sensitive tothe bunch length, and, during the measurements, we couldnot avoid some bunch length variations cycle by cycle. Inany case, a factor 3 is quite high, and it is hard to imagineone or more unidentified devices in the machine giving aloss factor higher than that of all the kickers, in particular forlong bunches as those used for these measurements. A pos-sible reason of the discrepancy could be due to the presenceof one or more HOMs which do not affect the inductive cou-pling impedance at low frequency, but produce energy lossesinteracting with the beam spectrum. These HOMs, depend-ing on their resonant frequencies, may not necessarily excitecoupled bunch instabilities. In order to check this hypothesis,we investigated some characteristics of HOMs that couldproduce a high energy loss. In Fig. 6 we show the energyloss as a function of resonant frequency at a fixed qualityfactor (Q f = 25, red line) and as a function of the qualityfactor at a fixed resonant frequency ( fr = 114 f0, black line)for constant shunt resistance Rs = 50 kΩ. The shape of theloss factor as a function of frequency remains approximatelyconstant for different quality factors. From the figure we seethat a singe HOM with Q f = 25 and fr = 114 f0 has a lossfactor of about 0.085 V/pC, which, added to that given bythe kickers and RF cavities, could explain the results of themeasurements. It is also worth mentioning that the 80 MHzcavities have a resonant frequency of about 168 f0.Of course there could be more than one single HOM pro-ducing energy losses. In Fig. 7 we show a possible scenarioadding, to the broadband impedance model, two HOMs, onewith Q f = 30, fr = 146 f0, Rs = 15 kΩ, and the other withQ f = 20, fr = 50 f0, Rs = 15 kΩ. These two modes donot affect the measurements of the imaginary broadbandimpedance, producing a small perturbation, as shown in thefigure, but, added to the kickers and RF cavity impedances,give a total energy loss of about 0.135 V/pC, this last results0 100 200 300 400 500 600 700 800 900 1000f/f000.511.52loss factor (V/C) x1011Qf=2510 20 30 40 50 60 70 80 90 100Qf00.511.52fr=114f0Figure 6: Loss factor vs frequency (Q f =25, red), and vsquality factor ( fr = 114 f0, black) for the PS parameters.being also confirmed by the simulation code MuSiC [8] andvery close to the measurements. The choice of the param-eters is quite arbitrary: other parameters and other HOMscan be suited to give the same results.0 100 200 300 400 500f/f0-1-0.500.511.52Ohm#104bunch spectrum (a.u.)Re[Ztot]Im[Ztot]Im[Z/n]=18 +Figure 7: Bunch spectrum (blue), impedance real (red) andimaginary (yellow) part with two HOMs, imaginary mea-sured impedance (green).CONCLUSIONSIn this paper we have described the measurements ofthe synchronous phase shift vs bunch intensity of the PSaccelerator. The results give us the value of the loss fac-tor, which, together with measurements of the incoherentquadrupole synchrotron frequency, allows to obtain informa-tion on the longitudinal coupling impedance. Its imaginarypart results to be about 18-19 Ohm, confirming previousmeasurements and the impedance model described in [2].The loss factor at 100 kV is about 0.138 V/pC. In this casethe impedance model gives only 0.044 V/pC, a factor threelower. A possible explanation of the discrepancy in the realpart of the impedance could be the presence of HOMs whichdo not affect the measurements of the imaginary part of theimpedance, whilst they contribute to the total loss factor.ACKNOWLEDGEMENTWe acknowledge the help and collaboration of the PS OPteam, and CERN impedance team.MOPOR014 Proceedings of IPAC2016, Busan, KoreaISBN 978-3-95450-147-2628Copyright©2016CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsREFERENCES[1] D. Boussard et al., in Proc. of PAC’79, San Francisco, Califor-nia, 1979, p. 3568.[2] M. Migliorati, S. Persichelli, H. Damerau, S. Gilardoni, S.Hancock, and L. Palumbo, Phys. Rev. ST Accel. and Beams,vol. 16, p. 031001, 2013.[3] S. Persichelli, M. Migliorati, N. Biancacci, S. Gilardoni, E.Metral, and B. Salvant, Phys. Rev. Accel. and Beams, vol. 19,p. 040101, 2016.[4] S. Persichelli, M. Migliorati, N. Biancacci, S. Gilardoni, E.Metral, B. Salvant, in Proc IPAC’14, pp. 4096-4098.[5] S. Gilardoni et al., in Proc. of IPAC’11, p. 2520.[6] J. F. Esteban Muller et al., in Proc. of HB’12, pp. 183-6.[7] R. Boni et al., Nucl. Instr. Meth. in Phys. Res. A, vol. 418, pp.241-8, 1998.[8] M. Migliorati and L. Palumbo, “Multibunch and multiparticlesimulation code with an alternative approach to wakefieldeffects”, Phys. Rev. ST Accel. and Beams, vol. 18, p. 031001,2015.Proceedings of IPAC2016, Busan, Korea MOPOR01405 Beam Dynamics and Electromagnetic FieldsD04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsISBN 978-3-95450-147-2629 Copyright©2016CC-BY-3.0andbytherespectiveauthors

Measurements of the CERN PS longitudinal resistive coupling impedance

The longitudinal coupling impedance of the CERN PS has been studied in the past years in order to better understand collective effects which could produce beam intensity limitations for the LHC Injectors Upgrade project. By measuring the incoherent quadrupole synchrotron frequency vs beam intensity, the inductive impedance was evaluated and compared with the impedance model obtained by taking into account the contribution of the most important machine devices. In this paper, we present the results of the measurements performed during a dedicated campaign, of the real part of the longitudinal coupling impedance by means of the synchronous phase shift vs beam intensity. The phase shift has been measured by using two different techniques: in one case, we injected in the machine two bunches, one used as a reference with constant intensity, and the second one changing its intensity; in the second case, more conventional, we measured the bunch position with respect to the RF signal of the 40 MHz cavities. The obtained dependence of the synchrotron phase with intensity is then related to the loss factor and the resistive coupling impedance, which is compared to the real part of the PS impedance model

Measurements of the CERN PS longitudinal resistive coupling impedance

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