The current knowledge of the transverse beam coupling impedance of the CERN Proton Synchrotron (PS) has been established with beam-based measurements at different energies. The transverse coherent tune shift as a function of the beam intensity has been measured in order to evaluate the total effective imaginary part of the transverse impedance in the accelerator at the energies of 7, 13 and 25 GeV. Measurements have been performed changing the vertical chromaticity
for each vertical tune scan with intensity. The data analysis revealed an increase of impedance with chromaticity for all the considered energies. The transverse impedance
can be compared with the previously evaluated theoretical impedance budget taking into account the individual contribution of several machine devices

BIANCACCI, NICOLÒ

Gilardoni, S.

Huschauer, A.

Metral, E.

MIGLIORATI, Mauro

PERSICHELLI, SERENA

Salvant, B.

Wasef, R.

English

The current knowledge of the transverse impedance of the Proton Synchrotron (PS) has been established with beam-based measurements at different energies. The transverse coherent tune shift as a function of the beam intensity has been measured in order to evaluate the total effective imaginary part of the transverse impedance and its localization in the accelerator at the energies of 2, 7, 13 and 25 GeV. Measurements have been performed changing the chromaticity for every tune shift scan with intensity. The data analysis revealed an increase of impedance with chromaticity for all the energies considered. That transverse impedance can be compared with the previously evaluated theoretical impedance budget taking into account the individual contribution of several machine devices. The missing impedance is finally highlighted

Persichelli, Serena

Biancacci, Nicolo

Gilardoni, Simone

Huschauer, Alexander

Migliorati, Mauro

Métral, Elias

Salvant, Benoit

Wasef, Raymond

CERN Document Server

Chromaticity Dependence of the Transverse Effective Impedance in the CERN Proton Synchrotron

BIANCACCI, NICOLÒ

Archivio della ricerca- Università di Roma La Sapienza

CHROMATICITY DEPENDENCE OF THE TRANSVERSE EFFECTIVEIMPEDANCE IN THE CERN PROTON SYNCHROTRONS. Persichelli∗, CERN, Geneva, Switzerland and University La Sapienza, Rome, ItalyM. Migliorati, University La Sapienza, and INFN-Roma1, Rome, ItalyN. Biancacci, S. Gilardoni, A. Huschauer, E. Métral, B. Salvant, R. Wasef,CERN, Geneva, SwitzerlandAbstractThe current knowledge of the transverse beam couplingimpedance of the CERN Proton Synchrotron (PS) has beenestablished with beam-based measurements at different ener-gies. The transverse coherent tune shift as a function of thebeam intensity has been measured in order to evaluate thetotal effective imaginary part of the transverse impedancein the accelerator at the energies of 7, 13 and 25 GeV. Mea-surements have been performed changing the vertical chro-maticity for each vertical tune scan with intensity. The dataanalysis revealed an increase of impedance with chromatic-ity for all the considered energies. The transverse impedancecan be compared with the previously evaluated theoreticalimpedance budget taking into account the individual contri-bution of several machine devices.INTRODUCTIONCoherent Transverse Tune ShiftThe number of betatron oscillations per turn of the bunchcenter of mass is called coherent betatron tune, and it isdefined asQ0 =ωβω0, (1)where ω0 is the machine angular revolution frequency andωβ is the angular betatron frequency. To perform tune mea-surements, a chirp signal is used to excite the beam, andthe variation of the intensity of the bunch allows to observea tune shift that is linear with the measured intensity. Thetransverse tunes can be measured in the PS with a BaseBand Tune system based on diode detectors, known as theBBQ [1]. The transverse position of the bunch is acquiredevery turn by a beam position monitor (BPM). High ampli-tude short pulses measured by the BPM are then sent to adiode detector, which converts the modulation of the BPMpulses, related to beam oscillations, into a signal in the audiofrequency range. This signal is then processed in order todeliver the tune content. BBQ measurements are performedhere on a single circulating bunch of particles.Measuring the tune shift with intensity gives informationon the total reactive transverse impedance. For a Gaussianbunch of r.m.s. bunch length σz traveling with velocityv = βc, the coherent tune shift with intensity ∆Q is pro-portional to the imaginary part of the total (driving plus∗ serena.persichelli@cern.chdetuning) transverse effective impedance Ze f ft by [2]∆Q = − βeI04σz√piω20 γ Q0 m0={Ze f ft}, (2)where I0 is the bunch current,Q0 is the unperturbed betatrontune, γ is the relativistic factor, e the particle charge and m0the particle mass at rest. The effective transverse impedanceis defined as the impedance weighted by the transverse bunchpower spectrum centered at the chromatic frequency ωξ :Ze f ft =∞∑p=−∞Zt (ω′)h(ω′ − ωξ )∞∑p=−∞h(ω′ − ωξ ), (3)where ω′ = ω0(p +Q0) with p an integer, ωξ = ω0 Q0 ξ/η,with ξ the chromaticity and η the slippage factor, and thepower spectrum of the Gaussian zero azimuthal bunch modeis h(ω) = exp−(ω2σ2z/c2). If the bunch length does notchange with intensity, Eq. 2 predicts a tune shift linear withbunch intensity, with a slope proportional to the imaginarypart of the transverse total effective impedance.ChromaticityThe tune variation with the momentum is a machine pa-rameter called chromaticity, defined asξ =∆Q/Q0∆p/p0, (4)where p0 is the particle momentum on the nominal closedorbit and ∆p is the momentum deviation. Chromaticities inthe PS can be measured by acquiring the tune shift whilevarying ∆p/p0. Introducing a radial offset, we generate amomentum offset that lead to a variation of the revolutionfrequency. The tune can be written as a Taylor series of ∆pp0Q(∆pp0)= Q0+Q′∆pp0+Q′′2!(∆pp0)2+...+Qnn!(∆pp0)n, (5)whereQ′ =∆Q∆ f / f0(6)and Qn are the higher order terms. The chromaticity iscomputed applying a polynomial fit on the measured data:from the linear term we can calculate the linear chromaticityasξ =Q′Q0. (7)6th International Particle Accelerator Conference IPAC2015, Richmond, VA, USA JACoW PublishingISBN: 978-3-95450-168-7 doi:10.18429/JACoW-IPAC2015-MOPJE0475: Beam Dynamics and EM FieldsD04 - Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsMOPJE047395ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2015).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.Control of the Working PointIn the PS, bending and focusing of the beam is provided bythe main magnet units; the working point, in absence of anyauxiliary magnet or coils, is determined by the momentumof the beam. For example, the bare machine at the energyof 2 GeV is working in linear condition (natural workingpoint) with measured tunes of Qx = 6.253 and Qy = 6.285,chromaticities of ξx = -0.83 and ξy = -1.12, correspondingto chromatic angular frequencies of 213 MHz and 280 MHz,respectively. To correct the effects of linear and second or-der chromaticity in the PS, the magnetic field higher ordercomponents are needed and kept under control with auxil-iary windings, called Pole Face Windings (PFW) [3]. PFWconsist of four auxiliary coils mounted on the iron pole ofeach magnet (two coils for the focusing and two for the de-focusing yoke) and they are used to control the workingpoint and chromaticity. In addition, the figure-of-eight loopcreates opposite fields in the two yokes. In this way, thehorizontal and vertical tunes, horizontal and vertical chro-maticities and non-linear chromaticity, can be controlled byfive parameters.TUNE SHIFT MEASUREMENTS AT ZEROCHROMATICITYExtraction EnergyThe measurements at the extraction kinetic energy of25.48 GeV have been performed during several MachineDevelopment (MD) sessions [4] on a dedicated cycle, pro-vided by a long extraction energy plateau, as shown in Fig. 1.The measured vertical tune shift as a function of the beamintensity is shown in Fig. 2.0 500 1000 1500 2000 2500−5000050001000015000Time [ms]Magnetic field [G]Figure 1: Magnetic field applied along the cycle used fortune shift measurements at kinetic energy of 25.48 GeV.0 50 100 150 200 2500.240.24050.2410.24150.242Intensity [1e10 ppb]Q y  MeasurementsLinear fitFigure 2: Vertical tune as a function of beam intensity mea-sured at the kinetic energy of 25.48 GeV.Intermediate EnergiesTo better understand the transverse effective beam cou-pling impedance and the indirect space charge contribution,two intermediate kinetic energies of 7.25 and 13.09 GeVhave been considered for tune shift measurements. The mea-surements have been performed in several MD sessions ona dedicated MD cycle with several long plateaux at differentenergies. The measured vertical tune shift as a function ofthe beam intensity is shown in Figs. 3 and 4. In Table 10 50 100 150 200 2500.3010.3020.3030.3040.3050.306Intensity [1e10 ppb]Q y  MeasurementsLinear fitFigure 3: Vertical tune as a function of beam intensity mea-sured at the kinetic energy of 7.25 GeV.0 50 100 150 200 250 3000.3030.3040.3050.3060.307Intensity [1e10 ppb]Q y  MeasurementsLinear fitFigure 4: Vertical tune as a function of beam intensity mea-sured at the kinetic energy of 13.09 GeV.the imaginary part of the total vertical effective impedancemeasured at different energies and zero chromaticity is sum-marized.Table 1: Imaginary part of the total vertical effectiveimpedance measured at different energies and zero chro-maticityEkin [GeV] ={Ze f ft}[MΩ/m] 4σz [ns] ξy7.25 3.51 ± 0.13 55 -0.0213.09 3.06 ± 0.12 55 -0.0225.48 2.23 ± 0.05 45 0.02TUNE SHIFT MEASUREMENTS WITHCHROMATICITY SCANSeveral MD sessions have been dedicated to investigatethe change of the imaginary part of the effective verticalimpedance with the chromaticity. To perform this measure-ment, a vertical chromaticity value was initially set usingthe PS working point application. Vertical and horizontaltunes and horizontal chromaticity were kept to fixed value,6th International Particle Accelerator Conference IPAC2015, Richmond, VA, USA JACoW PublishingISBN: 978-3-95450-168-7 doi:10.18429/JACoW-IPAC2015-MOPJE047MOPJE047396ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2015).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.5: Beam Dynamics and EM FieldsD04 - Beam Coupling Impedance - Theory, Simulations, Measurements, Code Developmentsfar from possible resonances. The setting was then remotelysent through the working point application in the CERNcontrol center to the PFW in the ring. The PS figure-of-eightloop was kept to zero. A measurement of the vertical chro-maticity was performed after each change in the workingpoint to asses the effective value. Three sets of measure-ments were performed at the kinetic energies of 7.25, 13.09and 25.48 GeV. For each energy, about ten values of verticalchromaticity have been set and measured with a dedicatedapplication. Above transition the PS operates with zero orslightly positive chromaticity. The possibility of pushingthe chromaticity to values far from zero, as well setting anegative chromaticity, was limited by the stability of thebeam in the specific magnetic cycle and by the beam lossesin the machine. After each chromaticity measurement, atune scan with intensity was performed in order to calculatethe effective vertical impedance for the given chromaticityand for the given bunch length. The three sets of tune shift−20 0 20 40 60 80 100 12002468Z y [MΩ/m]Chromatic frequency [MHz]  Ekin=7.25 GeVEkin=13.09 GeVEkin=25.28 GeVFigure 5: Imaginary part of the effective vertical impedancescan with chromatic frequency at different energies.measurements show the same increasing trend of the verticaleffective impedance with the chromatic frequency, as shownin Fig. 5.TRANSVERSE IMPEDANCE BUDGETFROM SIMULATIONSTheoretical estimations based on numerical codes andanalytical formulas have been performed in order to con-firm the measured impedance budget. The sum of transverseimpedances of each machine element, calculated analyticallyand with electromagnetic simulations, allows to computethe frequency dependence of the total machine impedance.The computed impedance model takes into account the con-tributions of indirect space charge, resistive wall, kickers,vacuum equipment (pumps, bellows, flanges valves and steptransition) and RF cavities. In Table 2, the vertical effec-tive impedances computed at different energies for the mainmachine elements groups, are summarized. Kicker mag-nets, followed by vacuum equipment, are predicted to be themost important source of transverse impedance in the PSat high energies, while RF cavities introduce a negligiblecontribution [5] [6]. The indirect space charge contributionbecomes dominant only at injection energy. In Table 3, acomparison between the impedance calculation of the ma-chine elements and impedance measurements at differentenergies, is shown.Table 2: Imaginary part of the vertical effective impedanceexpressed in MΩ/m calculated at different energies for themain machine elements groupsEkin [GeV] Kickers Vacuum SC+RW7.25 1.4 0.55 0.5813.09 1.4 0.55 0.3425.48 1.4 0.55 0.25Table 3: Comparison between the measured zero chromatic-ity vertical effective impedance and the computed verticaleffective impedance, expressed in MΩ/mEkin [GeV] Measured Computed={Ze f fy}={Ze f fy}7.25 3.51 ± 0.13 2.5413.09 3.06 ± 0.12 2.2925.48 2.23 ± 0.05 2.20CONCLUSIONSThe vertical effective impedance at zero chromaticity ofthe PS has been measured at different energies. The mea-sured impedance revealed a good agreement with the to-tal impedance of the machine computed with simulationsand numerical codes at 25 GeV. The computed impedanceslightly underestimates the measurements at intermediateenergies. This observation suggests that improvements areneeded in the indirect space charge impedance computation.A scan of the imaginary part of the vertical impedance withchromaticity has been performed, revealing an increasingtrend for all the measurements at different energies. Thiseffect, not yet predicted by the computed impedance model,is in the process of being further confirmed with other mea-surements.ACKNOWLEDGEMENTSThe authors acknowledge G. Sterbini and the CERN OPteam for useful discussions.REFERENCES[1] M. Gasior, CERN-LHC Project Report 853 (2005).[2] A.W. Chao, “Physics of Collective Beam Instabilities in HighEnergy Accelerators”, JohnWiley&Sons, (1993).[3] S. Gilardoni (ed.), “Fifty Years of the CERN Proton Syn-chrotron”, CERN, 2011.[4] S. Persichelli, “The Beam Coupling Impedance Model of theCERN Proton Synchrotron”, PhD thesis, 2015.[5] S. Persichelli, M. Migliorati, N. Biancacci, S. Gilardoni,E. Métral, B. Salvant, “The Proton Synchrotron TransverseImpedance Model”, Proc. of IPAC14, 2014, p. 4096.6th International Particle Accelerator Conference IPAC2015, Richmond, VA, USA JACoW PublishingISBN: 978-3-95450-168-7 doi:10.18429/JACoW-IPAC2015-MOPJE0475: Beam Dynamics and EM FieldsD04 - Beam Coupling Impedance - Theory, Simulations, Measurements, Code DevelopmentsMOPJE047397ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2015).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.[6] M.Migliorati, S. Persichelli, H. Damerau, S. Gilardoni, S. Han-cock, and L. Palumbo, “Beam-wall Interaction in the CERNProton Synchrotron for the LHC Upgrade”, Phys. Rev. STAccel. Beams, 16 3 (2013).6th International Particle Accelerator Conference IPAC2015, Richmond, VA, USA JACoW PublishingISBN: 978-3-95450-168-7 doi:10.18429/JACoW-IPAC2015-MOPJE047MOPJE047398ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2015).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.5: Beam Dynamics and EM FieldsD04 - Beam Coupling Impedance - Theory, Simulations, Measurements, Code Developments

Chromaticity dependence of the transverse effective impedance in the CERN Proton Synchrotron

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Chromaticity dependence of the transverse effective impedance in the CERN Proton Synchrotron

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