On-line monitoring of beam quality for high brightness beams is only possible using non-invasive instruments. For matching measurements, very few such instruments are available. Therefore, a new type of quadrupole pick-up, sensitive to the beam width, has been developed for the CERN PS. A measurement system consisting of two such pick-ups has been installed in the accelerator. Using the information from these pick-ups, it is possible to determine not only the injection matching in the two planes, but also the emittances. Both measurements use the periodicity of the circular machine to eliminate a number of systematic error sources, while the statistical error is reduced by using data from several turns. The analysis can be done on each bunch separately. This is required because of the PS filling scheme, where each injected bunch comes from a different Booster ring, and therefore can have different properties. After an overview of the measurement system, some of the first measurement results are presented along with a discussion on the measurement error

Jansson, A

Søby, L

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A NON-INVASIVE SINGLE-BUNCH MATCHING AND EMITTANCEMONITOR FOR THE CERN PS BASED ON QUADRUPOLE PICK-UPSA. Jansson and L. Søby, CERN, Geneva, SwitzerlandAbstractOn-line monitoring of beam quality for high brightnessbeams is only possible using non-invasive instruments. Formatching measurements, very few such instruments areavailable. Therefore, a new type of quadrupole pick-up,sensitive to the beam width, has been developed for theCERN PS. A measurement system consisting of two suchpick-ups has been installed in the accelerator. Using the in-formation from these pick-ups, it is possible to determinenot only the injection matching in the two planes, but alsothe emittances. Both measurements use the periodicity ofthe circular machine to eliminate a number of systematicerror sources, while the statistical error is reduced by usingdata from several turns. The analysis can be done on eachbunch separately. This is required because of the PS fillingscheme, where each injected bunch comes from a differentBooster ring, and therefore can have different properties.After an overview of the measurement system, some of thefirst measurement results are presented along with a discus-sion on the measurement error.1 INTRODUCTION AND BACKGROUNDA quadrupole pick-up is a non-invasive device that mea-sures the quadrupole momentκ = σ2x − σ2y + x¯2 − y¯2. (1)of the transverse beam distribution. Here, σx and σy arethe r.m.s. beam dimensions in the x and y directions, whilex¯ and y¯ denote the beam position.The use of quadrupole pick-ups for emittance measure-ments was pioneered at SLAC[1], where six pick-ups alongthe linac were used, and the emittance and Twiss param-eters were obtained by solving a matrix equation derivedfrom the known transfer matrices between pick-ups.In rings, beam size oscillations due to injection mis-match produce sidebands to the revolution frequency har-monics at twice the betatron frequency, frev(n ± 2qh,v).The use of quadrupole pick-ups in rings has largely focusedon determining the phase and amplitude of these frequencycomponents in the raw pick-up signal[2].This paper develops the idea behind the SLAC methodfor use in rings. The quadrupole pick-ups used for thispurpose have been specially developed for the PS and op-timised to measure the quadrupole moment[3]. Two pick-ups have recently been installed in consecutive straight sec-tions (numbers 3 and 4) of the machine[4]. The optical pa-rameters at the pick-up locations are given in Table 1.The PS pick-ups measure the evolution of both positionand quadrupole moment of each bunch over several hun-Table 1: Optical parameters at pick-up locationsName βx βy Dx ∆µx ∆µyQPU 03 22.0 m 12.5 m 3.04 m0.365 0.368QPU 04 12.6 m 21.9 m 2.30 mdred turns. It is therefore possible to subtract the beam po-sition contribution from the measured quadrupole moment,and retain only the beam-size related part. Throughout therest of this paper, when referring to κ, it will be assumedthat this ’artificial centring’ has been performed. Such acorrected measurement is shown in Fig. 1.1015202530354045500 50 100 150 200Quadrupole moment, κ [mm2]Machine revolutionsQPU03QPU04Figure 1: Quadrupole moment κ measured with the PSpick-ups immediately after injection. Note the fast fila-mentation (i.e. damping) of beam size oscillations due tospace charge. The constant value after filamentation indi-cates that the correction for beam position works well.2 SIGNAL COMPONENTSThe quadrupole moment of a beam can be expanded interms of the optical parameters asκ = σ2x − σ2y = εxβx − εyβy + σ2pD2x − σ2pD2y (2)assuming linear optics with no coupling between planes.If the beam is initially mismatched in terms of Twiss func-tions or dispersion, the value of κ will vary with the numberof machine revolutions n performed as[5]κ(n) = β¯x(εx +∆εx)− β¯y(εy +∆εy) + D¯2x σ2p+ β¯xεxδβx cos(2νxn−φβx)+ β¯xσ2pδ2Dx cos(2νxn−2φDx)− β¯yεyδβy cos(2νyn−φβy)− β¯yσ2pδ2Dy cos(2νyn−2φDy )+√β¯xσ2pD¯x δDx cos(νxn− φDx) (3)0-7803-7191-7/01/$10.00 ©2001 IEEE.Proceedings of the 2001 Particle Accelerator Conference, Chicago528Here, barred parameters refer to properties of the lattice,and νx,y = 2πqx,y. The terms have been ordered so thateach line corresponds to one oscillation frequency. Startingfrom the bottom, the fourth line is a signal at the horizontalbetatron frequency, which is due to dispersion matching.This mismatch is parametrised by the vectorδDx = ∆Dx√β¯x√β¯x∆D′x + α¯x∆Dx√β¯x (4)There is no corresponding signal at the vertical betatronfrequency due to the absence of vertical lattice dispersion.The middle lines of Eq. (3) are signal components attwice the horizontal and vertical betatron frequencies.They arise from both dispersion and betatron mismatch.The betatron mismatch is parametrised byδβx =(βxβ¯x− β¯xγx+γ¯xβx−2α¯xαx2α¯xβx−αxβ¯xβ¯x)≈(∆βxβ¯xα¯x∆βxβ¯x−∆αx)(5)where the last approximation is valid for small mismatch.The first line of Eq. (3) contains the constant terms,which correspond to the steady state that is reached whenthe oscillating components have damped away. The steadystate (filamented) emittance is given byεx +∆εx = εx12(β¯xγx + γ¯xβx − 2α¯xαx)++ σ2p(∆Dx)2 + (β¯x∆D′x + α¯x∆Dx)2β¯x≈≈ εx + εx δβ2x2+ σ2pδD2x2(6)where, again, the last approximation is valid for small be-tatron mismatch.There is also an emittance increase due to mis-steeringat injection that is not included here, since normally beamsize oscillations filament much faster than beam positionoscillations due to the incoherent space charge tune shift.3 EMITTANCE MEASUREMENTIf the circulating beam is stable, the two pick-up signalsare the same each turn and given byκ1 = xβ¯x 1 − yβ¯y 1 + D¯2x 1σ2pκ2 = xβ¯x 2 − yβ¯y 2 + D¯2x 2σ2p (7)If the momentum spread is known, the system of equationscan be solved for the emittances, sinceβ¯x 1β¯y 1= β¯x 2β¯y 2(8)Thus, measuring the emittance of a stable circulating beamwith quadrupole pick-ups is rather straightforward.The statistical error due to random fluctuations in themeasurement of κ are small (less than 0.5 mm2 r.m.s.), andcan be further reduced by averaging over many consecu-tive beam passages. The dominant errors will thereforebe systematic, coming from offsets in the pick-ups and er-rors in the beta functions, lattice dispersion and momentumspread. The pick-up offsets are known from measurementsin the laboratory. Furthermore, by comparing the ampli-tude of position oscillations as measured by the two pick-ups the ratios βx1/βx2 and βy1/βy2 can be determined.The main uncertainty is thus the absolute value of thebeta function, as for any other measurement of stable-beamemittance (e.g. with a wire-scanner). The accuracy cantherefore be expected to be comparable to these methods.An emittance measurement using the pick-up system isshown in Fig. 2, and compares well with wire-scanner re-sults.00.511.522.5Emittance, ε (1σ) [µm]HorizontalQPUsWS H54WS H6400.10.20.30.40.50.60.7VerticalQPUsWS V65Figure 2: Filamented emittance of a proton beam measuredwith quadrupole pick-ups (QPU) and wire-scanner (WS).There is a good agreement. The error bar is the standarddeviation for 10 measurements.4 MATCHING MEASUREMENTAt injection, the quadrupole moment of the beam is notconstant if the beam is mismatched. To determine the pa-rameters of the injected beam, the SLAC method can bedirectly applied if the quadrupole moment is measured ona single-pass basis.An advantage in a ring, with respect to a linac, is thateach pick-up can be used several times on the same bunch,so that six separate pick-ups are not necessary (at least twopick-ups are however needed to disentangle the horizontaland vertical contributions). This reduces both the cost andthe systematic error sources. In a ring, the matrix equationto be solved is a function of only a few parameters, namelythe Twiss parameters at the pick-ups, the machine tunes,and the pick-up phase separations. The tunes and the pick-up phase separations can be determined experimentally bymeasuring phase differences and frequency of beam posi-tion oscillations in the two planes. Similarly, as pointed outpreviously, in each plane the ratio of beta functions at theProceedings of the 2001 Particle Accelerator Conference, Chicago529two pick-ups can be determined.However, space charge effects detune the beam width os-cillation frequencies. The tunes, as measured from positionoscillations, therefore only approximatively describe beamwidth oscillations. To account for this effect, instead ofsolving a system of equations derived for a fixed tune, theexpression in Eq. (3) is fitted to the measured data, witha variable tune (the phase advances between pick-ups areinsensitive to space charge effects since they are so close).In such a fit, it is also straightforward to include the ef-fect of dispersion mismatch, something that was not treatedin the original SLAC method.The horizontal dispersion mismatch is determined fromthe oscillation it induces at the betatron frequency. Dueto the absence of vertical lattice dispersion, it is not pos-sible to separate betatron and dispersion mismatch in thevertical plane, but a large vertical dispersion mismatch isnot expected. Note that the beam size oscillations due todispersion mismatch are also detuned by space charge, andtherefore the effect of dispersion can not, in general, bemeasured separately (by changing the energy of the beamand measuring the coherent response) and subtracted fromthe beam size.The new free parameters (tunes and dispersion) requiremore data points, bringing the total necessary to ten (fivemachine turns with two pick-ups). Some more pointsshould be used in the fit to control and quantify the er-ror, but using too many machine turns would deterioratethe result, since the signal is damped. Fortunately, due tothe physics of the filamentation process, the decay is notexponential, but rather follows a Gaussian-like curve. Theoscillation amplitude is therefore almost unchanged by thefilamentation process over the first couple of turns.As in the previous case, random errors are suppressed byusing data from several turns, so systematic errors arisingfrom erroneous input parameters are the main issue for theaccuracy of the measurement. The fit result can be unstable010203040500 2 4 6 8Quadrupole moment, κ [mm2]Machine revolutionsQPU03QPU04Figure 3: Theoretical expression for the quadrupole mo-ment fitted to measured data. Ten turns (20 data points)were used to determine the ten free parameters (emittances,betatron and dispersion mismatches, and the tunes).for tunes close to 0.25, and for qx = qy = 0.25 the methoddoes not work at all (which is not a great problem sincethere are beam dynamics reasons for avoiding these tunes).An example is shown in Fig. 3. Comparative measure-ments have been done using a turn-by-turn SEM grid[6],which is destructive and can only be used in rare dedi-cated machine development sessions. The results so farhave been encouraging, but is has not yet been possible tomake a quantitative comparison.5 POSSIBLE EXTENSIONSIn the PS, there are only two sets of locations (even andodd straight section) with significantly different optical pa-rameters. This is why only two pick-ups were installed.In another machine a third pick-up, suitably located, wouldenable independent measurement of the momentum spread,by adding a third line to Eq. (7).This would be possible for example in the SPS, by in-stalling two pick-ups in a dispersion-free straight section(one at large horizontal beta, and one at large vertical beta)and one pick-up in an arc, where the dispersion is large.6 CONCLUSIONSA system for non-invasive measurement of emittanceand matching has been installed in the PS. The initial expe-rience with this system is good, and comparison with otherinstruments has given encouraging results. Further tests onbeams with varying characteristics will be performed. Thenext step is to attempt to correct the measured mismatches,with the ultimate aim of making the system an operationaltool, linked to the existing automatic beam correction sys-tem for betatron and dispersion matching[7].7 REFERENCES[1] R.H. Miller et al, “Non-Invasive Emittance Monitor”, Proc.12th Int. Conf. on High Energy Accel., Batavia, IL, 1983.[2] V. Chohan et al, “Measurement of Coherent QuadrupoleOscillations at Injection into the Antiproton Accumulator”,Proc. European Part. Acc. Conf., Nice, France, 1990.[3] A. Jansson, D.J. Williams, “A New Optimised QuadrupoleDesign using Magnetic Coupling”, to be published in Nucl.Instr. Meth. in Phys. Res. A[4] A. Jansson, L. Søby, D.J. Williams, “Design of a MagneticQuadrupole Pick-up for the CERN PS”, DIPAC’01, Greno-ble, France, 2001[5] A. Jansson, “Non-Invasive Measurement of Emittance andOptical Parameters for High-Brightness Hadron Beams ina Synchrotron”, Dissertation, Stockholm University, Stock-holm, Sweden, 2001[6] M. Benedikt et al, “Injection Matching Studies using Turnby Turn Beam Profile Measurement in the CERN PS”, DI-PAC’01, Grenoble, France, 2001[7] M. Giovannozzi, A. Jansson, M. Martini, “SimultaneousMatching of Dispersion and Twiss Parameters in a TransferLine”, ABS’98, Geneva, Switzerland, 2001Proceedings of the 2001 Particle Accelerator Conference, Chicago530

A Non-Invasive Single-Bunch Matching and Emittance Monitor for the CERN PS Based on Quadrupole Pick-Ups

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