Fischer, W

Schmidt, F

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EUROPEAN LABORATORY FOR PARTICLE PHYSICSCERN SL/95-17 (AP)PRECISE DETERMINATION AND COMPARISON OF THE SPSDYNAMIC APERTURE IN EXPERIMENT AND SIMULATIONW. Fischer and F. SchmidtAbstractThe combined eect of nonlinear elds and tune ripple can lead tochaotic motion and particle loss in proton accelerators thereby lim-iting the dynamic aperture of these machines. The SPS DynamicAperture Experiment is performed to study a controlled nonlinearmachine under the inuence of power supply ripple. To this endeight strong sextupoles are used to make the SPS nonlinear. Thetune ripple is introduced with one special quadrupole which al-lows to vary the ripple frequency and depth. In parallel long-termelement-by-element tracking is done to investigate its applicabilityfor the estimation of the dynamic aperture of a real accelerator.The inuence of non-linear magnetic elds and tune ripple is ob-served at two working points using a ying wire of 8m diameter.The experimentally determined dynamic aperture is compared withsurvival plots obtained from the tracking and their dierences arediscussed.Paper presented at the 1995 Particle Accelerator Conference,Dallas, 1-5 May 1995Geneva, SwitzerlandMay, 1995PRECISE DETERMINATION AND COMPARISON OF THE SPSDYNAMIC APERTURE IN EXPERIMENT AND SIMULATIONW. Fischer, II. Institut fur Experimentalphysik, Universitat Hamburg, GermanyandF. Schmidt, CERN, Geneva, SwitzerlandAbstractThe combined eect of nonlinear elds and tune ripple canlead to chaotic motion and particle loss in proton acceler-ators thereby limiting the dynamic aperture of these ma-chines. The SPS Dynamic Aperture Experiment is per-formed to study a controlled nonlinear machine under theinuence of power supply ripple. To this end eight strongsextupoles are used to make the SPS nonlinear. The tuneripple is introduced with one special quadrupole which al-lows to vary the ripple frequency and depth. In paral-lel long-term element-by-element tracking is done to inves-tigate its applicability for the estimation of the dynamicaperture of a real accelerator. The inuence of non-linearmagnetic elds and tune ripple is observed at two workingpoints using a ying wire of 8m diameter. The experi-mentally determined dynamic aperture is compared withsurvival plots obtained from the tracking and their dier-ences are discussed.I. INTRODUCTIONNon-linearities of superconducting magnets, which can-not be completely avoided, may limit the dynamic apertureof accelerators. It is therefore of great interest to predictthe stability range due to these non-linearities. The SPSDynamic Aperture Experiment is used to compare experi-mental results with tracking which serves as the predictivetool in this study.After calibrating the instrumentation we have carefullymeasured the detuning curves as a function of betatron am-plitude and compared them with tracking results. An evenmodest disagreement between the two would cast doubt onthe validity of the model.We will report about measurements and calculations forthe dynamic aperture of the SPS with the following ma-chine set up: coasting beam at 120GeV, closed orbit cor-rection with horizontal and vertical rms below 0.3mm, lin-ear coupling compensation up to jQh  Qvj = 0:002, mo-mentum spread p=p  10 3, chromaticity in both planescorrected to Q=(p=p)  1. Strong non-linearities areintroduced by 8 powerful sextupoles. The natural tuneripple spectrum contains 7 major lines that add up to a to-tal amplitude of 0:5  10 4. We studied the working points(Qh; Qv)=(26.637,26.533) and (26.605,26.538) referred toas WP1 and WP2 respectively (see Fig. 1). The articialtune ripple, introduced by a single quadrupole, had a fre-Supported in part by CERN, Geneva, Switzerland andDESY, Hamburg, Germany.quency of 9Hz and an amplitude of Qh= 1:87  10 3andQh= 0:55  10 3at WP1 and WP2 respectively. The ra-tio of horizontal and vertical ripple depth is Qh=Qv=1:75. The beam is kicked horizontally until the aperture isreached.26.5326.53526.5426.54526.5526.57 26.59 26.61 26.63Horizontal tuneVertical tuneSum resonancesWP1WP25Qh+2Qv=1863Qh+4Qv=1867Qh=186Figure 1. Tune diagram with sum resonances up to order11 and both working points before and after the kick. Thedetuning is directed towards smaller horizontal and largervertical tune values. At the last tune values large scalelosses take place.II. INSTRUMENTATION AND DETUNINGPreconditions for these experiments are an exact knowl-edge of the applied kickstrength and a high precision of thewire scan readings. The kicker has been calibrated severaltimes and shows a very linear behavior down to small kickamplitudes. Whereas the measurement of 1993 showed adegradation of 10% compared to earlier measurements, thecalibration of 1995 showed practically no dierence to themeasurement of 1993.The kicked beam is observed by a ying carbon wire of8m diameter and 0:4m  s 1speed. The position of thewire can be measured via an opto-electronic ruler with aresolution of 16m. The intensity of the kicked beam is re-duced by 1:4 10 4per scan (in and out scan) but no beamblow up can be observed. The kicked beam produces a typ-ical double peak structure in the wire scan prole (Fig. 3).The kick strength calculated from the distance betweenthe peaks agrees within 10% with the kicker calibration.These beam proles were also compared with scans fromying wires at dierent locations. The agreement amountsto some 5-10% which also increases our condence in theknowledge of the -functions around the ring.An important test for a nonlinear accelerator model isthe dependence of the tunes on the betatron amplitudes. Inthe SPS the horizontal and vertical detuning is measuredas a function of the horizontal betatron amplitude. Thetunes are computed from up to 8192 turns after the kick byFFT and phase advance averaging leading to a precision of5  10 4[1]. Fig. 2 shows the comparison of the measuredand calculated detuning. The agreement is very good upto large amplitudes and the dependence of the detuningon action (x2max2h) is predominantly linear as expected fromsecond order perturbation theory.-0.02-0.015-0.01-0.00500.0050 0.5 1 1.5 2Horizontal action [mm mrad]Detuning dQh trackingdQv trackingdQh exp. 06/07/94dQv exp. 06/07/94Figure 2. Detuning measured at working point 1.III. DYNAMIC APERTUREFor practical reasons the dynamic aperture can be de-ned as stability limit after a certain time interval whichmay depend on the type of machine and operational consid-erations. A typical problem is to keep the beam circulatingseveral minutes during the injection period when nonlinear-ities and beam size are usually at their maximum. In theexperiment the observation was done up to 1000s whereaswith computer tracking only 345s (15 million turns) couldbe reached with reasonable computing eort.A limitation of the SPS experiment is the rather largenatural size of the beam before kick. This precludes anyne exploration of the amplitude distribution as is done intracking. In particular small chaotic regions within an oth-erwise stable part of the distribution cannot be detected.However the maximum amplitude above which no particlesurvives after a certain time gives a good measurement ofthe stability limit.A. MeasuredExperimentally, the dynamic aperture is determinedfrom the maximum bottom width of the wire scan proles(Fig. 3). At the edge of the beam prole 5  107protons(10 4of the intensity) can clearly be detected. In most0102030405060708090-20 -10 0 10 20 30Horizontal position [mm] at βh=100mSignal [arbitrary units]01:30:54h01:45:09hFigure 3. Evolution of the wire scan prole at WP1, tuneripple of 9Hz and Qh= 0:00187 (#78, no horizontalscraping).cases 15 scans have been taken at time intervals of about1min.In Fig. 4 four wire scan measurements at WP1 with ar-ticial tune ripple are depicted. These curves have beensmoothed and the estimated error bars are shown in case#91. The reproducibility of the experimental results hasbeen found to be within 2% for two measurements underthe same conditions but 5 months apart (#62 and #76).Due to the rather large beam size the results depend onthe measurement procedure: cases #62 and #76 have beenscraped horizontally after kicking, whereas cases #78 and#91 are left unscraped and in addition the latter case hasbeen kept for some extra 15min without articial tune rip-ple. Although these cases strongly dier initially, after 345sthe dierences reduce to about 5%.110100100017 18 19 20 21 22Horizontal amplitude [mm] at βh=100mSurvival time [s]Wire scan measurement(#62 06/07/94)Wire scan measurement(#76 13/12/94)Wire scan measurement(#78 13/12/94)Wire scan measurement(#91 14/12/94)Survived in TrackingLost in TrackingFigure 4. Dynamic aperture at WP1, tune ripple of 9Hzand Qh= 0:00187.Fig. 5 shows one of the two cases with natural ripple only.The results of all measured cases are summarized in Tab. I.B. ComputedThe computer code SIXTRACK [2] has been used for thetracking studies. The model included all sextupoles andhorizontal and vertical closed orbit, as well as the tune rip-ple. Tunes, chromaticities and linear coupling are adjustedsimilar to what is measured in the SPS. As the beam iskicked horizontally the particles are tracked with large hor-izontal displacements. Moreover, a vertical displacementsTable IComparison of measured and computed dynamic aperture. All values are given for h=100m. For the onset of chaosthere are two values: the larger one is the border above which no regular particles could be found, the lower (inbrackets) is the lowest amplitude at which large scale chaotic motion sets in.case measured onset of chaos loss border comparison betweendynamic (2  105turns) (1:5  107turns) measurement andaperture loss border[mm] [mm] [mm] [%]WP1, natural ripple only 20.0 (15.7) 23.1 24.4 22WP2, natural ripple only 20.9 (9.8) 23.6 25.7 23WP1, 9Hz, Qh= 1:87  10 317.4 (7.7) 14.3 19.2 10WP2, 9Hz, Qh= 0:55  10 319.5 (7.4) 8.3 22.3 140.1110100100017 19 21 23 25 27 29Horizontal amplitude [mm] at βh=100mSurvival time [s]Wire scan measurement(#73 23/10/94)survived in trackinglost in trackingFigure 5. Dynamic aperture at WP2, natural ripple only.of roughly one  of the vertical beam size has been consid-ered. In all tracked cases a wide amplitude range could befound (column three in Tab. I) where chaotic (after 200,000turns) and regular regions alternate. For each chaotic re-gion in that amplitude range a particular sum resonance isfound which apparently causes the unstable behavior. InFig. 4 the lost particles correspond to a coupled 7thorderresonance, in Fig. 5 the losses at large amplitudes corre-spond to the horizontal 7thorder resonance and the lossesat about 20mm are due to another coupled 7thorder reso-nance (for both cases see Fig. 1).The dynamic aperture as dened above and computedby long-term tracking is shown in column four in Tab. I.The last column in Tab. I shows the dierence in percentbetween the computed and the measured dynamic aper-ture. In the cases with additional ripple the dierence isabout 10% but without ripple this deteriorates by abouta factor of two. Moreover in the tracking we nd a broadregion of apparently regular motion outside of the experi-mental stability border (not present in the cases with ad-ditional ripple). From this we have to conclude that an es-sential destabilizing eect is missing in our tracking model.A very rough estimate for the scale of this eect is theadditional tune ripple because the experimental dynamicaperture without extra tune ripple agrees well with that ofthe tracking when this ripple is introduced (compare therst two entries in column two with the last two entries incolumn four of Tab. I). The nature of this eect is still un-known. However, neither some neglected systematic non-linearities nor extra tune ripple are likely candidates. Theformer would lead to measurable detuning with amplitude,while for the latter the tune ripple can be understood frommeasured voltage ripple of the SPS power supplies [3] andin addition it has been measured with good precision witha phase-locked loop.IV. CONCLUSIONThe detuning with amplitude of the SPS with controlledstrong sextupoles can be well reproduced with our trackingmodel. We also know to a good precision the tune ripple in-duced by power supplies. When an additional and sizeabletune ripple is applied the tracking model gives a value forthe dynamic aperture which is about 10% larger than theexperimental one. However, the cases without extra ripplereveal a more prominent dierence (larger than 20%) be-tween the theoretical and experimental dynamic aperture.We address this to some neglected and at present unknowneect which should be about as eective as tune ripple ofsome 10 3.V. ACKNOWLEDGMENTSThe authors are grateful to all engineers and technicianswho helped with the instruments. The operations teamand our colleagues in the accelerator physics group arethanked for their cooperation and help. Special thanks toF. McIntosh for his strong support performing the exten-sive computer simulations and to J. Gareyte for stimulatingdiscussions and reading the manuscript.References[1] W. Fischer et al., \The Million Turn Data AcquisitionSystem BOSC", Proceedings of the 1993 IEEE ParticleAccelerator Conference, Washington D.C. (1993).[2] F. Schmidt, \SIXTRACK Version 1.2", CERNSL/94-56 (AP) (1994), found in WWW under:http://hpariel.cern.ch/frs/Documentation/doc.html.[3] P. Burla et al., \Power Supple Ripple Study at theSPS", AIP Conference Proceedings 326 (1995).

Precise determination and comparison of the SPS dynamic aperture in experiment and simulation

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