Transverse emittance preservation will be an important issue for the LHC injector chain. Minimisation of the blow-up at injection by tuning independently the Twiss parameters (a,b), the dispersion D and the dispersion derivative D' is therefore mandatory. The optics of the transfer line between the PS and SPS machines was modelled and matched using the program package MAD. Tuning knobs were developed using a singular value decomposition (SVD) algorithm. Coupled to the measurement of the Twiss parameters at a given point downstream of the correction elements they provide a fast correction algorithm for the betatron mismatch

Arduini, Gianluigi

Hanke, K

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TUNING KNOBS FOR THE PS-SPS TRANSFER LINEG. Arduini, K. HankeCERN, Geneva, SwitzerlandAbstractTransverse emittance preservation will be an important issue for the LHC in-jector chain. Minimisation of the blow-up at injection by tuning independentlyTwiss parameters, dispersion and dispersion derivative is therefore mandatory.The optics of the transfer line between the PS and SPS machines was modelledand matched using the program package MAD. Tuning knobs were developedusing a singular value decomposition (SVD) algorithm. Coupled to the mea-surement of the Twiss parameters at a given point downstream of the correctionelements they provide a fast correction algorithm for the betatron mismatch.1. IntroductionThe transfer line between the PS and the SPS machines will be an important part of the LHC injectorchain [1]. In order to optimise beam and emittance transport, the line must be matched accurately tothe measured lattice functions at the PS extraction point and the nominal lattice functions at the SPSinjection point.The transfer line optics was modelled using the program package MAD [2]. The geometry of the modelwas verified versus the official CERN survey data [3], while the correct magnetic behaviour was ver-ified in a series of measurements [4]. Based on the model, the line was successfully re-matched [5].For the matched optics, we found a betatron mismatch after filamentation of 1.0 in both planes. Thisclearly fulfils the LHC requirements. The dispersion mismatch after filamentation was computed to 1.7in the horizontal and 1.0 in the vertical plane1. The residual mismatch is both due to the unavoidablediscrepancy between model and reality and due to the uncertainty in the measurement of the initial opti-cal parameters. It is therefore mandatory to tune selected beam parameters without changing the globalsetting of the line.2. Correction MechanismTo compensate for the unavoidable discrepancies between model and real machine as well as for the er-rors of the measurement, tuning knobs were developed to tune independently the beam parameters. Theyare based on the inversion of the matrix   			 where ﬀ ﬁﬃﬂ "!$#&%'	( "!)#&%*	+,"!$#&%'	+.-/!)#&% and 021 is the strength of the 43matching quadrupole2 . As a first attempt only the eight independentquadrupoles of the matching section controllable from the SPS control room have been considered.Frequently, as in our case, the coefficient matrix for a given optics will be either singular or numericallyclose to singular. Singular value decomposition (SVD) algorithms provide a tool to diagnose a matrixand to solve the resulting system of equations even for ill-conditioned matrices [7]. Simulations usingthe reconditioned matrix show that an independent linear variation of all the parameters can be obtainedexcept for ( 5 for which a non-linear behaviour is observed.3. Experimental ResultsThe tuning tool was tested with beam, using the SPS mismatch monitor [8]. This system is based on aturn-by-turn measurement of the beam size with an OTR screen and a fast CCD camera. The oscilla-1See Ref. [5] for details.2See Ref. [6] for details.62−20 −15 −10 −5 0 5 10 15 20708090100110120130140150160170180change of βx [m]β x [m]theoreticalMAD        measured   −5 0 515202530change of βy [m]β y [m]theoreticalMAD        measured   −20 −15 −10 −5 0 5 10 15 2011.522.5change of βx [m]horizontal mismatch factor−5 0 511.051.11.151.21.251.31.351.4change of βy [m]vertical mismatch factorFig. 1: Horizontal 6 -function (upper left plot), horizontal mismatch factor (lower left plot), vertical 6 -function (upper rightplot) and vertical mismatch factor (lower right plot) at the exit of the transfer line versus variation applied using the tuningknob. Starting from a matched optics ( 786 = 0), the 6 -function is detuned by 9 10% and 9 20%.tion of the beam size indicates betatron mismatch at injection into the SPS if no dispersion mismatch ispresent. While the oscillation of the beam size is a measure of the mismatch, it is important to obtainalso the values of ﬂ and ( . This can be done by measuring the beam profile at three consecutive turns inthe SPS. The Twiss parameters can then be obtained in the same way as from a multi-grid measurementin a transfer line.Since measurement of the Twiss parameters can be performed quickly, while measurement of the disper-sion is time consuming, it was decided to detune the horizontal and vertical ( -functions and to measureTwiss parameters and mismatch factor using the SPS mismatch monitor. Starting from a matched set-ting, the ( -functions were detuned by : 10% and : 20%. The upper left plot in Fig. 1 shows the expectedchange of the horizontal ( -function (dashed line), the result obtained from the simulation and the mea-sured values. It can be seen, that already in the simulation the expected variation is not achieved. Asfar as the measurement is concerned, only the points for  ( 5 = 0, -10 m and -20 m could be measureddue to a technical problem. For the initial setting (  (;5 = 0), the measured value lies already below thetheoretical one. This means that this setting is not perfectly matched, which is consistent with a geomet-rical mismatch factor of 1.3 obtained from a multi-grid measurement in the line [5]. The measurementsuffers from significant fluctuations in the horizontal plane which do not allow a conclusion. From themeasured Twiss parameters, the mismatch factor can be computed. The lower left plot in Fig. 1 showsthe geometrical blow-up versus change of (;5 for the same measurement. Again, the measurement suf-63−20 −15 −10 −5 0 5 10 15 20−5−4.5−4−3.5−3−2.5−2−1.5−1−0.50change of βx [m]αxtheoreticalMAD        measured   −5 0 500.20.40.60.811.2change of βy [m]αytheoreticalMAD        measured   Fig. 2: Horizontal < -parameter (left plot) for the tuning of 6>= and vertical < -parameter (right plot) for the tuning of 6>? shownin Fig. 1.fers from significant fluctuations. The ﬂ -parameter was computed from the same measurement. The leftplot in Fig. 2 shows the variation of ﬂ;5 , which is supposed to remain unchanged. Also in this case, thestatistical error is large and a conclusion impossible. All beam parameters were measured at the sametime in the vertical plane, where they are supposed to be unaffected by the variations in the horizontalplane. This is in fact the case. The results are presented in detail in [6].The same measurement was done in the vertical plane, where all five settings could be measured. The up-per right plot in Fig. 1 shows theoretical, simulated and measured values of (;@ for five different settingsof the tuning knob. All data agree within the statistical error. From the same measurement, the verticalmismatch factor was computed. The result is shown in the lower right plot in Fig. 1. For the matchedoptics (  ( @ = 0), a geometrical mismatch factor of 1.1 is found which is in perfect agreement with theresult obtained from a multi-grid measurement in the line. Detuning the ( -function at the injection pointin both directions leads to an increase of the mismatch factor as expected. The vertical ﬂ -parameteris shown for the same measurement in the right plot in Fig. 2. It remains unaffected by the variationof (;@ as specified. All beam parameters in the horizontal plane remained also unchanged during thismeasurement. The results are presented in detail in [6].4. Conclusion and OutlookA straight-forward analytical approach was used to develop a tool for selective tuning of beam parametersin the PS-SPS transfer line. Eight independent quadrupole strengths are used as free parameters to tuneeight beam parameters. A coefficient matrix which contains the variation of the Twiss parameters as afunction of eight quadrupole strength parameters was generated based on a MAD simulation of the line.It was reconditioned and inverted using a singular value decomposition algorithm. The resulting systemof equations can be solved and yields the change of quadrupole strength required to obtain a given changeof any of the Twiss parameters while the others remain unchanged.A MAD simulation showed that the tuning knob works fine for all beam parameters except the horizontal(-function. A first measurement with beam, carried out during the 1998 SPS run, showed that the tuningknob works fine for the vertical ( -function. For the horizontal ( -function the results do not allow aconclusion.It is planned to improve the tuning knob by using more magnets as degrees of freedom. It will thenbe implemented into the SPS control system and provide, coupled to the SPS mismatch monitor, anautomated mismatch correction mechanism.64AcknowledgementsThe authors would like to thank R. W. Assmann and P. Raimondi for fruitful discussions.References[1] P. Collier (ed.), The SPS as Injector for LHC, Conceptual Design, CERN-SL-97-07 DI (1997).[2] H. Grote, F. C. Iselin, The MAD Program, User’s Reference Manual, CERN-SL-90-13 AP (1990).[3] G. Arduini, M. Giovannozzi, K. Hanke, J.-Y. He´mery, M. Martini, MAD and BeamOptics Descrip-tion of the TT2/TT10 Transfer Lines - Part I: Optics without Emittance Exchange Insertion, CERNPS-Note-98-014 CA and CERN SL-Note-98-040 OP (1998).[4] G. Arduini, M. Giovannozzi, K. Hanke, J.-Y. He´mery, Study of the TT2/TT10 Transfer Line Opticsvia Transfer Matrix Measurement, CERN PS-Note-98-020 CA and CERN SL-Note-98-058 MD(1998).[5] G. Arduini, G. Crockford, C. Despas, M. Giovannozzi, K. Hanke, D. Manglunki, M. Martini,G. Me´tral, C. Niquille, Betatron and Dispersion Matching of the TT2/TT10 Transfer Line for the26 GeVc Fast Extraction, CERN PS-Note-99-007 CA and CERN SL-Note-99-003 MD (1999).[6] G. Arduini, J. Colchester, G. Ferioli, M. Giovannozzi, J.-J. Gras, K. Hanke, R. Jung, D. Manglunki,Mismatch Measurement and Correction Tools for the PS-SPS Transfer of the 26 GeV/c LHC Beam,in preparation.[7] B. P. Flannery, W. H. Press, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran, TheArt of Scientific Computing, 2A4B edition, Cambridge University Press (1986).[8] C. Bovet, R. Jung, A New Diagnostic for Betatron Phase Space Matching at Injection into a CircularAccelerator, LHC project report 3, rev. (1996).65

Tuning Knobs for the PS-SPS Transfer Line

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