The standard approach to measure the optical parameters and the emittance in a transfer line is based on the analysis of the profiles measured by three monitors. This is feasible, provided the dispers ion function is known a priori. In this paper we propose to measure the complete set of five parameters (the two independent Twiss parameters, the emittance, the dispersion function and its derivative ) by using five monitors with one bending magnet interleaved. The results of some measurements carried out in the transfer line connecting the CERN PS and SPS rings are presented

Arduini, Gianluigi

Giovannozzi, Massimo

Manglunki, Django

Martini, M

CERN Document Server

MEASUREMENT OF THE OPTICAL PARAMETERS OF A TRANSFERLINE USING MULTI-PROFILE ANALYSISG. Arduini, M. Giovannozzi, D. Manglunki, M. Martini, CERN, Geneva, SwitzerlandAbstractThe standard approach to measure the optical parametersand the emittance in a transfer line is based on the analysisof the profiles measured by three monitors. This is feasible,provided the dispersion function is known a priori. In thispaper we propose to measure the complete set of five pa-rameters (the two independent Twiss parameters, the emit-tance, the dispersion function and its derivative) by usingfive monitors with one bending magnet interleaved. Theresults of some measurements carried out in the transferline connecting the CERN PS and SPS rings are presented.1 THEORYThe standard way to measure the optical parameters ; and the emittance  in a transfer line is based on the use ofthree monitors [1, 2]. Under the following assumptions: The dispersion function D is zero or well-known allalong the section where the monitors are installed. The transfer matrices of the beam line sections be-tween the monitors are known. The particle motion is fully decoupled between themonitors.One can compute the optical parameter from the measure-ments of beam profiles.If iindicates the profile half-width measured in the ithmonitor, then2i= i; i = 1; 2; 3 (1)where the beam emittance is defined as the width of aGaussian-distributed beam at one sigma. Using the factthat the motion is fully decoupled, it is possible to use theinvariance of the emittance to express the Twiss parametersat the locations of the monitors 2 and 3 in terms of those atthe monitor 1, namely:i= C2i1  2CiSi1+ S2i1; i = 2; 3:(2)Here the transfer matrix between monitor 1 and i is givenbyTi=CiSiC0iS0i(3)and the parameter  = (1 + 2)= has been introduced.The set of Eqs. (1) can be solved using the relations (2),giving = 21 1=11= 2:Here  ; are given in terms of the measured profile widths  =[(3=1)2  C23]=S23  [(2=1)2  C22]=S22(C2=S2)  (C3=S3)2= (2=1)2=S22  (C2=S2)2+ (C2=S2)    2=4In the case where the hypothesis on the dispersion functionis not satisfied, the approach to be used in order to mea-sure the Twiss parameters and the beam emittance has tobe modified. The starting point is a different version ofEq. (1)2i= i+D2i2; (4)where  represents the relative momentum spread of thebeam at one sigma. It is customary to measure the disper-sion function independently. A shift of the beam energy isperformed and the corresponding variation of the averageposition on the monitors is recorded. A linear fit allows thedetermination of the dispersion at the location of the mon-itors. On the other hand, the energy spread can be easilymeasured by using a longitudinal pick-up. Hence, once theDis and  are known, it is possible to apply the methodpreviously described using Eq. (4) instead of Eq. (1).Although the measurement of the dispersion is concep-tually rather simple, in practice it perturbs the standard op-eration in order to vary the beam energy. Hence it is notadvisable to apply this method routinely. Furthermore, insome cases the extraction process is so complex that theenergy shift would completely destroy the ejected beam oralter the beam parameters with respect to the nominal situ-ation.For these reasons it is feasible to have an alternativemethod which measures the whole set of beam parameters; ;D;D0 and  at the same time without varying any ma-chine parameter. From simple arguments, the informationextracted from five monitors should be enough to computethe five unknowns. It turns out that this is the case, pro-vided at least one dipole is installed in the section of thebeam line delimited by the first and last monitor.Once again the starting point is Eq. (4), connecting theoptical parameters and the measured beam profile in thepresence of dispersion, and the transformation law (2) usedto propagate the Twiss parameters. In this case it is alsonecessary to consider the relation between the value of thedispersion function at the location of the monitors. Thepropagation of D is performed by using the same transfermatrix used to transform the optical parametersDi= CiD1+ SiD01+ ii = 2; 3; 4; 5 (5)where  is the contribution to the dispersion due to a dipolemagnet between the first and the ith monitor. By usingEqs. (2) and (5), (4) can be cast in the form of a system offive equations. It can be written in matrix form as =M; (6)where =0BBBB@2122  2223  3224  4225  521CCCCA =0BBBB@1+D2121 D1D0121+D0212D12D0121CCCCAandM =0BBBB@1 0 0 0 0C22 2C2S2S222C222S22C23 2C3S3S232C332S33C24 2C4S4S242C442S44C25 2C5S5S252C552S551CCCCAIn order to invert the matrixM it is sufficient that two  aredifferent from zero. This is certainly the case if a dipolemagnet is located upstream of the fourth monitor. In thiscase, from the solution given by M 1 = 0 one candetermine the Twiss parameters as followsD1= 04=2D01= 05=21= A=pAC  B2A = 01 024=21= B=pAC  B2 with B = 02+0405=2 =pAC  B2C = 03 025=22 THE MODELThe approach described in the previous section has beenapplied to the transfer line between the CERN Proton Syn-chrotron and the Super Proton Synchrotron. This line is di-vided into two parts: the TT2 line and the TT10 line. TT2transports the beam from the extraction point of the PS ma-chine to the TT10 part, which, in turn, connects the transferline to the SPS injection point. At the junction of the twolines, the beam is deflected  81 mrad to the right. Due tothe difference in height between the PS and SPS, a verticaldeflection angle of 60 mrad is imposed at the entrance ofTT10 and then cancelled before injection in the SPS.Three Secondary Emission Monitors are installed bothin TT2 and in the TT10 section. These two sets of moni-tors are routinely used to perform emittance and Twiss pa-rameter measurement in both lines. For this purpose, thestandard method based on Eq. (1) is used, with the disper-sion measured by performing an energy shift.In Fig. (1) the horizontal and vertical -functions (upperpart) are shown, together with the horizontal and verticaldispersion (lower part), for the TT2 and TT10 lines. TheTT2-TT10 transfer line has an important role in the LHCera. In fact, to achieve the LHC top performance [3], it is0204060801001201400 200 400 600 800 1000 1200s(m)ββ(m)βΗβςβHβV-8-6-4-202468100 200 400 600 800 1000 1200s(m)D(m)DH DVVDHMSG257       MSG277MSG267BSG1027       BSG1029BSG1028Figure 1: Horizontal and vertical -functions (upper part)and dispersion (lower part) for the TT2 and TT10 lines.The position of the beam profile monitors installed in thelines is also shown.important to avoid emittance blow-up along the injectionchain [4, 5]. Although a transfer line cannot generate sucha blow-up, nevertheless it can be a source of transverse orlongitudinal mismatch at injection in the subsequent ma-chine. Therefore it is important to be able to measure theoptical parameters to detect a potential mismatch. In thiscontext, the proposed approach represents a robust methodto measure the optical parameters during normal operation.3 MEASUREMENTSIn order to test the proposed method, a comparison hasbeen carried out between a set of measurements performedin the standard way, with a second set obtained by applyingour approach.At high energy, 26 GeV/c, the proton beam is extractedfrom the PS machine using a kicker magnet and deliveredto the SPS through the TT2-TT10 line. The beam intensityis about 1:1 1012 ppp, distributed into 20 bunches 6.1 nslong with a momentum spread  of about 0:26 10 3.3.1 Standard methodIn order to apply Eq. (1), it is necessary to measure thehorizontal and vertical dispersion at the monitor’s location.This can be done as described above. For each value of theenergy five measurements of the beam centroid have beentaken. The average of these values is used in the analy-sis, while the variance of the five measurements is used toestimate the error associated with the measurement. Theresults are reported in Table 1. A new set of five differ-Table 1: Horizontal and vertical dispersion at the monitor’slocation in TT2 and TT10 lines.DH[m] DV[m]MSG257 3.03 0.04 -0.56 0.02MSG267 -0.50 0.04 -0.547 0.008TT2MSG277 -3.56 0.06 -0.200 0.008BSG1027 -1.72 0.06 0.00 0.02BSG1028 -0.32 0.09 0.25 0.02TT10BSG1029 4.03 0.09 0.27 0.01ent measurements of the beam width for each of the moni-tors has been taken. The variance of the five measurementshas been used to estimate the error. The emittance and theTwiss parameters are then computed using Eqs. (1). Theresults are reported in Table 2.Table 2: Horizontal and vertical Twiss parameters andemittance on the first monitor of the TT2 and TT10 lines.The values shown are computed using the standard method.Beam TT2 TT10parameters MSG257 BSG1027H[m] 13.00.2 39.60.6H1.710.04 -1.150.04H[mm mrad] 0.660.01 0.720.01V[m] 52.70.5 53.10.7V-2.630.05 1.530.03V[mm mrad] 0.440.01 0.540.013.2 Multi-profile methodIn this case, the computation of the five optical parametersis performed without any change in the beam parameters,simply measuring the profile width on five different mon-itors. The geometry of the TT2-TT10 does not allow theapplication of this method to measure the vertical opticalparameters. In fact, two vertical dipoles are installed be-tween the three monitors in TT2 and those in TT10: thefirst one bends the beam down towards the SPS and the sec-ond one cancels the deflection. Therefore, the global effectis approximately equivalent to having no bending magnetat all.In the horizontal plane, the proposed technique can beapplied to measure the Twiss parameters. As only fivemonitors are needed, it is possible to obtain different setsof measured parameters according to the various combina-tions of five monitors out of the six available. In Table 3the results for three different combinations of monitors areshown. In the last two columns the average  of the threesets of values and the standard deviation s:d:, used as anestimate of the error associated with this method are re-ported. The combinations shown in Table 3 are made by thethree monitors in TT2 and two monitors in TT10, namelyTable 3: Horizontal Twiss parameters, emittance and dis-persion on the first monitor of TT2 computed using themulti-profile method.Beam Comb. Comb. Comb.  s:d:parameters 1 2 3H[m] 13.90 13.39 12.36 13.2 0.8H1.89 1.70 1.47 1.7 0.2H[mm mrad] 0.63 0.66 0.58 0.62 0.01DH[m] 2.68 2.49 5.50 3.6 1.7D0H-0.07 -0.47 -0.92 -0.5 0.4Comb. 1: MSG257, MSG267, MSG277, BSG1027,BSG1028Comb. 2: MSG257, MSG267, MSG277, BSG1027,BSG1029Comb. 3: MSG257, MSG267, MSG277, BSG1028,BSG1029The other possibilities, combining two monitors of TT2and three of TT10, provided results in poor agreement withthose obtained using the standard method. A possible ex-planation could be the different resolution of the monitorsinstalled in the two sections (0.5 mm for those in TT2 and2.5 mm for those in TT10).The results obtained are encouraging, showing a rathergood agreement with the outcome of the standard method.It is worth noting that although the average dispersion valueagrees within only 20 %, the average Twiss parameters andthe emittance show a better agreement (less than 10 %).4 ACKNOWLEDGEMENTSWe should like to thank J-Y. He´mery for his criticism andthe operation crew for the support during the experimentalsessions.5 REFERENCES[1] P. J. Bryant, K. Johnsen, “Circular Accelerators and StorageRings”, (Cambridge University Press, NY, 1993).[2] M. Arruat, M. Martini, “The new standard method to mea-sure emittance in the PS transfer lines”, CERN PS (PA) 92-59 (1992).[3] The LHC Study Group, “The Large Hadron Collider: Con-ceptual Design Study”, CERN AC (LHC) 95-05 (1995).[4] F. Blas, R. Cappi, V. Chohan, D. Cornuet, G. Daems,D. Dekkers, R. Garoby, D. Grier, J. Gruber, E. Jensen,H. Koziol, A. Krusche, K. D. Metzmacher, F. Pedersen,J. Pedersen, U. Raich, J-P. Riunaud, J-P. Royer, M. Sas-sowsky, K. Schindl, H. Scho¨nhauer, M. Thivent, H. Ull-rich, F. Vo¨lker, “Conversion of the PS Complex as LHCPre-Injector”, CERN PS (DI) 97-48 (1997).[5] P. Collier, B. Goddard, R. Jung, K. H. Kissler, T. Linnecar,F. Ruggiero, W. Scandale, K. Schindl, G. Schro¨der, E. Sha-poshnikova, L. Vos, “The SPS as Injector for LHC: Concep-tual Design”, CERN SL (DI) 97-007 (1997).

Measurement of the optical parameters of a transfer line using multi-profile analysis

Arduini, G

Giovannozzi, Μ

Manglunki, D

Martini,  Μ

Measurement of the optical parameters of a transfer line using multi-profile analysis

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