The CERN Low Energy Ion Ring (LEIR) commissioning started in the year 2005. O4+and Pb54+ion beams are transferred at 4.2 MeV/nucleon from Linac 3 to LEIR through a low energy transfer line, for which the constraints and the resulting optics design are presented. First trajectory and dispersion measurements agreed only poorly with the theoretical model. Iterations of a refined optics model and further measurements improved the agreement between experimental observations and expectations. In particular, the effect of quadrupole errors in the line dipole magnets is discussed

Carli, C

Chanel, M

Dumas, L

Roncarolo, F

Scrivens, R

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DESIGN AND VALIDATION WITH MEASUREMENTS OF THE LEIR INJECTIONLINEThe CERN Low Energy Ion Ring (LEIR) commissioning started in the year 2005. O4+and Pb54+ion beamsare transferred at 4.2 MeV/nucleon from Linac 3 to LEIR through a low energy transfer line, for which theconstraints and the resulting optics design are presented. First trajectory and dispersion measurementsagreed only poorly with the theoretical model. Iterations of a refined optics model and furthermeasurements improved the agreement between experimental observations and expectations. In particular,the effect of quadrupole errors in the line dipole magnets is discussed.EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN   -   AB DepartmentGeneva, SwitzerlandJune 2006AbstractCERN-AB-2006-057F. Roncarolo, C. Carli, M. Chanel, L. Dumas, R. ScrivensCERN, Geneva, SwitzerlandPresented atEPAC'06, Edinburgh, UK, June 26-30, 2006DESIGN AND VALIDATION WITH MEASUREMENTS OF THE LEIRINJECTION LINEF. Roncarolo, C. Carli, M. Chanel, L. Dumas, R. ScrivensCERN, Geneva, SwitzerlandAbstractThe CERN Low Energy Ion Ring (LEIR) commission-ing started in the year 2005. O4+and Pb54+ion beamsare transferred at 4.2 MeV/nucleon from Linac 3 to LEIRthrough a low energy transfer line, for which the constraintsand the resulting optics design are presented. First tra-jectory and dispersion measurements agreed only poorlywith the theoretical model. Iterations of a refined opticsmodel and further measurements improved the agreementbetween experimental observations and expectations. Inparticular, the effect of quadrupole errors in the line dipolemagnets is discussed.INTRODUCTIONThe LEIR accumulation ring is part of the acceleratorchain that will bring heavy ions in collision in the LargeHadron Collider (LHC) and the first stage of its commis-sioning with beam has been recently completed [1].The first phase of the commissioning concerned the iontransfer from Linac 3 to the LEIR injection region. Therelevant transfer lines are shown in Fig. 1.In the following we will discuss the matching of thetransfer line optics and then demonstrate how the opticsmodel has been improved and validated with beam basedmeasurements.TRANSFER LINES OPTICSThe optics matching concerned the transfer lines indi-cated in Fig. 1:- the last part of the ITH line, equipped with 2quadrupole triplets;- the ITE line, composed of 4 horizontal bendingdipoles deflecting the beam by 180 degrees and 5quadrupoles;- the ETL line, equipped with 2 horizontal and 2 verti-cal bending dipoles and 6 quadrupoles; this line is bi-directional and used, with different settings, to trans-fer the ions ejected from LEIR toward the PS;- the EI line, where the beam passes through 1 horizon-tal and 2 vertical dipoles (to adjust the beam positionat injection into LEIR) and 4 quadrupoles.The total length of the considered transfer line is about110 m.The optics matching has been calculated with MAD [2]in order to cope with the following conditions and con-straints:- matching the Twiss parameters at the beginning of theITH line, that can be inferred from the Linac 3 opticsmodel and measurements.- having the Twiss parameters along the loop in the ITEline symmetric with respect to the centre, by forcingthe two parameters αx and αy to be zero at this loca-tion;- keeping, in the ETL line, the betatron function am-plitudes βx and βy smaller than 25 m and the hori-zontal dispersion Dx within ±10 m, in order to avoidphysical aperture limitations and to obtain a reason-ably smooth focusing structure;- reaching the LEIR injection at the end of the EI linewith Dx ≈ 0 and with βx = βy =2 m in order toenhance the multi-turn injection efficiency [3].The last two items require a particular minimizationalgorithm using the available free parameters (i.e. thequadrupole strengths), since a strong betatron phase ad-vance (i.e. rapid variation of the betatron functions) isneeded to achieve a vanishing dispersion at the end of theline.The linac settings were tuned in order to optimize thebeam dynamics, at first with O4+and then Pb54+ions. Thevalues of the Twiss parameters at the beginning of the ITHline, to which the downstream optics must be matched,were measured by means of quadrupole scans that gave dif-ferent results for the two ion species, as summarized in Ta-ble 1, where the resulting emittances are indicated too.In addition, the linac design optics is expected to givevanishing Dx and D′x. Measurements provided very smallbut non-zero values for these parameters, that were usedin the model to compute the dispersion function along theline.With the updated optics model and the measured initialvalues, good agreement between computed and measureddispersion was found for both ion species, by means ofdedicated measurements that will not be presented in thispaper.Table 1: Twiss parameters and RMS geometric emittancesas measured at the beginning of the ITH line.αx βx αy βy x y[m] [m] [μm] [μm]O4+ 2.2 38 -2.8 22 1.5 2Pb54+ 0.4 13 2.1 18 1.9 2.1LEIREI LineITH LineLINAC 3ITE LineETL Line106 deg Sector BendFigure 1: Transfer line drawing, the injection into LEIR is after the EI line.SECTOR MAGNET MODELThe accelerator modeling program MAD represents asector magnet by means of its length L, the bending an-gle α and the half gap HGAP. Additional parameters canbe given to the model in order to consider imperfectionsin the magnet design and construction. Such parametersaccount for the pole-face rotation angles and the focusingeffects due to the non uniformity of the field in the core andfringe field regions.As it will be shown in the next section, after the firsttrajectory measurements, it was particularly significantto consider these additional parameters for the two 106-degree bending dipoles in the ITE line. Information aboutthe properties of the magnets could be retrieved from mag-netic measurements performed before their installation, at80 % of the maximum coil current. If the centre of the mag-net is at the curvilinear coordinate s=0, the following pa-rameters could be determined:FINT =∫ 0−∞By(s)[B0 −By(s)]2 · HGAP · B20ds = 0.47K1 =1B0ρ∂B0∂x∣∣∣∣core= 0.02 [m−2]where By(s) is the bending field and B0 the field in themagnet core.It is important to remark that, for both the parametersFINT and K1, an increase of their positive value implies astronger vertical defocussing.The pole face rotation angles resulted to be negligibleand kept at zero in the model.MEASUREMENTS WITH O4+IONSIn the first part of the commissioning the aim was totransport the O4+beam along the line with quadrupole set-tings provided by the MAD model discussed above. Aftera straight forward adjusting of the steering, trajectory mea-surements along the line have been carried out. The methodconsists in applying a kick (of known strength) with a cor-rector magnet situated at the beginning of the ITH line andmeasuring the beam position at several locations down-stream. The measured position can be compared to thes [m]0 20 40 60 80 100 x [mm/A]Δ-6-4-20246ModelMeasurmentITH ITE ETL EIFigure 2: O4+ions horizontal trajectory measurements andcomparison with the optics model prediction.s [m]0 20 40 60 80 100 y [mm/A]Δ-10-50510ModelModel CorrectedMeasurmentITH ITE ETL EIFigure 3: O4+vertical trajectory measurements comparedwith the optics model prediction before and after the cor-rection for the ITE bending dipoles quadrupole error.value predicted by the beam transport model. To improvethe measurement precision, we repeated the measurementfor different kick strengths and plotted the results as beamdisplacement per unit of current fed to the corrector.In total, there are 2 secondary emission monitors in theITH line and 7 scintillation screens in the ITE, ETL and EIlines.In the model, the ITE sector magnets parametersdiscussed in the previous section were set at first asFINT=0.35 (corresponding to a linear decay of the bendingfield from the core of the magnet to the field free region)and K1=0 (no gradient/focusing effects).The results of the horizontal trajectory measurementsare shown in Fig. 2. The agreement with the model iswell within the measurement error, as it was verified alsowith Pb54+ions. Therefore, no further investigations wereneeded.On the contrary, the vertical trajectory measurements ex-hibited a disagreement with the initial model, as shown bythe dashed blue line and the square red dots in Fig. 3. Addi-tional vertical defocussing along the ITE loop was evident.For this reason, we decided to refine the model of the ITEdipole magnets profiting from the magnetic measurementsresults discussed above. The change of the FINT parame-ter from 0.35 to 0.47 lead to a model prediction in betteragreement with the measurements, by a small but visibleamount. The agreement improved in a more evident wayafter inserting the parameter K1=0.02 [m−2]. Then we ap-plied a minimization algorithm with K1 as free parameterin order to find the best accordance with the measurements.This resulted in K1=0.039 [m−2] and in the model predic-tion indicated by the black solid line in Fig. 3.Therefore, the quadrupole effect inferred from the trajec-tory measurements is almost twice the one estimated fromthe magnetic measurements. This could be related to thefact that the magnetic measurements were taken severalsyears before and above all because, with O4+ions, the ITEbends are operated in saturation in order to accomplish thesteering in the ITE loop.It must be noted that a residual descrepancy between themodel and the measurements remains at the end of the ETLline and it will discussed at the end of the next section.The correction for the ITE dipoles K1 factor introducesonly neglibile effects in the horizontal trajectory, since thetwo magnets are located in regions where the horizontalbetatron function is much smaller than the vertical one.MEASUREMENTS WITH Pb54+ IONSThe same kind of measurements were carried out withPb54+ions. The transfer line settings differred from theones used for O4+because of the lower magnetic rigidityand different initial values of the Twiss parameters. As foroxygen, the horizontal trajectory agreed very well with themodel, while the initial model for the vertical optics exhib-ited a disagreement with the measurements dowstream theITE loop.Also in this case the model accounting the quadrupoleerror in the ITE bending magnets better fits the data, eventhough the best gradient value was found to be K1 =0.025 [m−2], smaller than the value found for oxygen. Thereason for this difference can be well explained by the factthat the magnets were less saturated. Another explanationcould be that, due to the higher magnetic rigidity, oxy-gen ions could not be correctly steered in the center of thedipoles and experienced a higher gradient effect.Similarly to what was observed for oxygen ions, a dis-crepancy between model and measurements remains in theEI line. This disagreement has not been fully understoodyet, but it can be related to the presence of two other sectorbend magnets at the end of the ETL line and at the begin-ning of the EI line. Also these two elements are locateds [m]0 20 40 60 80 100 y [mm/A]Δ-6-4-202468 Initial ModelCorrected Model 1Corrected Model 2MeasurementITH ITE ETL EIFigure 4: Pb54+vertical trajectory measurements and com-parison with the optics model prediction before and afterthe correction for the bending dipoles quadrupole error (seetext for the difference between Model 1 and Model 2).in regions with horizontal betatron function much smallerthan the vertical ones and additional vertical focussing bestfits the measurements.The comparison between the vertical trajectory measure-ments and the model prediction is shown in Fig. 4. Thethree curves describing the MAD prediction refer to the ini-tial model, to the insertion of K1=0.025 [m−2] to the ITEdipoles (Model 1) and to the additional parameter K1=-0.025 [m−2] in the two dipoles at the end of the ETL lineand the beginning of the EI line (Model 2).CONCLUSIONSThe Linac 3-LEIR tranfer line optics was validated bymeans of trajectory measurements with O4+and Pb54+ions.The initial poor agreement between the optics model andthe measurements has been successfully improved account-ing for quadrupole effects in the ITE line sector bendingmagnets. Such a correction is consistent with the availablelaboratory magnetic measurements. A disagremeent be-tween the model and the measurements remains in the lastpart of transfer line. An additional correction, assumingquadrupole effects in other two bending dipoles should beverified with new measurements and preferably with stud-ies about the geometry and field quality of the two mag-nets. Furthermore, the proper matching of the line was con-firmed by the achievement of good injection efficiency intothe LEIR ring [1].AcknowledgmentsMany thanks to G.Arduini for the fruitful discussionsand to all the members of the LEIR commisioning teamwho helped in preparing and performing these studies.REFERENCES[1] C. Carli et al., “LEIR Commissioning”, these proceedings.[2] MAD, “Methodical Accelerator Design”, CERN, URL:http://mad.web.cern.ch[3] “LHC Design Report Vol.3 - The LHC Injector Chain”,CERN-2004-003-V-3, p.277

Design and Validation with Measurements of the LEIR Injection Line

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