The effect of magnet misalignments in the beam orbit and linear optics functions are reviewed and correction schemes are applied to the negative momentum compaction lattice of PS2. Chromaticity correction schemes are also proposed and tested with respect to off momentum optics properties. The impact of the correction schemes in the dynamic aperture of the lattice is finally evaluated

Barranco, J

Bartmann, W

Benedikt, M

Carli, C

de Maria, R

Papaphilippou, Y

Peggs, S

Trbojevic, D

CERN Document Server

ORBIT, OPTICS AND CHROMATICITY CORRECTION FOR PS2NEGATIVE MOMENTUM COMPACTION LATTICESY. Papaphilippou, J. Barranco, W. Bartmann, M. Benedikt, C. Carli, CERN, Geneva, SwitzerlandR. de Maria, S. Peggs, D. Trbojevic, Brookhaven National Laboratory, Upton, NY, USAAbstractThe effect of magnet misalignments in the beam or-bit and linear optics functions are reviewed and correctionschemes are applied to the negative momentum compactionlattice of PS2. Chromaticity correction schemes are alsoproposed and tested with respect to off-momentum opticsproperties. The impact of the correction schemes in the dy-namic aperture of the lattice is ﬁnally evaluated.INTRODUCTIONThe replacement of the aging Proton Synchrotron atCERN with a new ring (PS2) is a key element in the in-jector upgrade strategy for exploiting the full physics po-tential of LHC [1]. The 1346.4 m long ring with race-track shape will avoid transition energy, as the ring’s lat-tice is tuned to provide Negative Momentum Compaction(NMC) [2]. Among the different correction packages forcontrolling and reducing the effect of magnet errors andmisalignments, particularly important are those for orbitand chromaticity control. The efﬁciency and performanceof these two correction systems is being evaluated. For thechromaticity correction, particular emphasis is given to theinduced off-momentum optics distortion and the impact tothe dynamic aperture (DA).ORBIT CORRECTION56 horizontal and 54 vertical correctors for a total of 110beam position monitors are distributed around the ring, ad-jacent to quadrupoles, in order to take advantage of the lo-cal beta function peaks. The corrector length is 30cm whilethe monitors are 10cm long. In all the studies, the nominaloptics of the NMC ring are used with the working pointat (Qx, Qy) = (13.25, 8.21). Random errors, includingrelative dipole ﬁeld distortion, transverse quadrupole andlongitudinal dipole shifts and dipole tilts around the beamaxis, are distributed around the ring with a Gaussian cut at3σ. Their magnitude is chosen following the experiencefrom the PS or similar synchrotrons. The rms values of theerrors are displayed in Table 1 along with average maxi-mum displacement of their individual contribution for 50random machines. The maximum effect of the average dis-placement is around 9mm, a typical value observed at thePS before correction.For the orbit correction, the CORRECT module inMADX [3] was used with the MICADO (most effectivecorrector) algorithm [4]. 100 correctors out of 110 wererandomly chosen and a failure of 5% of the monitors wasError RMS value 〈(Δx/Δy)max〉 [mm]Rel. dipole ﬁeld error 5 · 10−4 8.8 / —-Trans. quad. shift 0.2 mm 8.8 / 8.6Long. dipole shift 0.3 mm 0.3 / —-Dipole tilt 0.3 mrad —- / 5.4Table 1: Error sensitivity of the NMC lattice for a sampleof 50 machines.Before correction After correctionΔx Δy Δx Δy〈(Δ)max〉 [mm] 13.6 11.6 0.5 0.4〈(Δ)rms〉 [mm] 5.2 5.0 0.2 0.1Table 2: Average maximum and rms orbit distortion beforeand after correction, for a sample of 500 random seeds.simulated. Only one third of the total number of correctorsis necessary, although, different sets are used for the dif-ferent machines. The orbit is corrected by a factor of 25with a resulting average maximum displacement of around0.5mm which is considered to be a relatively small orbitFigure 1: Distribution of the maximum orbit deviationat the horizontal (top) and vertical plane (bottom), before(left) and after correction (right).TH6PFP043 Proceedings of PAC09, Vancouver, BC, Canada3802Beam Dynamics and Electromagnetic FieldsD01 - Beam Optics - Lattices, Correction Schemes, TransportFigure 2: Orbits before (blue) and after correction (red) forthe horizontal (left) and vertical plane (right).deviation for machine operation. Fig. 1 presents the distri-bution of the maximum orbit deviation in the horizontal andvertical plane, before and after correction. The distributionsharpens around the average of 0.4-0.5mm after correctionand less than 1% of the machines exceed 1mm maximumorbit distortion. The good efﬁciency of the correction isalso visible in Fig. 2, where the orbits from 30 machinesare displayed, before and after correction. Note that theobtained corrector kicks do not rise above 0.2mrad whichresults in a bending ﬁeld of around 0.12T. As the availabledrift space is tight and the quadrupole strengths high, onemay foresee to cut the corrector length down to 20cm byincreasing the maximum ﬁeld to 0.2T.CHROMATICITY CORRECTIONThe chromaticity is controlled by a set of 40cm-long sex-tupoles placed in the NMC module in a way that they takeadvantage of the peaks on the beta functions and disper-sion, as shown in Fig. 3. They may form up to 4 familieswith 2 symmetric members, apart from MS.4 which hasonly one member as the symmetric position is taken by anorbit corrector. Three correction schemes have been tested.The simplest one is using two families to correct only chro-maticity by connecting in series the two symmetric centralsextupoles (MS.2 and MS.3). A second variant is formedby connecting in series MS.1 with MS.3 and MS.2 withMS.4. The MS.1 and MS.4 have opposite polarities withrespect to MS.1 and MS., as the dispersion in these loca-tion has opposite sign. The last scheme is by using all fourfamilies powered individually and in principle is able tocorrect two more parameters.For the chromaticity correction, the matching moduleof MADXPTC [3] is used. All schemes are able to setthe chromaticity to zero. The last one is also attemptingto reduce the horizontal and vertical off-momentum beta-beating. The maximum normalized sextupole strength is0.25m−2, which translates to 0.5T at top energy and 7cmpole tip. The effect of the sextupoles in the off-momentumbeta beating is presented in Fig. 4. In all the plots , themaximum and rms value of the horizontal and vertical betavariation is displayed over a range of momentum spreads,from -1% to +1%. The top left plot corresponds to the un-corrected case. At momentum spreads close to 1% the hori-zontal beta beating becomes very large due to the approach????? ?????????? ????Figure 3: Optics of the NMC module with the positions ofthe four chromaticity sextupole families.of the integer tune Qx = 13. After correction the horizon-tal beating is signiﬁcantly reduced for all 3 schemes andthe vertical peak value is slightly increased to about 25%.Actually the 4-family scheme, which is supposed to correctalso the beta beating, affects mostly the vertical plane.??????????????????????????????????? ??????? ??????? ??????? ??????? ?? ?????? ?????? ?????? ?????? ?????????????????????????????? ??????????????????????? ???Figure 4: Off-momentum beta beating before (top left) andafter chromaticity correction, for the 3 schemes, using onlythe two central sextupole families (top right), connectingall sextupoles in two families (bottom left) and using allfour families (bottom right). The curves correspond to hor-izontal maximum (blue) and horizontal rms (red), verticalmaximum (purple) and vertical rms beta beating (green).The off-momentum beta beating estimation before andafter correction suggests that the 2nd order chromaticity isnot affected by the inclusion of chromaticity sextupoles.The variation of the horizontal and vertical tune with mo-mentum displayed on the tune diagram, can be found on theleft of Fig. 5. The curves correspond to different sextupolecorrection schemes and the momentum varies from -1% to1%. The green curve corresponding to the scheme whereonly MS.2 and MS.3 are used presents the larger tune-shiftwith momentum. Even in this case, the maximum tune-shift is around 6×10−3 in the horizontal and 12×10−3 inthe vertical plane. In the other two schemes the 2nd orderProceedings of PAC09, Vancouver, BC, Canada TH6PFP043Beam Dynamics and Electromagnetic FieldsD01 - Beam Optics - Lattices, Correction Schemes, Transport 3803chromaticity is reduced by more than a factor of two.13.249 13.25 13.251 13.252 13.253 13.254 13.255 13.2568.2048.2068.2088.2108.2128.2148.2168.218QxQy13.20 13.21 13.22 13.23 13.24 13.25 13.26 13.27 13.288.198.208.218.228.238.248.25QxQyFigure 5: Tune-shift with momentum spread from -1% to1% (left) and ﬁrst order tune-shift with amplitude up to10σ and zero momentum spread (right) for the differentchromaticity correction schemes, using only the two cen-tral sextupole families (green), connecting all sextupoles intwo families (purple) and using all four families (blue).IMPACT TO NON-LINEAR DYNAMICSThe sextupoles introduce non-linear ﬁelds and may re-duce the DA. The ﬁrst order detuning with amplitude isshown in the tune diagram for amplitudes of up to 10σ inthe right plot of Fig.5, for the different sextupole schemes.The resonant lines up to 4th order in the vicinity of theworking point are also traced. The red lines are system-atic resonances, blue are random and the full and dashedlines represent normal and skew resonances. The evalu-ation includes the leading order effect of magnet fringe-ﬁelds which is sextupole-like in the dipoles and octupole-like in the quadrupoles [5], both inducing a linear tune-shiftwith the action. The tune-shift with amplitude in all 3 casesis of the order of 5×10−2 at 10σ. The smallest footprintcorresponds to the case of all sextupoles connected in 2families (purple). The only resonance crossed by the othertwo tune footprints (2 central sextupoles only and four fam-ilies) is the coupling (1,−1) which corresponds also tothe 4th order (2,−2) resonance, excited at ﬁrst order byquadrupole fringe ﬁelds and to 2nd order by sextupoles.Figure 6: Amplitude of 3rd (left) and 4th order (right) res-onance driving terms for the different chromaticity correc-tion schemes, using only the two central sextupole families(blue), connecting all sextupoles in two families (red) andusing all four families (yellow).Another indication of the induced non-linear effects isthe 3rd and 4th order Hamiltonian resonance driving termamplitudes (Fig. 6). The different bar colors correspondto the various chromaticity sextupole arrangements. Thesmallest impact comes from the scheme using only 2 sex-tupole families (blue bars) and the largest corresponds tothe 2 family scheme with all systematic sextupoles con-nected in series, although the ﬁnal performance may beheavily inﬂuenced by the choice of the working point andamplitude detuning. 0 5 10 15 20 25 30-20 -15 -10 -5  0  5  10  15  20? y?xDA onDA +0.01DA -0.01Geometrical Aperture 0 2 4 6 8 10 12 14 16-20 -15 -10 -5  0  5  10  15  20? y?xDA onDA +0.01DA -0.01Geometrical Aperture 0 2 4 6 8 10 12 14 16 18 20-20 -15 -10 -5  0  5  10  15  20? y?xDA onDA +0.01DA -0.01Geometrical ApertureFigure 7: Horizontal versus vertical dynamic aperture in σfor the 3 sextupole schemes, using only the two central sex-tupole families (top left), connecting all sextupoles in twofamilies (top right) and four families (bottom). Differentcurves correspond to 1% (blue), -1%(green), and zero mo-mentum spread (red) and the geometrical aperture (purple).The resonance driving terms amplitudes are well corre-lated with the DA, after tracking particles in 5D for 1000turns with MADXPTC [3]. The different curves corre-spond to 1% (blue), -1% (green), and zero momentumspread (red) and the geometrical aperture is traced in pur-ple. The 2 central sextupole scheme shows the largest DA(especially in the vertical plane) followed by the 4 familyscheme and the 2 families with all symmetric sextupolesin series. All the schemes provide a conformable DA ascompared to the physical aperture.In conclusion, the orbit and chromaticity correction donot represent major challenges for the dynamics of the PS2NMC ring. Both correctors may be reduced in size (steer-ers) or number (chromaticity sextupoles) in order to in-crease the available drift space for other equipment or thelength of the adjacent quadrupole magnets and thereby en-larging the tunability of the lattice. Detailed non-linear dy-namics studies are in progress to evaluate the interplay be-tween space-charge and magnetic non-linearities.REFERENCES[1] R. Garoby, EPAC08, Genova, Italy, p.3734, 2008.[2] Y. Papaphilippou et al., these proceedings.[3] http://mad.web.cern.ch/mad/[4] B. Autin and Y. Marti, CERN-ISR-MA-73-17,1973.[5] E. Forest, Beam dynamics, A new attitude and framework,Harwood Acad. Pub., 1998.TH6PFP043 Proceedings of PAC09, Vancouver, BC, Canada3804Beam Dynamics and Electromagnetic FieldsD01 - Beam Optics - Lattices, Correction Schemes, Transport

Orbit, optics and chromaticity correction for PS2 negative momentum compaction lattices

The effect of magnet misalignments in the beam orbit and linear optics functions are reviewed and correction schemes are applied to the negative momentum compaction lattice of PS2. Chromaticity correction schemes are also proposed and tested with respect to off-momentum optics properties. The impact of the correction schemes in the dynamic aperture of the lattice is finally evaluated

Papaphilippou,Y.

Barranco, J.

Bartmann, W.

Benedikt, M.

Carli, C.

De Maria, R.

Peggs, S.

Trbojevic, D.

UNT Digital Library

. ,..";:::;:} :..;.-:;....BROOKHAVENN/\TION·J("L LABO RAT ORYBNL-81811-2009-CPOrbit, optics and chromaticity correction for PS2negative momentum compaction latticesY0 Papaphilippou, J & Barranco, W 8 Hartmann,M"Benedikt, C8 CarliCERN, Geneva, SwitzerlandR. de Maria, S. Peggs, D. TrbojevicBrookhaven National Laboratory, Upton, NY, USAPresented at the Particle Accelerator Conference (PAC09)Vancouver, B.C. , CanadaMay 4-8, 2009Coliider-Accelerator DepartmentBrookhaven National LaboratoryP.O. Box 5000Upton, NY 11973-5000'vvvvw.bnLgovNotice: This manusc ript has been authored by employees of Brookhaven Science Associates, LLC underContract No. DE-AC02-98CH10886 with the U.S. Department of Energy. The publish er by accepting themanuscript for publicati on acknowledges that the United States Government retains a non-exclusive, paid-up,irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow othersto do so, for United States Government purposes.This preprint is intended for publication in a journal or proceedings. Since changes may be made beforepublication, it may not be cited or reproduced without the author's permission.DISCLAIMERThis report was prepared as an account of work sponsored by an agency of theUnited States Government. Neither the United States Government nor anyagency thereof, nor any of their employees, nor 2J.""1Y of their contractors,subcontractors, or their employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, completeness, or anythird party' s use or the results of such use of any information, apparatus, product,or process disclosed, or represents that its use would not infringe private ly ownedrights. Reference herein to any specific commercial product, process , or serviceby trade name, trademark, manufacturer, or otherwise, does not necessarilyconstitute or imply its endorsement, recommendation, or favoring by the UnitedStates Government or ~l1Y agency thereof or its contractors or subcontractors.The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agency thereof.ORBIT, OPTICS AND CHROM.4.TICITY CORRECTION FOR PS2NEGATIVE lVIOIVIENTUM COMPACTION LATTICESY. Papaphilippou, J. Barranco, W. Bartmann, M. Benedikt , C. Carli, CERN, Geneva, SwitzerlandR. de Maria, S. Peggs, D. Trbojevic, Brookhaven National Laboratory, Upton, NY, USATable 1: Error sensitivity of the N1'vfC lattice for a sampleof 50 machines.AbstractThe effect of magnet misalignments in the beam or-bit and linear optics function s are reviewed and correctionschemes are app lied to the negati ve momentum compactionlattice of PS2. Chromaticity correction schemes are alsoproposed and tested with res pect to off-momen tum opticsproperties . The impact of the correction schemes in the dy-namic aperture of the latti ce is finally evaluated.ErrorReI. dipole field errorTrans. quad. shiftLong. dipole shiftDipole tiltRMS value5 .10 4O.2 mmO.3 1Tlm0.3 mrad(( 6.x/ flY)max) (rom]8.8/ -8.8 /8.60.3 / -- / 5.4Table 2: Average maxim um and rm s orbit distortion beforeand after correction, for a sample of 500 random seeds .simu lated. Only one third of the total number of correctorsis necessary, although, different set s are used for the dif-ferent machines. The orb it is corrected by a factor of 25with a resulting average maximum displ acement of aroundO.5mm whic h is considered to be a relatively small :orbi tINTRODUCTIONThe replacement of the aging Pro ton Synchrotron atCERN with a new rin g (PS2 ) is a key element in the in-jector upgrade strategy for exploiting the full physics po-tential of LHC [1]. The 1346.4 m long ring with race-track shape will avoid transition energy, as the ring's lat-tice is tuned to provide Negative Momentum Compact ion(NMC) [2]. Among the different correction packages forcontrolling and reducing the effect of magnet errors andmisalignments, particularly important are those for orb itand chro maticity control. The efficie ncy and performanceof these two correction systems is being evaluated. For thechromaticity correction , particu lar emphasis is given to theinduced off-momentum optics distortion and the impact tothe dynamic aperture (DA).((6.)max) [mm] I( ( fl ) nn~ ) [mm] i 0.1lI,..., [mm!..c.=Etl !oOiE:J (0 .J!: .Figure l : Distribution of the maximum orbit deviationat the horizontal (top) and vertical plane (bottom), before(left) and after correction (right) .56 horizontal and 54 vertical correctors for a total of 110beam position monitors are distributed around the ring, ad-jacent to quadrupoles , in order to take advantage of the lo-cal beta function peaks. The corrector length is 30cm whilethe monitors are lOcm long. In all the studies, the nominaloptics of the NMC ring are used with the working pointat (Q:1:' Qy ) = (13.25,8.21). Random errors, includingrelat ive dipole field distort ion, transverse qu adrupole andlongitudinal dipole shifts and dipole tilts around the beamaxis, are distribu ted around the ring with a Gaussian cut at30'. Their magnitude is chosen following the experiencefrom the PS or similar syn chrotrons. The rm s values of theerrors are displayed in Table 1 along with average maxi-mum displacement of their individual contribution for 50random machi nes . T he maximum effect of the average dis-placement is around 9mm, a typical value observed at thePS before correction.For the orbit correction, the COR..~ECT module inMADX [3} was used with the MICADO (most effect ivecorrector) algorithm [4). 100 correctors out of 110 wererandomly chosen and a failure of 5% of the monitors wasORBIT CORRECTIONMS.l ~~; .s.:'M5.:?:V: S.>:""r-·· ··_ · ·.,_·_-_·_~·_- --_ · _- ---- --l".;i I\1jFigure 2: Orbits before (blue) and after correction (red) forthe horizontal (left) and verti cal plane (right).s tm sFigure 3: Optics of the NlvIC module with the po sitions ofthe four chromaticity sextupole families.of the integer tune Q x = 13. After correction the horizo n-tal beating is significantly red uced for all 3 schemes andthe vertical pea k value is slightly increased to about 25% .Actually the 4-family scheme, which is supposed to correctalso the beta beating , affects mostly the vertical phme./."lICI~!; ~ l ~ ijaJ!!t(~ i,~~,;-~-;,.c;';-';;'.~j~7.:v;;~· · ·~~':'·o:X:C- jii:~· ·Q;i:';· · ·5;;:~ ···~~UIa.~.!'~ ·" I ·o.nIl}-~ rI'" .~l -ccce 4.i.~ 4(44 4(r~ ;;:~ .:a.~ t~'", C'"n oJ<A... ~_'lIIQ1~ r·The off-momentum beta beating estimation before andafter correction suggests that the 2nd order chromaticity isnot affected by the inclus ion of chro mat icity sextupoles.The variat ion of the horizontal and vertical tune with mo-mentum displayed on the tune diagram, can be found on theleft of Fig. 5. The curves correspond to differen t sex tupolecorrection schemes and the momentum varies from -1% tol %. Th e green curve corresponding to the scheme whereonly MS.2 and MS.3 are used presents the larger tune-shiftwith momentum. Even in thi s case , the maximum tune -shift is around 6 x 10- 3 in the horizontal and 12x 10- 3 inthe vertical plane. In the other two schemes the 2nd orderFigure 4: Off-momentum beta beating before (top left) andafter chro maticity correction, for the 3 schem es, using onlythe two central sextupole families (top right), connectingall sext upoles in two fam ilie s (bo tto m left ) and using allfour families (bottom right) . The curves corres pond to hor-izontal maximum (blue) and horizontal rms (red), vert icalmaximum (purple) and vertical rms beta beating (green).CIIROMATICITY CORRE CTIONdeviation for machine operation . Fig. 1 presents the distri-bution of the maximum orbit deviation in the horizontal andvertical plane, before and after correction. The dis tribut ionsharpens around the average of OA-O.5mm after correctionand less than i % of the machines exceed Irnm maximumorbit distortion. The good efficiency or the corre ction isalso visible in Fig. 2, where the orbits from 30 machinesare displayed, before and after correction. No te that theobtained corrector kicks do not rise above O.2mrad whichresults in a bending field of around 0.] 2T. As the availabledrift space is tight and the quadru pole strengths high, onemay foresee to cut the corrector length down to 2Ucm byincreasing the maximum field to O.2T.The chromaticity is controlled by a set of 40cm-long sex-tupoles placed in the NMC module in a way that they takeadvantage of the peaks on the beta fu nction s and disper-sion , as shown in Fig. 3. They may form up to 4 familieswith 2 symmetric mem bers , apart from MS.4 which hason ly one member as the symmetri c po sition is taken by anorbi t corrector. Three correcti on schemes have been tested .The simplest one is usin g two fami lies to correct on ly chro -maticity by con necting in series the two symmetric centralsextupoles (1\I1S.2 and MS .3). A second variant is form edby conn ecting in series MS.l with MS.3 and MS. 2 withMS.4. The MSJ and MS.4 have opposite pol arities withrespect to MS.l and MS., as the dispersion in these loca-tion has opposite sign . The last scheme is by using all fourfamilies powered individually and in principle is able tocorrect two more parameters.For the chromaticity correction , the matching moduleof MA DXPTC [3J is used. An schemes are able to setthe chrom aticity to zero. The last one is also attemptingto reduce the horizontal and vertical off-momentum beta-beating. The maximum normalized sextupole strength isO.25m ··:'! , which translates to O.ST at top energy and 7cmpole tip . The effect of the sextupoles in the off-momentumbeta beati ng is presented in Fig. 4. In all the plots , themaximum and rms value of the horizontal and vertical betavariation is displayed over a range of momentum spreads,from -1% to +1%. The top left plot corresponds to the un-corrected case. At momentum spreads close to 1% the hori-zontal beta bea ting bec omes very large due to the approachchromaticity is reduced by more than a factor of two.Figure 5: Tune-shift with momentum spread from ..1% toI% (left) and first order tune-shift with amplitude up toi 0<7 and zero momentum spread (right) for the differentchromaticity correction schemes, usin g only the two cen-tral sextupole fam ilies (green), connecting all sextu poles intwo familie s (purple) and using an four families (blue).IMPACT TO NONNLINEAR DYNAl\-1ICSThe sextupoles introduce non- linear fields and may re-duce the DA. The first order detuning with amplitude isshown in the tune diagram for ampli tudes of up to lOa inthe right plot of Fig.5, for the different sextu pole schemes.The resonant lines up to 4th order in the vicinity of theworking point are also traced. The red lines are system-atic resonances, blue are random and the full and dashedtines renresent normal and skew resonances. The evalu-ation iu'd udes the leading order effect of magne t fringe-fields which is sextupole- like in the dipoles and octupo le-like in the quadrupoles [5] , both inducing a linear tune- shiftwith the action . The tune-sh ift with amplitude in all 3 casesis of the order of 5 x 10- 2 at lOo'. The smallest footprintcorresponds to the case of ail sextupoles connected in 2famil ies (purple). The only resonance crossed by the othertwo tune footprin ts (2 cen tral sextupoles only and four fam-ilie s) is the coupling (11 -1) which corresponds also tothe 4th orde r (2, - 2) reso nance, excited at first order byquadrupole fring e fields and to 2nd order by sextupoles.4~ ~ ~~! !JI~I.~jil~I-1!D=~]!I;=jd~~~-;ri~~C) (1,0) ~ 1 .2} ( t -.2) t~.Oi HU\1 \::"4' fl.-21 {/J,2} W.4iFigure 6: Ampli tude of 3rd (left ) and 4th order (right) res-onance driving tenns for the different chromaticity correc-tion schemes, using only the two central sex tupole fam ilies(blue), connecting all sextupoles in two families (red) andusing all four families (yellow).Another indication of the induced non-linear effects isthe 3rd and 4th order Hamiltonian resonance driving termamplitudes (Fig . 6). The different bar colors correspondto the various chromaticity sextupole arrangements. Thesmal lest impact comes from the scheme using only 2 sex-tupo le families (blue bars) and the larges t corresponds tothe 2 family scheme with all systematic sextupoles con-nected in series , altho ugh the final perform ance may beheavily influenced by the choice of the work ing po int andamplitude detu ning.Figure 7: Horizontal versus vertical dynamic aperture in afor the 3 sextupole schemes, using only the two central sex-tunole families (top left ), connecting all sextupoles in twofa~i1ies (top fight) and four fa milies (bottom). Differentcur ves correspond to 1% (blue), -1%(green), and zero mo-mentum spread (red) and the geometrical apert ure (purple).The resonance driving tenus ampli tudes are well corre-lated with the DA, after tracking particles in 5D for 1000turns with MADXPTC [3]. The different cur ves corre-spond to 1% (blue) , -1% (green), and zero momentumsoread (red) and the geometrical ape rture is traced in pur-pie . The 2 central sextupole scheme shows the larges t DA(especi ally in the vert ical plane) followed by the 4 familyscheme and the 2 fam ilie s with all symmetric sextupolesin series. All the schemes pro vide a confo rmable DA ascompared to the phy sical aperture .In conclusion , the orbit and chromaticity correction donot represent major challenges for the dynamics of the PS2NMC ring. Both correctors may be reduced in size (steer-ers) or number (chromatic ity sextupoles) in order to in-crease the availab le drift space for other equipment or thelength of the adjacent quadrupole magnet" and thereby en-larging the tunability of the lattice. Detailed non-linear dy-namics studies are in pro gress to evaluate the interplay be-tween spac e-ch arge and magnetic non-linearities.REFERENCES[1] R. Garoby, EPAC08, Genova, Italy, p.3734, 2008.[2] Y. Papaphilippo u et al ., these proceedings.(3] http://m ad.web.cern .ch/m adl[4J B. Autin and Y. Marti. CERN-ISR -MA- 73- 17,1973.(5J E. Forest, Beam dynam ics. A new attitude and framework,Harwoo d Acad. P ub., 199 8.

Orbit, optics and chromaticity correction for PS2 negative momentum compaction lattices

Abstract

Similar works

Full text

Available Versions

CERN Document Server

UNT Digital Library