Optics and Lattice Optimizations for the LHC Upgrade Project - CERN

Proceedings of IPAC2012, New Orleans, Louisiana, USA

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OPTICS AND LATTICE OPTIMISATIONS FOR THE LHC UPGRADE PROJECT*

Abstract The luminosity upgrade of the LHC collider at CERN is based on a strong focusing scheme to reach lowest values of the beta function at the collision points. Several issues have to be addressed in this context, that are considered as mid term goals for the optimisation of the lattice and beam optics: Firstly a number of beam optics have been developed to establish a baseline for the hardware R&D, and that will define the specifications for the new magnets that will be needed, in Nb3Sn as well as in NbTi technology. Secondly, the need for sufficient flexibility of the beam optics especially for smallest β* values, the need for a smooth transition between the injection and the collision optics, the comparison of the optics performance between flat and round beams and finally different ways to optimise the chromatic correction, including the study of local correction schemes. This paper presents the status of this work, which is a result of an international collaboration, and summarises the main parameters that are foreseen to reach the HL-LHC luminosity goal.

for β*=10cm which is considered as ultimate limit of a feasible squeeze optics [2]. As can be seen in the plot, the ATS scheme has a strong impact on the optics of both the matching section of the high luminosity IPs but also on the optics of the neighboring LHC sectors. Therefore a large optics investigation has been launched to study the flexibility of the overall upgrade optics, taking into account especially the β functions at Q4 in IP1/5 where crab cavities will be installed. In addition, beam optics scenarios have to be studied for a variety of different beam optics in the neighboring sectors where special boundary conditions have to be observed in proton as well as heavy ion operation.

INTRODUCTION The goal of the LHC upgrade project is the production of a total integrated luminosity of approximately 3000 fb -1 over the lifetime of the HL-LHC. To achieve this, a considerable reduction of the beta function at the high luminosity Interaction Points (IP) is needed, as values as low as β*=15cm are aimed for. The fundamental concept is based on a Achromatic Telescopic Squeezing (ATS) scheme [1] which has been proposed in this context and that allows both the production and the chromatic correction of very low β* values. This scheme relies essentially on a two-stage approach: First a pre-squeeze optics is established by using exclusively the matching quadru-poles of the high luminosity insertions IR1 and IR5. In a second stage, β* can be further reduced using only on the insertions on either side of IR1 and IR5 creating sizable β-beating bumps in the four neighboring sectors. These waves of β-beating create the required β* reduction and at the same time boost, at constant strength, the efficiency of the chromaticity sextupoles located in the sectors 81, 12, 45 and 56. Figure 1 shows the optics ___________________________________________

* The research leading to these results has received funding from the European Commission under the FP7 project HiLumi LHC, GA no. 284404, co-funded by the DoE, USA and KEK, Japan.

01 Circular and Linear Colliders A01 Hadron Colliders

Figure 1: ATS optics with β*=10 cm, at IP5: The transverse beam sizes [mm] are plotted between the neighboring sectors IR4 and IR6. Table 1 summarises the main parameters for the HL-LHC project, compared to the standard LHC design values [3]. Table 1: HL-LHC Parameters Compared to the LHC Nominal Values LHC nominal

HL-LHC

Np [10 ]

1.15

2.2

nb

2808

2808

β [m]

0.55

0.15

εn[μm]

3.75

2.5

bunch distance

25ns

25ns

x-angle [μrad]

300

11

*

Lpeak

590

1*10

34

7.3*1034

ISBN 978-3-95450-115-1 151

c 2012 by IEEE – cc Creative Commons Attribution 3.0 (CC BY 3.0) — cc Creative Commons Attribution 3.0 (CC BY 3.0) Copyright ○

B. Holzer, R. De Maria, CERN, Geneva, Switzerland , A. Chance, B. Dalena, J. Payet, CEA-SACLAY DSM/Irfu/SACM, France, A. Bogomyagkov, BINP SB RAS, Novosibirsk, Russia R. B. Appleby, L. Thompson, The University of Manchester and the Cockcroft Institute, UK, M. Korostelev, K. M. Hock, A. Wolski, University of Liverpool and Cockcroft Institute, UK. C. Milardi, INFN, Frascati, Italy, A. Faus-Golfe, J. Resta Lopez, IFIC (CSIC-UV), Valencia, Spain


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Based on nnew supra connducting tripleet quadrupolees and depending oon the technology that willl be availablle for these magneets (NbTi / Nb3Sn) N gradiients betweenn 120 T/m and 1770 T/m can be b assumed and a accordinggly a variety of different beaam optics has h been stuudied. However noot all the bouundary conditions (namelyy the betas in fronnt of Q4) assuure the possib bility to matcch the new triplet in the LHC C high lumiinosity interaaction regions to tthe existing arc a structure. In order to find acceptable innitial boundarry conditions,, we have scaanned the optics vaalues in the horizontal and vertical v plane aat the location of Q4 in a wide w range, th hus verifyingg the possibility too match the generated trriplet into thee arc structure of tthe two LHC beams. Figure 2 shows thee area in the βx andd βy space whhere an optim mal convergennce of the matchingg of the new w triplet with h the two rinngs is obtained. It is mainly determined by b the consstraint imposed by tthe magnets inn the LHC maatching sectioons of the two LHC C rings, i.e. Q44 ... Q7 in thee interaction reegion layout - witth one of thee most criticaal limits beingg the maximum alllowed strengtth of the Q7 qu uadrupole.

Figure 2: Hoorizontal and vertical v β-funcctions in front of Q4, which leeads to the connvergence of the matchingg. The plot comparres the situaation of two o different ttriplet gradients. The solutioons plotted in Figure 2 defiine the pre-squueeze optics in thee sense that - for a given optics o parametter at the location of the crab caavities - and for a β-functiion at the IP of β*= 40cm, the laayout of the trriplet quadruppoles, following a well-definedd strategy [4 4], is determ mined. However noot all the bouundary conditions (namelyy the betas in fronnt of Q4) alloow the possib bility to matchh the new triplet in the LHC C high lumiinosity interaaction regions. Thhe successful beam b optics shown s in Figuure 2 are equivaleent in terms of maximum beta funcctions reached in the tripleet quadrupolles and naatural chromaticity of the lattice.. The resulting g parameters oof the triplet quadrrupoles differr only slighttly from the predefined valuues in magnett length and maximum m feaasible gradient of gg=170 T/m. In a moree detailed appproach the β--functions thaat are achievable inn the pre-squueeze optics have h been stuudied: Assuming a gradient in i the tripleet quadruplees of g=170T/m thhe convergencce of the optics match has been studied for ddifferent β* values. v Again,, the optics aat the position of Q4 is inclluded as add ditional bounndary condition. F Fig. 3 summ marises the results: Whiile a comfortable variety of different beam optics is obtaained ISBN 978-3-95450-115-1 152

for the t standard value of β*==40cm in thee pre-squeezee opticcs, the flexibiility of the laattice shrinks if smaller β* valuees are aimed for. In the eextreme case of β*=35cm m of posssible optics iss obtained. only in a limited number n Moree severely, a successful application of the ATS scheme is possible only for pree-squeeze optiics that allow w β*-v han β*=37cm values larger th ost promisingg m. For the mo case of βx=510m and βy=770m on of Q4 (seee m at the locatio Fig. 2), the properties of the laattice have beeen studied inn moree detail, includ ding:  The posssibility to com ptics with thee mbine the op ATS scheme to reducee the β*-functions from thee pre-squeeeze values of β*=40cm dow wn to the finall values off β*=15cm, matic aberratioons  the chrom pact of the ATS scheeme on thee  the imp neighboring LHC sectoors.

Figu ure 3: Horizontal and verticaal beta functio ons in front off Q4 which w lead to the convergen ence of the maatching of thee new triplet (170 T/m) with thhe LHC latticee in the highh lumiinosity interacction regions. Th he chromatic aberration inn the case off β*=15cm is show wn in Fig. 4. Given the nnominal LHC C momentum m spreaad of Δp/p=of 1*10-4 the ccurve of Fig. 4 reflects thee comffortable momentum acceptaance that is ob btained.

Figu ntal and verttical tune forr the upgradee ure 4: Horizon opticcs as a function of Δp/p. The figure compares thee c situaation of two allternative tripllet gradients.

OPTICS FLEXIBIL DIES LITY STUD Th he flexibility of o the nominaal LHC opticss is limited inn nd attempts too reach smalllest β* valuess several aspects an are limited l by thee betatron phaase advance frrom the innerr tripleet to the arcc sextupoles, by the strengths of thee matcching quadrup poles and by aperture requ uirements. To 01 Circular and Linear Colliders A01 Hadron Colliders

overcome thhese inherent optical boun ndaries alternnative LHC long sttraight sectionn (LSS) layouts are studiedd. The existing latticce, designed to t match the optical o functioons at the collision point to the periodic p arc op ptics, was frozzen in the early LH HC design annd, given the hardware chaanges associated w with HL-LHC, may be upgraaded. The goaal is to explore thhe limits of thhe nominal op ptics, using a case study of the Q5 andQ6 maatching quadru upoles replaceed by equivalent haardware doubblets (the replaacement of booth is needed to m maintain the FODO structture of the L LSS). Figure 5 shoows a possiblle resulting LSS L optics forr this case study. The optical flexibility f maanifests itselff in a lower attainaable beta functtion at the IP, β*=23cm, wiithout the need of tthe ATS squeeeze techniquee. In a furtherr step we shall atttempt to gett highest latttice flexibility ty by studying alll necessary modificationss in the exiisting quadrupoles from Q4-Q7.. Based on a standard minii beta scheme in thhe LHC insertiions LSS1 and d LSS5 we aim m for the target betta* of the HL--LHC project,, β*=15cm.

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 β*=40cm pree-squeeze optiics in IP1/ β*=50cm = in IP8  β*=5.5m injeection optics inn IP1 / β*=10m m in IP8 In addition to the optics requirementss at the IPss addittional constraaints have beeen taken into account: thee samee phase advan nce in beam 1 and beam 2 of o LHC and a satisfactory solutio on for all optiics scenarios with w the samee overall phase advance. To determine the area off satisfactory opticcs convergennce for thee first fourr scenarios, the horrizontal and vvertical phasee advances inn LSS 8 have been n varied andd the optics has been rematcched according to the new boundary conditions. Thee resullts are shown n on Figure 6.. Depending on the opticss consstraints, acceptable results aare obtained for a numberr of different d phasse advances across the IR. I The areaa surro ounded by th he black linee indicates th he values forr whicch obeying all a optics reqquirements fo or luminosityy operation in IP8 8 and a com mmon phasee advance iss achieevable. ϕy

Figure 5: Thhe optics of the long straigh ht section, shoowing the horizontaal (blue) and vertical (red d) β-functions as a function of longitudinal distance fro om IP5, withh the matching quaadrupoles Q5 and Q6 replacced by doubleets. The studyy of lattice modifications m on a longer time scale includees a new layoout of the maatching sectioon, in particular reeplacing each Q5 and Q6 by a doubleet (as presented heere), reinforcing Q7 by a longer quadruupole and replacingg Q4 by a quaadrupole tripleet.

OPTICS S IN NEIG GHBORING G SECTOR RS The beam m optics in thhe neighborin ng LHC sectoors is strongly affeected by the ATS A scheme. As can be seeen in Figure 1, thhe beta beatinng wave whiich is essentiial to reduce the beeta function inn IP1 and IP5 5 and obtain vvalues well below tthe pre-squeezze optics, is created deliberrately in the matcching sectionns of the neiighboring secctors. However thee optics in thhese regions may m have to obey special bounndary conditioons. This is notably n true inn IP2 and IP8 wheere the high-energy experiments LHCbb and ALICE are loocated and soo the low beta insertion has to be kept flexiblee enough to guarantee g succcessful data taaking of these expperiments. In an extensivee study the ooptics conditions oof these neighboring seectors have been investigated with five diffferent conditiions that had been identified: m round beam m optics in IP1 1/ β*=3m in IP P8  β*=10cm *  β =5cm m/20cm flat beeam optics in IP1/ I β*=3m inn IP8  β*=20cm m/5cm flat beeam optics in IP1/ I β*=3m inn IP8 01 Circular and Linear Colliders A01 Hadron Colliders

ϕx Figu ure 6: Area of stable phase aadvance over IR8 I that lead to su uccessful opticcs convergencce: For four different scenarios the phasse advances arre plotted that lead to possible solutions. The black linne shows the region r where for one o common phase p all opticcs conditions can c be satisfied. An n example of one of the new w optimised beam b optics iss show wn in Figure 7, corresponnding to the situation off β*=3 3m in IP8 and d β*=10cm in IP1. On the left l hand sidee of th he lattice the non-ATS FO ODO optics is i maintainedd wherreas on the rig ght hand side tthe large β-fu unction valuess in th he arc show thee onset of the ATS beta wav ve.

Figu ure 7: Optical solution s for IPP8, combining g the standardd FOD DO optics (leftt ) with the AT TS optics (righ ht of IP).

REFEREN NCES [1] S. Fartoukh, Breaching the Phhase I Optics Limita-tions L forr the HL-LHC, LHC perform mance worksho op, Chamonix, 2012. [2] S. Fartoukh, R.. De Maria, MO OPPC011, thesee proc. [3] O. Bruening: HL-LHC H Param m. Space and Scenarios, S LHC C performance workshop, w Cham monix, 2012. [4] R. De Maria, MOPPC010, M theese proc.

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