The Q0 scheme of the LHC insertion region is based on the introduction of a doublet of quadrupoles at 13 meters from IP. In this scenario the value of can be reduced to 0.25 m with a moderate increase of the function inside the inner triplet. We present here an optical layout, with the requiredmagnets parameters such as gradients, lengths, positions and apertures. We also discuss in some details the tolerance on alignment and the energy deposition

Laface, E

Santoni, C

Scandale, Walter

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Q0 Status ∗E. Laface† , W. Scandale, CERN, Geneva, Switzerland,C. Santoni, Universite´ Blaise-Pascal, Clermont-Ferrand, FranceAbstractThe Q0 scheme of the LHC insertion region is based onthe introduction of a doublet of quadrupoles at 13 metersfrom IP. In this scenario the value of β∗ can be reduced to0.25 m with a moderate increase of the β function insidethe inner triplet. We present here an optical layout, withthe required magnets parameters such as gradients, lengths,positions and apertures. We also discuss in some details thetolerance on alignment and the energy deposition.INTRODUCTIONOne possible option for the LHC IR upgrade [1] is basedon the introduction of two new quadrupoles inside the ex-perimental devices, at 13 meters from IP.The potential of this scenario, discussed in [2], is toreduce the quadratic growth of the β function, since thetwo new quadrupoles should introduce an oscillation ofβ between the IR triplet and the IP. Ideally, the modifiedshape of the β function should allow to interconnect theoptics with β∗ = 0.25 m in the IP-side to the optics withβ∗ = 0.55 m in the inner triplet side, as shown in Fig. 1.02505007501000IP Q1! functionQ0A-Q0B ideal effectFigure 1: β shift with Q0.This ideal behavior is the starting point for a new opti-mization of the interaction region based on five magnets, inwhich the two Q0s should reduce the quadratic increase ofthe β function and the inner triplet should provide the finalfocusing at the interaction point.In this paper we present an IR layout compatible withLHC optics, in which β∗ = 0.25 m, while the maximum βvalue is limited to 5820 m (Fig. 3).∗Work supported by the European Community-Research Infrasctruc-ture Activity under the FP6 ”Structuring the European Research Area”programme (CARE, contract RII3-CT-2003-506395).† Emanuele.Laface@cern.chOPTICS LAYOUTGeometryThe proposed configuration of the interaction region isrepresented in Fig. 2 and summarized in Table 1. The op-tical functions are shown in Fig. 3 for the first 70 metersfrom IP and in Fig. 4 for the whole interaction region.IPQ0B Q0AQ3 Q2 Q1TripletQ0BQ0AQ3Q2Q1TripletFigure 2: Q0 Layout.Table 1: IR Layout.Magnet L∗ [m] Length [m] Gradient [T/m]Q0A 13.0 7.2 240Q0B 20.8 3.6 196Q1 25.8 8.6 200Q2 37.1 11.5 172Q3 52.0 6.0 1600 1000 2000 3000 4000 5000 6000 70000100020003000400050006000s [cm]β [m]  βxβyFigure 3: β function in the Q0-Triplet region when β∗ =0.25 m.With the nominal LHC IR layout and with β∗ = 0.25 m,the maximum value of β is of about 9700 m (Fig. 5 andFig. 6).IR’07 PROCEEDINGS6712.63 12.89 13.15 13.41 13.67 13.93s (m)   [*10**(  3)]lhc.ir5.b1 7tev MAD-X 3.03.41  13/06/07 11.03.460.0500.1000.1500.2000.2500.4000.4500.5000.5500.6000.βx(m),βy(m)βx βy3000.3500.Figure 4: β function with Q0 layout and β∗ = 0.25 m.0 1000 2000 3000 4000 5000 6000 7000010002000300040005000600070008000900010000s [cm]β [m]  βxβyFigure 5: β function in the nominal layout when β∗ = 0.25m.By using the Q0 doublet, the maximum value of β de-creases to 5820 m. The increase of the initial luminosity isof a factor 2 with respect to the LHC optic at β∗ = 0.50either in a zero-crossing angle scheme [3] or when compen-sating the far beam-beam effect. Otherwise it is mandatoryto increase the crossing angle according to [4] and [5]:θc = θc0√β0∗β∗(6.5 + 3√NbnbnLRNb0nb0nLR0) (1)where nb is the number of bunches, Nb is the numberof protons for each bunch, nLR is the number of long-range beam-beam collisions and the 0 index represents thenominal values. The crossing angle affects the luminosity,through the geometric factor, expressed by:F ≈ 1√1 + ( θcσz2σ∗ )2(2)(where σz is the rms bunch length and σ∗ is the transverse12.63 12.89 13.15 13.41 13.67 13.93s (m)   [*10**(  3)]lhc.ir5.b1 7tev MAD-X 3.03.41  21/03/07 10.39.590.01.2.3.4.5.6.7.8.9.10.βx(m),βy(m)[*10**(3)]βx βyFigure 6: Nominal layout at β∗ = 0.25 m.rms beam size). The luminosity is given by:L = FnbNb2frev4piσ∗2(3)where frev is the revolution frequency of the bunch. If thecrossing angle is of 403 µrad, then the gain of the initialluminosity is of 1.75.ApertureThe minimum value of the quadrupole aperture Dmin isestimated by means of the formula [6]:Dmin > 1.1 · (10+2 ·9)σ+2 · (d+3 mm+1.6 mm) (4)with a beam envelope of 9 σ, a beam separation of 10 σ, aβ-beating of 20%, a peak orbit excursion of 3 mm, and amechanical tolerance of 1.6 mm. The parameters depend-ing on β are the rms beam radius σ and the spurious dis-persion orbit d. The values for beta function, the aperturesand the peak field are summarized in Table 2.Table 2: Magnet apertures and peak field.Magnet β Max [m] Dmin [mm] Peak field [T]Q0A 2300 60 7.2Q0B 4300 72 7.1Q1 5780 80 8.0Q2 5820 80 6.9Q3 5770 80 6.4The required integrated gradients may be reached usingNbTi superconductor technology or with Nb3Sn but withan higher margin for the energy deposition. In an furtheroptimized solution should be possible to decrease the gra-dient of Q1 increasing the Q3 with minor changes into theβ function. It should also be possible to have the same gra-dients for the five magnets (Q0A-Q3) saving the number ofpower supply.IR’07 PROCEEDINGS68DetuningThe injection optics corresponds to a β∗ of 5 m. Thecorresponding β function along the IR is shown in Fig. 7.12.63 12.89 13.15 13.41 13.67 13.93s (m)   [*10**(  3)]lhc.ir5.b1 7tev MAD-X 3.03.41  13/06/07 10.43.310.050.100.150.200.250.300.350.400.450.500.550.600.βx(m),βy(m)βx βyFigure 7: β function at injection.The transition between injection and collision is per-formed by varying the gradients of Q4-Q11 as shown inFig. 8. In a more careful optimization, polarity changesshould be prevented. Note that, during the detuning, thegradients of Q0-Q3 remain unchanged.Injection CollisionQ4LQ4RQ5LQ5RQ6LQ6RQ7LQ7RQ8LQ8RQ9LQ9RQ10LQ10RQ11LQ11R200150100500-50-100-150-200Gradient [T/m]Figure 8: Q4-Q11 gradients from injection to collision.MISALIGNMENTSFollowing the arguments in [7] and [8] it is possible toestimate the misalignment tolerance of Q0A and Q0B. Wehave to consider two cases, one in which there is a relativemisalignment in between Q0A and Q0B, the other in whichQ0A-Q0B are in a rigid structure and misaligned with re-spect to the inner triplet.In thin lens approximation, the shift δx(s) of the closedorbit, resulting from quadrupole displacements ∆XQi , isgiven by:δx(s) = ξ[∑i(θ√βx)icos (piQx − |∆µi|)](5)where θi = Kili∆XQi is the deflection angle of the dipolarcomponent of the misaligned magnet Qi, ∆µi = µx(s) −µx(si), Qx is the tune, and the ξ parameter is√βx(s)2 sin(piQx).Note that the sign of δx(s) depends on two factor: thebeam and the quadrupole. A positive dipolar componentfor beam 1 corresponds to a negative one for beam 2. Analignment error in the shared region creates a different ef-fect respect to a misalignment in the not-shared sequence.On the other hand, if the Q0A and Q0B magnets move inphase, the kicks of the quadrupoles tend to be compensatesince the positive dipolar component for the focusing mag-net corresponds to a negative dipolar component for the de-focusing magnet. This is why, quadrupoles with oppositegradients in a rigid structure, tend to compensate the mis-alignment error of the structure itself.A numerical estimation of δx(s) induced by Q0A mis-alignment can be performed using Qx = 64.31, K =0.01027 m−2, l = 7.2 m, βx = 2300 m and |µx(s) −µx(si)| = pi2 . In this case δx(s) ≈ 0.825√βx(s)∆XQxthat means a closed orbit error of 1.5 mm for a displace-ment of 50µm.For Q0B one should use K = −0.0084m−2, l = 3.6 m,βx = 4300 m, Qx = 64.31 and |µx(s) − µx(si)| = pi2 .Then one has δx(s) ≈ −0.459√βx(s)∆XQx and a closedorbit error of 0.8 mm for a misalignment of 50µm.This displacements of the orbits is disruptive for the lu-minosity: a 7.5µm of counter-phase misalignment decreasethe luminosity of 10%. It’s evident that a system of correc-tors is mandatory to compensate this kind of effects.If the Q0 doublet is mounted in a rigid structure, theclosed orbit error induced by a misalignment of the struc-ture itself is compensated to a large extent and the align-ment tolerance becomes of some hundreds of µm.ENERGY DEPOSITIONA preliminary evaluation of the energy deposition inQ0A and Q0B magnet is performed using the design ofFig. 9Figure 9: Q0 design.and the regions inside the magnet are schematized as illus-IR’07 PROCEEDINGS69trated in Fig. 10.57mm62.85mm125mm280mm300mmCopperSSSSHeliumFigure 10: Q0 structure for the FLUKA model.Here the aperture of the magnet is 57mm because isbased on a preliminary model of Q0A magnet. The mag-netic field map is obtained from a 2D ROXIE model andthe total energy absorbed by this geometry is evaluated in asimulation with the FLUKA code. The results of the sim-ulation is in Fig. 11 for the Q0A and in Fig. 12 for theQ0B. 1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1 10 100-30 -20 -10  0  10  20  30[cm]-30-20-10 0 10 20 30energy [mW/cm3]Figure 11: Total energy absorbed by Q0A.For this simulation was used a luminosity of 1035 eventsper second per cm2 and a 1 meter long TAS in front ofQ0A.The power on the magnets is 106W (14.7W/m) for Q0Aand 42.5 W (11 W/m) for Q0B. These powers exceeds thecapabilities of the cryogenic system that can extract at most∼ 10 W/m in ideal conditions. Some solutions can be eval-uated to reduce the energy deposition as proposed in [9]. 1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1 10 100-30 -20 -10  0  10  20  30[cm]-30-20-10 0 10 20 30energy [mW/cm3]Figure 12: Total energy absorbed by Q0B.CONCLUSIONSThe Q0 layout is rapidly evolving from the original ideaproposed in [2] towards a full integration into the LHCnominal optic (v6.5). The optics proposed in this paper re-quires a Q0A quadrupole with a gradient of 240 T/m, justcompatible with NbTi technology.Misalignment tolerances for Q0A and Q0B are similar tothose required for the inner triplet; it’s reasonable to thinkthat the same system of correctors used in the triplet can beapplied for Q0A-Q0B.The energy deposition is an issue that must be fully ex-plore to propose reasonable solutions compatibles with asystem of energy extraction in a limited volume such asinside the detector.REFERENCES[1] F. Zimmermann, “LHC Upgrade Scenarios”, Proceedings ofPAC 2007, Albuquerque, New Mexico, USA.[2] E. Laface et al., “Interaction region with slim quadrupoles”,Proceedings of EPAC 2006, Edinburgh, United Kingdom.[3] J.-P. Koutchouk and G. Sterbini, “An early beam separationscheme for the LHC”, Proceedings of EPAC 2006, Edin-burgh, United Kingdom.[4] Y. Papaphilippou and F. Zimmermann, “Weak-strong beam-beam simulations for the LHC”, Proceedings of LHC99,Workshop on beam-beam effects, CERN-SL-99-039 AP p.103,1999.[5] Y. Papaphilippou and F. Zimmermann, “Estimates of Dif-fusion due to Longe-range Beam-beam Interactions”, Phys.Rev. Special Topics Accel. Beams 5:074001, 2002.[6] F. Ruggiero et al., “Performance limits and IR design of apossible LHC luminosity upgrade based on NbTi SC magnettechnology”, Proceedings of EPAC 2004, Lucerne, Switzer-land, p. 608.[7] S.Weisz, “Alignment of the low-β quadrupoles”, LHCProject Note 59, CERN, Switzerland.[8] T.Sen, “Alignment Tolerances of IR Quadrupoles in theLHC”, FERMILAB-Conf-99/304, Batavia, Illinois, USA.[9] E. Wildner “Are large aperture NbTi magnets compatiblewith 1e35?”, Proceedings of LUMI 2007 Workshop, Frascati,Italy.IR’07 PROCEEDINGS70

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