The optimization of the new CLIC Final Focus System (FFS) with L*=3.5m is presented for a collection of CLIC beam parameters. The final performance is computed for the full Beam Delivery System including the new diagnostics section. A comparison to previous designs is also presented

Jørgensen, M

Tomás, R

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN - AB DIVISIONCLIC-Note-735Optimizing the CLIC Beam Delivery SystemR. Toma´s and M. JørgensenAbstractThe optimization of the new CLIC Final Focus System (FFS) with L∗=3.5m is presented for a collec-tion of CLIC beam parameters. The nal performance is computed for the full Beam Delivery Systemincluding the new diagnostics section. A comparison to previous designs is also presented.Geneva, SwitzerlandMarch 13, 2008.11 IntroductionSince 2005 the CLIC Beam Delivery System (BDS) and, more in particular, the FFS are undergoingdifferent optimizations to maximize their performance, namely total and peak luminosities. The startingpoint of these optimizations is based on the minimization of the non-linear aberrations of the FFS,presented in [1]. Basically non-linear elements are used to minimize the horizontal and vertical IP spotsizes using the Simplex algorithm [2]. In this paper we refer to sextupole optimization when only latticesextupoles are considered to minimize the IP spot sizes. By full non-linear optimization we imply thatextra non-linear elements like octupoles and decapoles are introduced in the beam line to better cancelhigh order aberrations.Later this procedure was extended to optimize the lattice dispersion as well [3, 4]. Lowering dis-persion reduces the emittance growth due to synchrotron radiation but enlarges chromatic aberrations,therefore there must be an optimum dispersion for which the IP spot size is minimum.All these optimizations are carried out using MAPCLASS [5], which is a Python code that readsmap coefcients and twiss parameters from MADX-PTC [6, 7] output to compute beam sizes at theIP. MAPCLASS has an implementation of the Simplex algorithm to minimize IP beam sizes. It hasalso been used in the totally different environment of the LHC IR upgrade studies [8]. Minimum beamsizes at the IP do not guarrantee maximum peak luminosity. The last step of the optimization involvescomputing the luminsotiy using the GUINEA-PIG code [9], always taking into account radiation effects.From the point of view of optics and cost, shorter focusing systems are preferred since, for a givenβ∗, beta functions are smaller and the tunnel is also shorter. However detector integration becomesmore difcult for shorter L∗. We have considered 3 cases with L∗ having the values: 4.3m, 3.5m and2.8m. The longest one with 4.3m was the original FFS. Fig. 1 shows the total luminosity versus theFFS length for the different stages of the optimization, namely: sextupole optimization, full non-linearoptimization and dispersion optimization. The initial design in 2005 is labeled as Nominal FFS onthe plot. It is the longest FFS with an L∗=4.3m. A shorter L∗ implies lower beta-function and lowerchromatic aberrations. The rst shortening attempt at L∗=2.8m (360m FFS length) showed a cleargain in luminosity without having applied all the steps of the optimization. However this L∗ could poseproblems in the integration of the detector. It was decided to set L∗ to 3.5m (≈460m FFS length) to avoidany possible conict with the detector. In the meantime the CLIC beam parameters have changed. Thebunch length and the normalized vertical emittance have increased from 35µm to 44µm and from 10nmto 20nm, respectively. The new lattice with L∗=3.5m and the new set of CLIC beam parameters requirea thorough re-optimization. In the following sections the optimizations for this and other interesting setsof parameters are presented.2 Optimization of the L∗=3.5m FFSTo illustrate the non-linear optimization procedure, described above, Fig. 2(a) shows the luminosity inthe 1% energy peak at all stages of the optimization. A strong dependence of the peak luminosity onthe horizontal beam size is observed. Figure 2(b) shows a zoom of the clear borderline that encloses theachievable beam sizes. At this level reducing the horizontal beam size implies increasing the verticalsize and vice-versa. The maximum luminosity can be found in the lower right corner of Fig. 2(b).Lowering the dispersion implies less synchrotron radiation in the FFS while it requires strongernon-linear elements to cancel the chromatic aberrations. To nd the optimum dispersion along the FFSvarious optics are prepared having different dispersion levels. The non-linear optimization is ran for thedifferent optics. Lastly the luminosities of these options are computed to select the best. Figure 3(a) and(c) show the IP beam sizes with and without radiation versus dispersion reduction for y = 10nm and2 4 5 6 7 8 9 340  360  380  400  420  440  460  480  500  520  540  560Total luminosity [a.u.]FFS Length [m]FFS shortening and optimization chart? Disp optim.Full non-linear optim.(2007) (2007)Sextupole optimizationDisp optim.Full non-linear opt.(2006)(2005) Nominal FFSFigure 1: Chart of the optimization of the CLIC Final Focus System showing total luminosity versus thelength of the FFS. The starting point is the nominal conguration in 2005. The rst optimizations aresextupole and full non-linear. Only after a full non-linear optimization the dispersion is optimized too.After the rst sextupole optimization the FFS length starts being reduced (red line) without substantialgain in luminosity. Further optimizations on top of length reductions prove successful. Dispersionoptimization was not computed for the shortest system.(a)10nm(b)10nmFigure 2: Peak luminosity per bunch crossing taking into account synchrotron radiation effects versushorizontal and vertical beam sizes. Peak luminosity is in arbitrary units and has an uncertainty of 5%.(a) shows all stages of the optimization. (b) shows a zoom containing the maximum peak luminosity.Beam sizes are computed without taking into account synchrotron radiation.3(a)10nm(b)10nm(c)20nm(d)20nmFigure 3: Plots on the left,(a) and (c), show the beam size versus dispersion reduction for the twovertical emittances. Plots on the right, (b) and (d), show the total and peak luminosities versus dispersionreduction. The top plots have a vertical emittance of 0.01µm while the bottom plots have 0.02µm.y = 20nm, respectively. The horizontal beam size (considering radiation) reduces signicantly withlower dispersion. This has a direct impact on the luminosities shown in Fig 3(b) and (d), with maximaat about 30% dispersion reduction, both for y = 10nm and y = 20nm. Table 1 summarizes all thenumerical values of all these plots.2.1 The longer bunchNext we investigate the effect of increasing the bunch length from 0.35µm to 0.44µm. The beam sizesand luminosities are shown in Fig. 4 and summarized in table 1. Beam sizes with and without syn-chrotron radiation and total luminosities behave similarly to those for the shorter bunch length shownabove. However peak luminosity shows a totally different dependence on dispersion. For the verticalemittance of 0.02µm there is no longer a clear peak luminosity maximum, while the total luminositystill has its maximum at about 30% dispersion reduction.4We believe that the saturation of the peak luminosity is due to the increase of beamstrahlung for thelonger bunch. The mean beamstrahlung parameter is given in [10] asΥmean =56Nr2eγασs(σx + σy)(1)and the number of emitted photons is given bynγ =52α2σsreγΥ√1 + Υ2/3. (2)Using the above equations and that Υ >> 1 in the CLIC regime,nγ ∝σ1/3sσ2/3x(3)Therefore longer σs implies more Bremsstrahlung photons. These photon emissions reduce the energyof the particle directly affecting the luminosity at the energy peak but not the total luminosity. Reducingthe horizontal spot size also increases the number of photons and this explains why the dispersionoptimization does not improve peak luminosity but total luminosity only. We conclude that with theseparameters the peak luminosity has been saturated and further reductions of transverse sigmas couldenhance total luminosity but not peak luminosity.3 Performance of the new BDSSo far we have only considered the last part of beam line, the FFS. In this section we compute theperformance of the new BDS and compare it to previous designs.Right at the BDS entrance there is a section that has been recently added: the diagnostics sec-tion, Fig. 5. The goals of the diagnostics section are to compensate the transverse coupling errors and tomeasure emittances and beam energy. The peaks of the vertical βy have been chosen so that the verticalbeam size is 1µm for y = 20nm. Present laser wire technology can measure this beam size with a 10%resolution [11].After the diagnostics section comes the collimation section that has not been modied for the newCLIC parameters yet, although the survival of the beryllium collimators is at risk after having doubledthe CLIC number of bunches. The optics and layout of the new BDS is shown in Fig. 6, with at totallength of 2750m that could be reduced by 100m if the rst 100m were lled with accelerating cavities.Presently there are three BDS designs with different L∗. The original one with 4.3m, the not fullyoptimized one with L∗=2.8m and the latest one with 3.5m L∗. The peak luminosities obtained fromsimulations of these three designs are shown in Fig. 8. For these simulations the latest beam parametershave been used: y =20nm and σs = 44µm. The shortest FFS shows the worst performance only dueto the fact that it was not fully optimized. The other two designs show a very similar performance. Thisobservation is consistent with the above mentioned saturation of the peak luminosity while optimizingthe FFS dispersion.To verify that we have indeed improved the chromatic aberrations by reducing the L∗ we comparethe energy bandwidths of the systems in terms of IP spot sizes and luminosity. Figure 9 shows thesebandwidths for the old 4.3m L∗ and the new 3.5m L∗ systems. The new shorter FFS has a largerbandwidth for the horizontal IP spot size. It shows a similar effective bandwidth for the vertical IP spotsize but left-to-right inverted. Most importantly the bandwidth for the peak luminosity is larger for theshorter system. On the plots an extra curve is shown to which we will refer below.5(a)10nm(b)10nm(c)20nm(d)20nmFigure 4: Plots for σz = 44µm. On the left,(a) and (c), show the beam size versus dispersion reductionfor the two vertical emittances. Plots on the right, (b) and (d), show the total and peak luminositiesversus dispersion reduction. The top plots have a vertical emittance of 0.01µm while the bottom plotshave 0.02µm.60.0 50. 100. 150. 200. 250. 300. 350. 400.                               s (m)End of Linac  -  Diagnostics section0.050.100.150.200.250.300.350.400.βx(m),βy(m) β x β yFigure 5: Layout and optics of the diagnostics CLIC section. The peaks of the vertical beta functioncorrespond to 1µm beam size for y = 20nm.0.0 750. 1500. 2250. 3000.                               s (m)New BDS0.050.100.150.200.250.300.βx(m),βy(m)[*10**(3)]-0.050.00.050.100.150.200.250.300.350.400.45Dx(m)β x β y DxFigure 6: Layout and optics of the full BDS with L∗ =3.5m.72300. 2450. 2600. 2750.                               s (m)New BDS0.050.100.150.200.250.300.βx(m),βy(m)[*10**(3)]-0.045-0.040-0.035-0.030-0.025-0.020-0.015-0.010-0.0050.00.0050.010Dx(m)β x β y DxFigure 7: Layout and optics of the FFS with L∗ =3.5m.8 1.6 1.8 2 2.2 2.4 2.6 2.8 3 2.6  2.8  3  3.2  3.4  3.6  3.8  4  4.2  4.4-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4Peak Luminosity per crossing [au]σy[nm]L*[m]charge=4e9, σz=44µm, εy=20nmL1% with SRL1% without SRσy with SRσy without SRFigure 8: Peak luminosity for the three BDS designs versus L∗. Note that the design with L∗=2.8m wasnot fully optimized.Since the nal doublet is different for the different FFS designs it is interesting to evaluate andcompare the Oide effect [12]. To this end we have tracked with and without synchrotron radiation onlythrough the nal doublet until the IP and computed the nal beam rms spot sizes. Figure 10 shows theincrease in the vertical spot size caused by considering synchrotron radiation in the nal doublet. It isclear that the 3.5m L∗ option is the most affected by the Oide effect. A rst attempt to reduce the Oideeffect for this option has been exercised by increasing the length of the nal doublet magnets by 0.1m,corresponding to a relative increase of about 7%. After a full optimization of this new FFS the Oideeffect has decreased by a factor of two (even below the other systems). A much more modest increasein the peak luminosity by about 5% has been found since it is well known that the Oide effect affectsmostly the tails of the bunch, which do not contribute much to the luminosity. However the bandwidthof this new system with a radiation optimized doublet has also been computed and it has been found tobe slightly worse than the previous 3.5m L∗ FFS, see Fig. 9.4 Summary and conclusionA full optimization of the CLIC BDS has been presented for the new L∗ = 3.5m and new beam param-eters. During the optimization processes it has been observed that further reductions of the horizontalspot size do not translate into a peak luminosity gain for the new parameters, contrary to the trend forthe old parameters (shorter bunch and smaller vertical emittance). We conclude that the new parametershave caused a saturation of the peak luminosity due to the enhanced Beamstrahlung at the IP. Basicallythe machine performance is limited by the beam-beam interaction and not by the machine optics.The Oide effect has been investigated, observing that it has been enhanced for the new L∗ = 3.5mFFS. A minimization of this effect has been achieved by a small increase on the length of the nal9 0 1 2 3 4 5 6 7-0.01 -0.005  0  0.005  0.01Vertical IP spot size (relative)dp/pL*=3.5m         L*=3.5m (opt.)L*=4.3m          0 1 2 3 4 5-0.01 -0.005  0  0.005  0.01Horizontal IP spot size (relative)dp/pL*=3.5m         L*=3.5m (opt.)L*=4.3m          0 0.2 0.4 0.6 0.8 1-0.01 -0.005  0  0.005  0.01Peak luminosity (relative)dp/pL*=3.5m         L*=3.5m (opt.)L*=4.3m         Figure 9: Bandwidth plots for three different FFS: the old 4.3m L∗, the new 3.5m L∗ and anotherradiation optimized 3.5m L∗ system with the label (opt). The latter corresponds to an FFS with 7%longer nal doublet in order to reduce the Oide effect. In descending order the plots show vertical spotsize, horizontal spot size and peak luminosity versus relative momentum deviation. The shorter systemexhibits a larger peak luminosity bandwidth.10 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 2.6  2.8  3  3.2  3.4  3.6  3.8  4  4.2  4.4 62 64 66 68 70 72 74 76 78 80 82∆σy from Oide effect [nm]β y [µm]L* [m]∆σyβy*Figure 10: Increase in the IP vertical beam size caused by considering synchrotron radiation in the naldoublet versus L∗. All cases are computed for a vertical normalized emittance of y=20nmdoublet. The Oide effect has been reduced by a factor two but peak luminosity showed only a moderateincrease in the percent level, as expected since the Oide effect does not affect the core of the beambut the tails. However this change in the optics of the system has turned out into a slight reduction ofbandwidth.In conclusion three different FFS designs exist with similar performance in terms of peak luminosityand with different features:• L∗=4.3m, easiest detector integration due to the longer L∗.• L∗=3.5m, largest energy bandwidth.• L∗=3.5m, radiation optimized, lowest synchrotron radiation at the nal doublet.All these lattices are stored in the CLIC lattice repository [13]. we choose the L∗=3.5m option as theCLIC BDS baseline design since it has a slightly larger bandwidth and needs a shorter tunnel.AcknowledgmentsThanks to H. Braun and D. Schulte for motivating this study and their fruitful suggestions.References[1] R. Tom·as, Non-linear Optimization of Beam Lines, Phys. Rev. ST Accel. Beams 9, 081001(2006).11y = 0.01µm, σz = 35µm for the FFSDisp. Red. Ltot L1% σx NoSR σy NoSR σx SR σy SR[%] [au] [au] [nm] [nm] [nm] [nm]0 7.51 2.80 40.26 0.557 52.77 1.455 7.53 2.86 40.15 0.570 50.94 1.5410 7.90 2.91 40.52 0.592 49.19 1.4715 8.28 2.96 40.26 0.631 47.46 1.2920 8.60 3.08 40.33 0.659 46.69 1.3330 8.97 3.06 41.06 0.788 45.01 1.3340 8.03 2.69 42.60 1.089 45.20 1.50y = 0.02µm, σz = 35µm for the FFSDisp. Red. Ltot L1% σx NoSR σy NoSR σx SR σy SR[%] [au] [au] [nm] [nm] [nm] [nm]0 5.03 1.90 40.38 0.555 52.61 2.255 5.15 1.91 40.15 0.570 50.75 2.3510 5.46 1.99 40.52 0.592 48.95 2.1615 5.66 2.01 40.32 0.623 47.55 2.2720 5.95 2.02 40.37 0.658 46.33 2.0930 6.12 2.05 41.16 0.786 45.13 2.1740 5.68 1.91 41.04 1.082 45.01 2.40y = 0.01µm, σz = 44µm for the FFSDisp. Red. Ltot L1% σx NoSR σy NoSR σx SR σy SR[%] [au] [au] [nm] [nm] [nm] [nm]0 7.28 2.68 40.33 0.556 52.72 1.425 7.45 2.73 40.15 0.570 50.94 1.5410 7.62 2.74 42.55 0.600 51.05 1.3815 8.08 2.80 40.25 0.616 47.38 1.4220 8.60 2.93 40.33 0.651 46.67 1.4130 8.71 2.92 40.75 0.765 44.78 1.4540 7.72 2.53 41.40 1.078 45.48 1.44y = 0.02µm, σz = 44µm for the FFSDisp. Red. Ltot L1% σx NoSR σy NoSR σx SR σy SR[%] [au] [au] [nm] [nm] [nm] [nm]0 5.06 1.90 40.38 0.555 52.61 2.255 5.00 1.80 40.15 0.570 50.75 2.3510 5.26 1.85 40.24 0.590 48.73 2.2715 5.41 1.92 40.31 0.623 47.55 2.2720 5.74 1.88 40.32 0.651 46.37 2.2030 6.09 1.92 40.77 0.765 44.74 2.4140 5.55 1.77 40.89 1.083 44.45 2.39Table 1: FFS summary tables. Luminosities and IP beam sizes for the different beam parameters anddispersion reductions.12[2] J.A. Nelder and R. Mead, Computer Journal, 1965, vol 7, pp 308-313.[3] R. Tom·as , Nonlinear optimization of beam lines, CERN-OPEN-2006-023 ; CLIC-Note-659(2006).[4] P. R. Jarnhus, R. Tom·as, Optimization of the CLIC Final Focus dispersion without using extramultipolar components CERN AB-Note-2007-006.[5] R. Tom·as, MAPCLASS: a code to optimize high order aberrations CERN AB-Note-2006-017(ABP).[6] H. Grote and F. Schmidt, MAD-X - An Upgrade from MAD8, CERN-AB-2003-024, ABP.[7] E. Forest, F. Schmidt and E. McIntosh, Introduction to the Polymorphic Tracking Code, KEKReport 2002-3.[8] R. Tom·as, M. Giovannozzi and R. de Maria, IR multipolar correction for the LHC upgrade, inproceedings of IR’07 CARE-HHH-APD, Frascati 2007.[9] D. Schulte, Beam-Beam Simulations with GUINEA-PIG, ICAP98, Monterey, CA., USA (1998).[10] L. Z. Rivkin, Beamstrahlung and Disruption CERN 95-06 vol. 2, prepared for CERN AcceleratorSchool: Course on Advanced Accelerator Physics (CAS), Rhodes, Greece (1993).[11] S. T. Boogert et al, A LASER-WIRE SYSTEM AT THE ATF EXTRACTION LINE, EPAC2006.[12] K. Oide, Synchrotron-Radiation Limit on the Focusing of Electron Beams, Phys. Rev. Lett. 61,1713 - 1715 (1988).[13] CLIC lattice repository: http://clicr.web.cern.ch/CLICr/13

Optimizing the CLIC Beam Delivery System

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