We optimize the nominal final focus system for CLIC to maximize the luminosity at the IP. We investigate the effect of quadrupole optimization after sextupole optimization for high and low dispersion reductions. Finally we try to improve our optimization further via a small corrective optimization and check that the optimal dispersion reduction also holds for the entire Beam Delivery System (BDS)

Jarnhus, P R

Tomás, R

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN – AB DEPARTMENTAB-Note-2007-006Optimization of the CLIC Final Focus dispersion withoutusing extra multipolar componentsP. R. Jarnhus, R. Toma´sAbstractWe optimize the nominal final focus system for CLIC to maximize the luminosity atthe IP. We investigate the effect of quadrupole optimization after sextupole optimization forhigh and low dispersion reductions. Finally we try to improve our optimization further viaa small corrective optimization and check that the optimal dispersion reduction also holdsfor the entire Beam Delivery System (BDS).Geneva, SwitzerlandJanuary 22, 2007IntroductionThe nominal final focus system (FFS) of the CLIC follows the design given by P. Raimondi and A. Seryiin [1]. This design, in its original configuration, contains high order aberrations visible, for instance, indeformations of the phase-space shape. In [3] it was shown that a reduction of the dispersion led to aluminosity increase for a modified version of the FFS with more non-linear elements. It is the scope ofthis paper to find the optimum dispersion for the nominal FFS and evaluate the luminosity gain.Optimization Method and Solution StabilityWe use the MAPCLASS [2] to maximize the luminosity for different dispersions. The different disper-sion levels are obtained by scaling the bending angles of the FFS dipoles. The optimization is done intwo steps, first optimizing the sextupole strengths and secondly the quadrupole strengths (the magnetnames are given in Table 1). We do the calculations up to sixth order and only introduce synchrotronradiation in the luminosity calculation.First step SF6, SF5, SD4, SF1,SD0Second step QF8, QD7, QF3a, QF3b, QD2Table 1: Sextupoles and quadrupoles used in the two steps of the optimization. The numbers appearingin the names are ordered in increasing distance to the IP.To test the stability of the solution, we started a calculation from zero sextupole strength for all thesextupoles. Even when doing so, the Simplex method still converges to the right solution.ResultsWe see from Figure 1, that by decreasing the dispersion, we can achieve a luminosity of  	 ﬀﬁﬃﬂ, which is a 28% increase from the nominal FFS. The Figure furthermore shows, that theeffect of changes in the quadrupole strength is greatly decreased as the dispersion decreases, as it wouldbe expected. At around 25% reduction of the dispersion, the effect of quadrupole optimization is, withinthe errorbars, completely negligible.2 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 0  5  10  15  20  25  30  35Luminosity [1034 cm-2 s-1 ]Dispersion Reduction [%]Luminosity (Energy =1.496 TeV)SextSext+QuadNominalFigure 1: Luminosity versus dispersion reduction through the FFS.As a test of validity, we ran an optimization of all ten parameters, starting from the optimized valuesfound after the quadrupole optimization. This was done to check for any cross correlations between thetwo parameter-sets. This attempt did not yield any improvement of the luminosity beyond the error-bars,and we therefore believe, that the two parameter-sets are only weakly correlated. 0 0.5 1 1.5 2 0  5  10  15  20  25  30  35σy [nm] and σ x [100nm]Dispersion Reduction [%]Beam size after Sext and Quad optimizationσy (with SR)σy (no SR)σx (with SR)σx (no SR)Figure 2: Beam size after optimization of sextupoles and quadrupoles. Values are shown for calculationswith and without synchrotron radiation.We see in Figure 2 that the vertical beam size is roughly constant, when we include the synchrotronradiation, while the horizontal beam size decreases with the dispersion. This means that the generalgain we see in the luminosity is contributed by a change in the horizontal size of the beam. We would3expect the curves with and without radiation considered to go asymptotically toward each other as thedispersion goes to zero, as the radiation of the beam is mainly due to the dispersion. For the horizontalbeam size, this is verified by Figure 2. In the vertical case the dispersion reduction is not investigated toa low enough value for it to be verified, but we do see the two curves approach each other.Based on these results, a dispersion reduction of 21 % is the best choice. Furthermore, a decreasein dispersion would mean an increase in multipole strength, which would lead to an increased orbitinstability. We find for this dispersion reduction, that the multipole values should be increased from thenominal values by the percentage given in Table 2.Name Strength Correction [%] Name Strength Correction [%]SD0 27.0 QD2 0.03SF1 27.4 QF3a 0.08SD4 26.6 QF3b -0.26SF5 24.6 QD7 -0.64SF6 8.2 QF8 1.10Table 2: Optimized multipole strengths for a 21 % dispersion reduction.Plotting the horizontal phase-space distribution (Figure 3) and beam profile (Figure 4) for the 21 %dispersion reduction, we see that there are still a few particles in the far outer rims of the beam, but thisis only about 0.1 % of the particles. This could probably be improved by adding higher order multipolarcorrectors.-30-20-10 0 10 20 30-0.4 -0.2  0  0.2  0.4pxx [µm]Phase-space plot for 21% Dispersion Reduction (104 particles)Figure 3: Phase-space plot of the (   , )-planefor 21% dispersion reduction.-0.04-0.02 0 0.02 0.04-0.4 -0.2  0  0.2  0.4y [µm]x [µm]Beam profile for 21% Dispersion Reduction (104 particles)Figure 4: Beam-profile at the IP for 21% dis-persion reduction.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0  5  10  15  20  25  30  35∆K / K 0Dispersion Reduction [%]SF1-dataSD0-dataf1*x**2+f2*x+f3d1*x**2+d2*x+d3Figure 5: Relative increase in the sextupole strength.The evolution of the strengths of SD0 and SF1 as a function of the dispersion reduction in the FFSare shown in Figure 5. The coefficients of parabolic fits are given in the Table 3Coefficients:        SF1 SD0a 	  a 	    b     b     c      c      Table 3: Fitting parameters for SDF1 and SD0.Verification of dispersion reductionPerforming the same optimization to the entire BDS, we get Figure 6 by doing the optimization de-scribed in Table 4.5 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 0  5  10  15  20  25  30  35Luminosity [1035  cm-2 s-1 ]Dispersion Reduction [%]OptimizedFine-tunedreferenceFigure 6: Luminosity versus dispersion reduction through the BDS.First step SF6, SF5, SD4, SF1,SD0Second step OF1, OD0, OF4, OD4Third step DD0, DF0, DF4Fourth step QF8, QD7, QF3a, QF3b, QD2Fine-tuning All of the aboveTable 4: Sequence for adjusting the relevant circuits.This shows that the optimum of 21% dispersion reduction also holds for the entire BDS. We see thatthe luminosity increase is reduced from the previous 28% to 18%, when the entire BDS is taken intoconsideration.ConclusionWe have found that a 21 % reduction in the final focus dispersion of CLIC, increases the luminosity by18 %. This reduction also gives a more Gaussian shape of the beam.References[1] P. Raimondi and A. Seryi, “Novel Final Focus Design for Future Linear Colliders”Phys. Rev. Lett.86, 3779-3782, 2001.[2] R. Toma´s, “MAPCLASS: A code to optimize high order aberrations”, CERN-AB-Note-017 ABP,2006.[3] R. Toma´s, “Non-Linear Optimization of Beam Lines”, CLIC Note 659, 2006.6

Optimization of the CLIC Final Focus Dispersion without Using Extra Multipolar Components

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