Non-linear optimization of the CLIC BDS R. Tomás Thanks to H. Braun, D. Schulte & F. Zimmermann Daresbury - 9 th of January 2007 Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.1/19
CLIC BDS 6 8 1/2 β y 1/2 β x 5 D 6 Dispersion[0.1m] 4 β 1/2 [100m 1/2 ] 4 3 2 2 1 0 0 0 500 1000 1500 2000 2500 Longitudinal location [m] Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.2/19
Motivation 30 particles at IP (with SR) 20 10 0 -10 p x -20 -30 -40 -50 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 x → Deformation reveals non-linear aberrations → Can we correct them? → Can we focus more? → Can we reduce the SR effect? Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.3/19
Correction: Beam size as observable We need an observable that quantifies aberrations: → The most natural is the beam size at the IP Given the transfer map between one location of the accelerator and the IP in the form: � � X jklmn x j p k x y l p m y δ n � x IP = and given the particle density at the initial location, the rms beam size at the IP is given by: � � σ 2 x j + j ′ p k + k ′ y l + l ′ p m + m ′ δ n + n ′ ρdv X jklmn X j ′ k ′ l ′ m ′ n ′ IP = x y X jklmn are obtained from MADX-PTC to any order. Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.4/19
Correction: Beam size order-by-order By truncating the map at order q ( q = j + k + l + m + n ) we obtain σ q related to: σ 1 Quadrupoles and dipoles σ 2 chromaticity & sextupoles σ 3 chromaticity & octupoles σ 4 ... → From σ q the leading orders of the aberrations are inferred and therefore the most suitable correctors. → By evaluating σ q,δ =0 for a monochromatic beam the chromatic part of the aberrations is also inferred. Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.5/19
Correction: Evaluation of BDS aberrations Optical rms beam sizes using MAPCLASS (no SR) 0.9 0.8 σ y [nm] and σ x [100nm] σ y at IP σ x at IP 0.7 σ y at IP ∆ δ =0 σ x at IP ∆ δ =0 0.6 0.5 0.4 0.3 1 2 3 4 5 6 7 8 9 Maximum order considered → Almost pure chromatic aberrations → Sextupolar, octupolar and decapolar correctors are needed Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.6/19
Correction: Algorithm Variables to minimize: σ x,q , σ y,q at the IP, from MAPCLASS without SR Variables to vary: Strengths of all sexts, otcs and decapoles (octs and decapoles need to be placed in the FFS. We first assume that the existing sextupoles are combined magnets with oct and decapolar fields) Variables not to vary: Strengths of dipoles since this will impact SR, which is not considered yet. Optimization algorithm: Simplex Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.7/19
Correction: Collimation section First, only the sextupoles at the collimation section are varied 0.9 0.8 σ y [nm] and σ x [100nm] σ y at IP 0.7 σ x at IP σ y at IP, optimized coll. σ x at IP, optimized coll. 0.6 0.5 0.4 0.3 1 2 3 4 5 6 7 8 9 Maximum order considered Sextupoles of the collimation section were overpow- ered! Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.8/19
Correction: FFS The FFS sextupoles are combined magnets with oct and decapolar fields 0.9 0.8 σ y [nm] and σ x [100nm] σ y at IP 0.7 σ x at IP σ y at IP, fully optimized σ x at IP, fully optimized 0.6 0.5 0.4 0.3 1 2 3 4 5 6 7 8 9 Maximum order considered → Almost total correction of aberrations → Phase space plot? Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.9/19
Correction: Phase space illustration 30 20 10 0 p x -10 -20 -30 particles at IP (with SR) -40 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 x → No comma shape! → Now, is it possible to focus more using the same algorithm but including quad strenghts? Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.10/19
More focusing The FFS quadrupoles are used to focus more 0.9 0.8 σ y [nm] and σ x [100nm] σ y at IP 0.7 σ x at IP σ y at IP, fully optimized σ x at IP, fully optimized 0.6 0.5 0.4 0.3 1 2 3 4 5 6 7 8 9 Maximum order considered → Need to stop focusing when aberrations arise → ∆ β QF x /β QF = + 42% , ∆ β IP x /β IP = − 19% x x → Good, but what about luminosity? Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.11/19
Luminosity Nominal Total Luminsoty=6.15 10 34 cm − 2 s − 1 Luminosity in energy peak (1%)=2.65 10 34 cm − 2 s − 1 σ rms =88 nm x − ∆ σ y − ∆ σ y ∆ L 1% L 1% − ∆ σ x − ∆ σ x ∆ L tot Case σ rms σ rms σ rms σ rms L tot L 1% L tot x x y y (no rad) (rad) (no rad) (rad) Nominal 0 0 0 0 0 0 43 Coll corrected 12 30 14 58 9 6 42 Non-linearities 20 35 35 69 31 19 39 More focusing 27 37 34 64 45 29 38 (All numbers are percent)(Tracking with PLACET including SR) Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.12/19
Can we reduce the SR effect? Radiation is not directly considered in the presented algorithm, however: • Lower dispersion in the FFS implies lower SR effect • But also implies stronger sextupoles for chromaticity and therefore stronger aberrations • There must be an optimum value of dispersion that maximizes luminosity → A scan in the FFS dispersion doing a full optimiza- tion (quads, sexts, octs...) at every step should reveal the optimum value for the dispersion. Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.13/19
FFS Dispersion reduction: example 0.01 Lower disp Original 0 -0.01 Dispersion[m] -0.02 -0.03 -0.04 -0.05 -0.06 2000 2100 2200 2300 2400 2500 Longitudinal location[m] → An example on dispersion reduction on the FFS by about a 40% Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.14/19
FFS Dispersion scan 0 disp reduction corresponds to the best former case Sextupole strength increase (sd0, sf1, sd4) [%] 75 55 50 70 45 65 40 60 35 55 ∆ L/L 0 [%] 30 50 25 45 20 40 15 35 10 L tot 30 L 1% 5 Sext. strength 25 0 0 5 10 15 20 25 30 35 Dispersion reduction [%] → Peak of L tot and L 1% at about 17% dispersion re- duction Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.15/19
FFS Dispersion scan: table − ∆ σ y − ∆ σ y ∆ L 1% L 1% − ∆ σ x − ∆ σ x ∆ L tot Disp. σ rms σ rms σ rms σ rms L tot L 1% L tot x x y y reduct. (no rad) (rad) (no rad) (rad) 0 27 37 34 64 45 29 38 4.3 27 39 34 65 54 37 38 17.4 30 40 29 69 72 43 36 21.8 30 40 27 67 72 42 35 34.9 32 26 18 68 62 35 36 (All numbers are percent)(Tracking with PLACET including SR) Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.16/19
Changing the combined function magnets Octupolar field in the sextupole is not very natural. What if we place the octupolar field in the quads? (Decapolar field still in the sextupoles) → A more natural field distribution gives the same luminosity. Shortening the BDS: Lower chromaticity and aberrations → High order correctors might not be needed, extra sextupoles could be enough (under study). Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.17/19
Conclussions and outlook • Non-linear correction, focusing and dispersion reduction led to a 72% total luminosity increase. • More realistic BDS configurations with similar performance under study: • Different configuration of non-linear correctors • Shorter BDS with extra sextupoles • What happens to alignment tolerances? Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.18/19
Quadrupole aperture • Present design, permanent magnet, aperture=3.8mm • Superconducting option is difficult due to small size ( CLIC note 506) � • 10 σ x = 10 ǫ x β x + D 2 δ 2 =3.1mm • More focusing needs larger β x . • Doubling β x implies 10 σ x = 3.5mm • Doubling β x and reducing D by 25% implies 10 σ x = 3.1mm Rogelio Tom´ as Garc´ ıa Non-linear optimization of the CLIC BDS – p.19/19
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