FCC Kickoff Meeting, 12-15 February 2014 1

A draft of Interaction Regionwith Crab Waist

A. Bogomyagkov, E. Levichev, P.Piminov, I.Okunev

Budker Institute of Nuclear Physics

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Why Crab WaistZ W H t

Energy [GeV] 45 80 120 1752 [mrad] 30Current [mA] 1431 142 29 6.3x[m]/y[m] 0.5/0.001x[nm]/y[pm] 0.14 / 1 0.44 / 2 1 / 2 2.1 / 4.25z[mm] 5.9 9.1 8.2 6.6x/y 0.032 /

0.1750.031 / 0.187

0.029 / 0.16

0.024 / 0.077

L/IP [1032cm-2s-1] 21200 3640 924 134

http://arxiv.org/abs/1311.1580

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Crab Waist (P.Raimondi 2006)• Large Piwinski’s

angle (z/x tan(∙ )) – to decrease the overlapping area

• Low y – luminosity increase

• Crab waist – to suppress betatron resonances (sextupoles in phase with IP)

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Crab Waist Optics requirements

• Sextupole at x=m, y=(2n+1)/2

• Sextipole is strong, therefore Wx=0, Wy=0.• Local chromaticity correction: two “–I” pairs of

sextupoles at m from FF quadrupoles.

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Final focus

D0=0.7 mQ0: L=4.6 m, G=95 T/m @ 175 GeVD1=0.4 mQ1: L=2 m, G=96 T/m @ 175 GeV

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Final Focus quadrupoles

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QD0•Compact SC iron yoke twin aperture magnet •Single aperture 2 cm•Gradient 110 T/m

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QD0, prototype manufacturing

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OpticsCRABX2X1Y2Y1

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OpticsCRABX2X1Y2Y1

FFT YXCCS CRAB

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Chromatic functions

Fine phase adjustment of sextupole pairs will help to reduce even more.

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Phase advance variation

• Sextupole at the end of FFT controls Qy’’’

• Additional sextupoles an octupoles will compensate higher order chromaticity.

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Effect of sextupole length𝑥1=−𝑥0−

𝐵1 (𝑆1 ,𝑆2 ,𝑘 )12 (𝑥03+𝑥0 𝑦 02 )𝐿4

𝑝𝑥 1=−𝐵2 (𝑆1 ,𝑆2 ,𝑘)

6 (𝑥03+𝑥0 𝑦02 )𝐿3

𝑦 1=− 𝑦0−𝐵1 (𝑆1 ,𝑆2 ,𝑘)

12 (𝑦03+𝑥02 𝑦0 )𝐿4

𝑝 𝑦 1=−𝐵2 (𝑆1 ,𝑆2 ,𝑘 )

6 (𝑦03+𝑥02 𝑦0 )𝐿3

𝐵1 (𝑆1,𝑆2,𝑘 )=(3+2k )𝑆12+6 (2+3 k+𝑘2 )𝑆1𝑆2+𝑆22

𝐵2 (𝑆1 ,𝑆2 ,𝑘 )=𝑆12+6 (1+𝑘 )𝑆1𝑆2+𝑆22

http://arxiv.org/abs/0909.4872A.Bogomyagkov, S.Glykhov, E.Levichev, P.Piminov

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Fringes and Kinematic (see W.P.2.3 HighLumi)

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Left: black -- sextupoles, kinematic, fringes.Left: blue -- sextupoles and compensators.Left: red -- sextupoles and compensators, kinematic, fringes.Right: plus two octupoles to compensate kinematic, fringes.

461 y

153

x

1000 y

Dynamic aperture

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Things to look at

• Kinematic term at IP (will increase drastically with larger L*, see Oide-san FF of SuperKEKB).

• FF quadrupoles fringes (will increase drastically with larger L*, see Oide-san FF of SuperKEKB).

• Sextupole length(Effect of the Sextupole Finite Length on Dynamic Aperture in the Collider Final Focus, 2009, http://arxiv.org/abs/0909.4872).

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Conclusion

• A first draft of IR with crab waist is ready.• We do not see any reason to make L*>0.7m.• Design of Q0, adjust length, distance from IP.• Bending angle of dipoles, of whole IR.• Quadrupole, Sextupole strengths.• Nonlinear optimization: chromaticity, dynamic

aperture.