Nonlinear Perturbations for High Luminosity e+e Collider Interaction Region

Transcription

1 Nonlinear Perturbations for High Luminosit e+e Collider Interaction Region A.Bogomagkov, E.Levichev, P.Piminov Budker Institute of Nuclear Phsics Novosibirsk, RUSSIA IAS HEP Conference, 18-1 Jan 016, Hong Kong

2 Outline Introduction (DA limiting factors and requirements) DA in the arcs Comparison of nonlinear sources of FF Simulation results, radiation influence Conclusion

3 High luminosit e+e- colliders Head-on collider with low IP beta (~1 mm) (precdr CEPC) Nanobeam collider (Super KEKB) CW collider (CW CEPC, FCC-ee, SuperB/Ital, SuperCT/BINP) 3

4 DA limiting factors ) Large dispersion is required for local chromaticit correction in the low-beta head-on collision as well as in the CW scheme. For this reason the IR design for both schemes is almost same. But the beam separation in the arcs (pretzel) for the head-on scheme can destro the smmetr and reduce the DA. ) Single aperture first quad is undesirable for large collision angle due to the strong fringe sextupole. 4

5 Beam lifetime due to bb effects. Recommendation from simulations b D.Shatilov: DA requirements DA 10σ x x 50σ (incl.errors, misalignments,etc.) Effective injection (conventional tpe, on-energ, off-axis) M. Aiba et al. FCCee review at CERN, Ax 13 mm N 16σ x J. Seeman. FCC week, Washington DC, March 5, 015 Ax 16 mm N 15σ x K. Oide. FCC-ee Optics Meeting, CERN, 11 Sep. 015 N 14.6σ GeV N 30σ GeV (@.5σ e ) Vertical beam tail growth example due to bb effects in FCC-ee at 10 GeV (D. Shatilov) Required DA 0σ x x 50σ 5

6 Interaction region DA Due to the low vertical beta ( 1 mm) at the IP a paraxial approximation is not longer valid and the next (octupole-like) terms should be included. Due to the low vertical beta at the IP chromatic effects are severe and require strong sextupoles for compensation. In spite the sextupoles are usuall arranged in the I pairs, the high order effects reduce the DA. Due to the high (~few km) betas in the first FF quadrupoles, the fringe field nonlinearities as well as the field errors are emphasized. 6

7 Optics blocks example First quad fringes: large strength and beta IP: Kinematic terms: low beta Strong Crab Sextupoles -I -I A. Bogomagkov, FCC-ee 015 Chromatic section: strong sextupoles, large beta 7

8 L(D0) QD0 Final focus example Old version, for example onl D0= m Q0: L=3.6 m, G= GeV D1=0.4 m Q1: L= m, G= GeV IP 8

9 DA size simple Strong low order resonance limits DA directl. Weak high order resonances overlap and form stochastic laer that also limits DA. Nonlinearit α = dν/dj brings particle to resonance Qx vs X0 α = dν/dj >> 1, DA small Qx OX=4 Ox=0 Ox= Ox=15 Ox=6 Ox=4.5 α = dν/dj 0, DA large Ox=3 α = dν/dj << 1, DA small X0 (mm) FODO lattice with fixed sextupoles but α = dν/dj varied b octupoles. 9

10 IR nonlinearities figure of merit How to compare power of different IR nonlinearities for different machines? Fortunatel all three main ones (kinematics, fringes and I sextupole pairs) are 3 rd order (octupole-like) in leading term and we propose to use the first order nonlinear detuning ν = αααα, JJ mmmmmm = AA ββ oooooo Advantages The detuning α is calculated b 1 st order of perturbation theor. α is additive for different sources ν = JJ αα 1 + αα + αα 3 + = JJ FF 1 + FF + FF 3 + dddd For estimation and comparison! 10

11 Final quad QD0 and chromaticit Defining the QD0 (thin lense) focusing requirements as α o = α I one can find ( K1L) = QD0 ( L + 0.5LQD0) The beta and its derivative in the end of L are given b β L e e FF vertical chromaticit(half of FF): β α L β L β µ + KL s β η s s QD0 natural chromaticit Correction b sextupoles Note: For FF µ corresponds to the chromatic function excitation introduced b B.Montague (LEP Note 165, 1979) µ = A W = A + B = A 11

12 Kinematics For the extremel low β and large transverse momentum the first order correction of non-paraxialit is given b 1 ( H ) = p x + p ν x = α xxj x + α xj ν = α x J x + α J 8 α k 3 ) = γ ( s ds 16π α 1 = γ x ( s) γ ( s ds 8π k x ) α k 3 ) = γ ( s ds 16π The main contribution comes from the IP and the first drift: α k = 3 16 L π β = 3 8π ξ β where L is the distance between QD0 quads around the IP. 1

13 QD0 Fringe Fields Quadrupole fringe field nonlinearit is defined b H = k ( s) x p / + k 4 ( 6x )/ and the vertical detuning coefficient is given b ( β β β ) 1 α 16π f = k β Or, with above assumptions (k 10 is the central strength): f α 1 k 4π 10 L β 3 = 1 k 4π 10 L ξ E.Levichev, P.Piminov, arxiv: A.V.Bogomagkov et al. IPAC13, WEPEA049,

14 Chromatic sextupoles Vertical chromatic sextupole pair separated b I transformer gives the following coordinate transformation in the first order ) Pair of sextupoles = p 0 ( K L ) s Ls = p ( x ) 0 0 Octupole = p = 0 p K 3 ( x ) B analog to the octupole and using the expression for the FF chromaticit we found for the vertical detuning ( pairs) 6 L 0 0 α sp = 1 16 π s s ( K L ) L β = ξ s s 1 L 4π η s L β 1 L 4π η s ) A.Bogomagkov, S.Glkhov, E.Levichev, P.Piminov 14

15 Discussion α k = 3 16 L π β = 3 8π ξ β Kinematic effect increases with L increase and β decrease. f α α sp 1 k 4π 10 L β 3 1 L s L 4π η s β 1 = k 4π = 1 L 4π η 10 s s L ξ ξ Fringe field effect increases fast with L increase and β decrease. It is sensitive to the QD0 central gradient k 10. Sextupole pair effect increases with L increase and β decrease. Short sextupole and large dispersion are desirable. In spite the estimations are ver rough, the seem reasonable and are confirmed b tracking simulation. 15

16 CEPC parameters CEPC-SppC PreCDR, March 015. L = 1.5 m, β = 1. mm, β FFmax 3 km, β CCY 6 km, η CCY 5 cm 16

17 V.detuning for different lattices LEP 3) CERN Super C-Tau 1) Novosibirsk SuperKEKB ) Japan FCC-ee/AB 015 4) CEPC ) IHEP 10 3 β(m) L(m) ξ K 1 (m - ) L QD0 (m) β SY (m) η SY (cm) α f (m -1 ) α k (m -1 ) α sp (m -1 ) NA ) SuperC-Tau CDR, Novosibirsk, 009. ) K.Oide, FCC Kick-off Meeting, Geneva, 14 Feb 014 3) T.M.Talor, PAC ) A.Bogomagkov, FCC-ee asmmetric design, BINP, Dec ) CEPC-SPPC PreCDR, v.ii, March 015. ) I have no precise data, man guesses. 17

18 Comparison with simulation Kin Fringe Sextupole pair Simulation α xx (cm -1 ) α x =α x (cm -1 ) α (cm -1 ) Estimation α (cm -1 ) Simulation considers all quads fringes (included those strong in the Y chromatic section) and realistic beta behavior 18

19 Simulation We use the following tracking codes: MAD8 and Acceleraticum 1) (BINP home made). The tunes are fixed at (0.53, 0.57) to get large luminosit. Dnamic aperture and other nonlinear characteristics are defined from tracking for different sources to found their power ranking. We tr to compensate (mitigate) ever source locall b optimizing the phase advance, insertion of additional sextupoles and octupoles. We collect all the ring sections together and optimize 6D DA globall (damping, tapering, errors, BB effects, etc. can be included at this stage). 1) D.Einfeld, Comparison of lattice codes, nd NL Beam Dnamics Workshop, Diamond Light Source,

20 FCC-ee DA optimization (November 015) Recent example P. Piminov Acceleraticum SY5 OY1 SY1 SY SY4 SY3 OY SD (arcs) SX6 SX5 OX1 SX1 SX SX4 SX3 OX SF (arcs) SY5, SX6, SX5 increase of the noninear (dnamic) bandwidth SY1, SY3 main vertical section for the FF chromaticit compensation. Arranged in the I pair. SY, SY4 sextupole corrector to compensate the finit length effect of SY1 and SY3. Also arranged in the I pair. SX1, SX3 main horizontal section for the FF chromaticit compensation. Arranged in the I pair. SX, SX4 sextupole corrector to compensate the finit length effect of SX1 and SX3. Also arranged in the I pair. OY1, OY, OX1, OX octupole correctors to mitigate the kinematic and FF fringes effects SD, SF vertical and horizontal sextupoles in the arcs. 0

21 DA FCCee with/without damping 1

22 Conclusion For high performance e+e- factories DA limitation is a challenging problem. Main limiting factors are: vertical sextupole chromatic section in IR, FF quads fringes, arc sextupoles. Local + global compensation can schemes provide reasonable DA. Damping at high energ is an important factor increasing the DA. Remaining problems: interference of CW sextupoles with other IR nonlinearities reduces the DA; proper (distributed) radiation in the arcs; quads radiation contribution ( damping DA ); magnet tapering; detector solenoid (and other MDI elements) effects; machine errors and misalignments; BB effects.