LER2011 Lattice Team K. Soutome, Y. Shimosaki, T. Nakamura, M. Takao, T. Tanaka K. Soutome (JASRI / SPring-8) on behalf of SPring-8 Upgrade Working Group SPring-8 Upgrade: Lattice Design of a Very Low-Emittance Storage Ring Talk based on the work by Y. Shimosaki, IPAC2011, "Lattice Design of a Very Low-emittance Storage Ring for SPring-8-II" 1

Ultimate Target of Machine Upgrading "Diffraction Limited" Light Source in Both H. and V. Directions for ~ 10keV Photons  ~ 10pmrad E = 6 GeV I = 100 mA  = 0.02   = 0.12%  x = 1 m  y = 1 m 10 keV Photon by Hybrid Undulator by T.Watanabe SPECTRA 2

Present Lattice Structure of the SPring-8 SR 4  [ 9  (Normal Cell, DB) + (Matching Cell) + (Long Straight) + (Matching Cell) ] Matching LS MatchingNormal C = 1436 m E = 8 GeV  = 3.4 nmrad （  eff = 3.7 nmrad ） 3

Way of Upgrading Convert present DB cell to Multi-Bend cell. Reuse the present machine tunnel. Keep the number and position of present ID-BLs. Lower the energy: 8GeV  6GeV (or lower) Hard X-ray is covered by undulator upgrading (short period). Reduce the emittance with damping wigglers. Control the coupling (if necessary). 2B: 1.9nmrad (Non-Achomat, 6GeV)  3B: 0.43nmrad  4B: 0.16 nmrad  6B: 0.07 nmrad (Achomat)  : Strong Q Large Nat. Chrom. Small Dispersion Strong SX Small DA "Chromaticity Wall" (J.Bengtsson, EPAC08) We set 6B lattice as a candidate of a new ring. 4

Multi-Bend Lattice 〜 3 × Theoretical Minimum Emittance (TME) ×M Half-Length B at Both Ends of Unit Cell (Achromat) D.Einfeld and M.Plesko, NIMA335 (1993) 402 5

Multi-Bend Lattice 2B (  eff = 2.09nmrad) 3B (  eff = 0.54nmrad) 4B (  eff = 0.19nmrad) 6B (  = 0.07nmrad)

Multi-Bend Lattice 6B Lattice LBLB LBLB LBLB LBLB L B /2  x 〜 1m  y 〜 1m  x = 0 matchin g unitmatchin g unit 7

Multi-Bend Lattice Inj. Point Normalized by  1/2 8

Multi-Bend Lattice  ∝ (N B -1) -3 NB: L B /2 at both ends → (N B -1) 8B 10B 12B 9

Multi-Bend Lattice Number of B ↓ Quad. Tune Chrom.(abs) Dispersion ↓ Chromaticity Cor. Sextupoles ↓ Dynamic Apt. 10 too small DA for M > 6

6B Lattice Design (typical) 11

2B (Double-Bend) Dispersion Leaked 6B (Sextuple-Bend) Achromat Unit Cell Length m Ring Circumference m Beam Energy8 GeV6 GeV Emittance3.4 nmrad (3.7 nmrad)0.068 nmrad Energy Spread0.109 %0.096 % Betatron Tune (H/V) / / Natural Chromaticity (H/V)-88 / / -191 Momentum Compaction1.68e-41.55e-5 Beta at Normal Straight22.6 m / 5.6 m1.0 m / 1.4 m Bending Field0.68 T0.70 T No. of Quadrupoles / Cell1026 (9 Family) Max. Quad. Str. B'L/(B  ) 0.40 m m -1 (B' = 79 T/m) No. of Sextupoles / Cell723 (12 Family) Max. Sext. Str. B''L/(B  ) 6.2 m m -2 (B''=13000 T/m 2 ) Radiation Loss9 MeV/turn4 MeV/turn 12 v

Bending Field Dependence of Chromaticity Use 6B lattice with 0.7 T / 0.9 T / 1.4 T bending field, vary QF and QD and find optics having the emittance of less than 90pmrad. 13 Nat. Chrom. & Rad. Power & Emit. Reduction by DW  0.7 T

SF/2 SF SD Interleaved SX Configuration within a Cell Basic Idea: Cancellation of SX Kicks within a Cell (Hor.) small but non-zero DA 14 - I transformation

SF/2 SF SD Interleaved SX Configuration within a Cell Actual Consraints we put in SX Optimization 15 - I transformation To increase SX degree of freedom, we relaxed the constraints and added harmonic SXs outside the arc. 12-family (mirror sym.) close but not the same strength

Betatron phase advance  x ~ 25   x ~  Interleaved SX Configuration between Cells Cell 1 Cell 3 Cell 5 Cell 1 Cell 3  y ~ 3  Cell 5 Horizontal Vertical - I transformation cf.) "sextupole symmetrization" in SLS 16 We found the vertical constraint is effective. DA becomes double in vertical direction.

Linear Optics “as low natural-chromaticity as possible” (so that SX becomes weak) Tune Selection (1) avoidance of strong resonances (2) phase adjustment for interleaved sextupole configuration Design of Nonlinear Optics harmonic method with interleaved SX for correcting (1) linear chromaticity (2) nonlinear resonances independent of  p/p (on- and off-mom.) (3) nonlinear resonances by Q and SX for off-mom. (4) higher order resonances for on-mom. (5) amplitude-depence of tune Iteration (tune survey, etc) Strategy of Lattice Design 17

+ “(On-momentum) Higher Order Resonant Potentials by Sx” Resonant Potential Induced by SX without  p/p (Qx, Qy): Tune (Off-momentum) Resonant Potential by Q (Off-momentum) Resonant Potential by Sx Cancel Set to ~ 0 Suppress Isolated Resonance Hamiltonian Design of Nonlinear Optics

Sextupole Optimization (latest) Amplitude- and Energy-Dependence of Tune 19

Sextupole Optimization (latest) 20

Sextupole Optimization (latest) 21 Frequency Map (  = 0%) Dynamic Aperture w/o Inj. Point (LSS)  x = 24.2 m,  y = 7.8 m  x = 40  m DA Boundary x: integer resonance y: sextupole resonance

Sextupole Optimization (latest) 22 DA w/ SX Alignment Error (  = 10  m, cutoff 2 

Sextupole Optimization (latest) Momentum Acceptance 23

Damping by Insertion Devices Residual dispersion must be suppressed:  x < 1mm Planar ID ( U = 14.4mm, L = 3m) ×28 （ the same number as normal straights ） At user-time: 67pmrad → around 30 pmrad 24

Damping Wigglers At user-time ： 67pmrad → around 30pmrad DWs are used to realize an extremely small emittance less than 20pmrad. They can also be used to keep the emittance at some value during user- time (compensation of ID gap change). Add DWs ( DW = 50mm, L DW = 4m) at LSSs. 25

Intrabeam Scattering & Touschek Lifetime Emittance and Energy Spread Ref.) K.Bane, PRST-AB 5 (2002) K.Kubo, PRST-AB 8 (2005) Touschek Lifetime cf.) 1nC/bunch  0.2mA/bunch Bunch Length (rms): 7.7 – 10 ps Control of bunch length is under consideration. 26 w/o ID

Brilliance About 10 3 times higher brilliance than that of the present storage ring (0.5 ~ 100 keV). by T.Tanaka New (6GeV, 300mA) Present (8GeV, 100mA)

ID Parameters (tentative) 28

30m-LSS for Beam Injection One example of LSS Optics (to be optimized) No Sextupoles (Linear) Low Natural Chromaticity Betatron-Phase Matched High  for Beam Injection also for Damping Wigglers / RF   x,  y  29

Injector A high-quality injection beam is needed. At SPring-8 we have XFEL Linac, which will be used as a full-energy injector to the storage ring. Energy: 8 GeV (max.) Emittance: 40 pm.rad Energy Spread: 0.01 % Bunch Length: 30 fs (rms) Electron Charge: 300 pC – 1 nC XFEL(SACLA) SR Booster Design Parameters (typical) 30

Summary SPring-8 upgrade plan is under discussion. 6B lattice is a current tagret :  〜 70 pmrad (natural, at 6GeV) → < 20 pmrad (w/ damping) Brilliance > Studies are ongoing including further optimization of lattice. DAY-3 K.Fukami, "Strong Magnets for Ultimate Storage Rings" T.Nakamura, "A Fast Kicker System for Beam Injection" 31

IPAC2011 Papers T. Watanabe, et al. Current Status of SPring-8 Upgrade Plan Y. Shimosaki, et al. Lattice Design of a Very Low-emittance Storage Ring for SPring-8-II T. Nakamura Bucket-by-bucket On/Off-axis Injection with Variable Field Fast Kicker M. Masaki, et al. A Proposal of Short X-ray Pulse Generation from Compressed Bunches by mm-wave iFEL in the SPring-8 Upgrade Plan K. Fukami, et al. Beam-based Alignment for Injection Bump Magnets of the Storage Ring using Remote Tilt-control System 32