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"

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Ultimate Target of Machine Upgrading

"Diffraction Limited" Light Source

in Both H. and V. Directions for ~ 10keV Photons e ~ 10pmrad

E = 6 GeVI = 100 mAk = 0.02sd = 0.12%bx = 1 mby = 1 m10 keV Photon byHybrid Undulator

by T.Watanabe

SPECTRA

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Present Lattice Structure of the SPring-8 SR

4 ´ [ 9 ´ (Normal Cell, DB) + (Matching Cell) + (Long Straight) + (Matching Cell) ]

Matching LS MatchingNormal

C = 1436 mE = 8 GeVe = 3.4 nmrad（ eeff = 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 DispersionStrong SXSmall DA

"Chromaticity Wall"

(J.Bengtsson, EPAC08)We set 6B lattice as a

candidate of a new ring.

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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

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Multi-Bend Lattice2B (eeff = 2.09nmrad)

3B (eeff = 0.54nmrad)

4B (eeff = 0.19nmrad)

6B (e = 0.07nmrad)

2009 6

Multi-Bend Lattice6B Lattice

LB LB LB LBLB/2LB/2

bx〜1mby〜1mhx = 0

matching

unit

matching

unit

unit

unit

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Multi-Bend LatticeDA @ Inj. Point

Normalizedby b1/2

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Multi-Bend Lattice

e (N∝ B-1)-3

NB: LB/2 at both ends → (NB-1)

8B 10B 12B

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Multi-Bend Lattice

Number of B　↓Quad. Tune Chrom.(abs) Dispersion 　↓ Chromaticity Cor.Sextupoles 　↓ Dynamic Apt.

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too small DA for M > 6

6B Lattice Design (typical)

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2B (Double-Bend)Dispersion Leaked

6B (Sextuple-Bend) Achromat

Unit Cell Length 29.9156 m

Ring Circumference 1435.9488 m

Beam Energy 8 GeV 6 GeV

Emittance 3.4 nmrad (3.7 nmrad) 0.068 nmrad

Energy Spread 0.109 % 0.096 %

Betatron Tune (H/V) 40.135 / 18.345 141.865 / 36.650

Natural Chromaticity (H/V) -88 / -42 -477 / -191

Momentum Compaction 1.68e-4 1.55e-5

Beta at Normal Straight 22.6 m / 5.6 m 1.0 m / 1.4 m

Bending Field 0.68 T 0.70 T

No. of Quadrupoles / Cell 10 26 (9 Family)

Max. Quad. Str. B'L/(Br) 0.40 m-1 1.49 m-1 (B' = 79 T/m)

No. of Sextupoles / Cell 7 23 (12 Family)

Max. Sext. Str. B''L/(Br) 6.2 m-2 110 m-2 (B''=13000 T/m2)

Radiation Loss 9 MeV/turn 4 MeV/turn12

v. 110921

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.

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Nat. Chrom. & Rad. Power & Emit. Reduction by DW 0.7 T

SF/2 SF/2SF SF SF SF SF

SD SD SD SD SDSD

Interleaved SX Configuration within a Cell

Basic Idea: Cancellation of SX Kicks within a Cell (Hor.)

small but non-zero DA

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- I transformation

SF/2 SF/2SF SF SF SF SF

SD SD SD SD SDSD

Interleaved SX Configuration within a Cell

Actual Consraints we put in SX Optimization

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- 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 Dyx ~ 25p

Dyx ~p

Interleaved SX Configuration between Cells

Cell 1 Cell 3 Cell 5

Cell 1 Cell 3

Dyy ~ 3p

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 Opticsharmonic method with interleaved SX for correcting (1) linear chromaticity (2) nonlinear resonances independent of Dp/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

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+ “(On-momentum) Higher Order Resonant Potentials by Sx”

+Δpp

U 2Qx ~ int .( )Sx+ U 2Qy ~ int .( )

Sx{ }

+Δpp

U 2Qx ~ int .( )QQ+ U 2Qy ~ int .( )

QQ{ }

Resonant Potential Induced by SX without Dp/p

(Qx, Qy): Tune

(Off-momentum) Resonant Potential by Q

(Off-momentum) Resonant Potential by Sx

Cancel

Set to~ 0

Suppress

Isolated Resonance Hamiltonian

H ∝ U Qx ~int.( )Sx+ U 3Qx ~int.( )

Sx+ U Qx ±2Qy ~int.( )

Sx

Design of Nonlinear Optics

Sextupole Optimization (latest)

Amplitude- and Energy-Dependence of Tune

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Sextupole Optimization (latest)

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Sextupole Optimization (latest)

21Frequency Map (d = 0%)

Dynamic Aperture w/o Error

@ Inj. Point (LSS) bx = 24.2 m, by = 7.8 m sx = 40 mm

DA Boundary x: integer resonance y: sextupole resonance

Sextupole Optimization (latest)

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DA w/ SX Alignment Error (s = 10mm, cutoff 2 )s

Sextupole Optimization (latest)

Momentum Acceptance

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Damping by Insertion Devices

Residual dispersion must be suppressed: 　 Dhx < 1mm

Planar ID (lU = 14.4mm, L = 3m) ×28 （ the same number as present @ normal straights ）

At user-time: 　 67pmrad 　→ around 30 pmrad

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Damping WigglersAt 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 (lDW = 50mm, LDW = 4m) at LSSs.

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Intrabeam Scattering & Touschek Lifetime

Emittance and Energy Spread

Ref.) K.Bane, PRST-AB 5 (2002) 084403. K.Kubo, PRST-AB 8 (2005) 081001.

Touschek Lifetime

cf.) 1nC/bunch 0.2mA/bunch

Bunch Length (rms): 7.7 – 10 ps

Control of bunch length is under consideration.

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w/o ID

Brilliance

About 103 times higher brilliance than that of the present storage ring (0.5 ~ 100 keV).

by T.Tanaka

New (6GeV, 300mA)

Present (8GeV, 100mA)

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1023

ID Parameters (tentative)

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30m-LSS for Beam Injection

One example of LSS Optics (to be optimized)No Sextupoles (Linear)Low Natural ChromaticityBetatron-Phase MatchedHigh b for Beam Injectionalso for Damping Wigglers / RF

p Dyx, Dyy2p

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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.radEnergy Spread: 0.01 %Bunch Length: 30 fs (rms)Electron Charge: 300 pC – 1 nC

XFEL(SACLA)

SRBooster

Design Parameters(typical)

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Summary

SPring-8 upgrade plan is under discussion.

6B lattice is a current tagret : e 〜 70 pmrad (natural, at 6GeV) → 　 < 20 pmrad (w/ damping) Brilliance > 1023

Studies are ongoing including further optimization of lattice.

DAY-3K.Fukami, "Strong Magnets for Ultimate Storage Rings"T.Nakamura, "A Fast Kicker System for Beam Injection"

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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. NakamuraBucket-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

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