Lattice Design for the Taiwan Photon Source (TPS) at NSRRC Chin-Cheng Kuo On behalf of the TPS Lattice Design Team Ambient Ground Motion and Civil Engineering for Low Emittance Electron Storage Ring Workshop July 21 ~ 22, 2005 NSRRC
Outline TPS 3 GeV linear lattice design TPS 3 GeV nonlinear sextupole configuration study TPS 3 GeV preliminary design of orbit correction scheme, aperture requirements, lifetime calculations, etc. TPS injector booster design Summary
Design Concept of the TPS Brightness ~ 10 21 ph/s/mm 2 /mrad 2 /0.1% λ/λ Flux ~ 10 16 ph/s/0.1% λ/λ Nominal energy: 3 GeV Ultra low emittance As many straights as possible Beam current > 300 ma at 3 GeV Lifetime > 10 hr Top-up injection
Theoretical Minimum Emittance For DBA: 2 3 Cqγ θ ε x (min) = F J F C θ = each dipole bend angle (rad) J q x = = 1/ 4 1/ 12 15 = 3.84 10 15 13 γ = E / 0.511(MeV) x m rads = horizontal partition number where F is lattice dependent. for separate bending, small angle, achromatic DB ( DBA) for distributed dispersion DB For 24-cell 3GeV, theoretical minimu emittance is 1.92 nm-rad for the achromatic DBA For TBA (achromatic): If center dipole is where θ 1 3 1/ 3 ~ 144. is the outer dipole. But if dipole lengths are equal then ε longer than outer dipole then ε (min) = 1/ 4 x ( 2 3 1.1064 Cqγ θ min ) = 4 15 J With same cells, TME(DBA) ~ 5 TME(TBA) In real machine, 2~3 times the TME x x 2 Cqγ θ 15 J x 3 1,
Minimum Emittance for DBA cell Minimum emittance (nm-rad) 12 10 8 6 4 2 0 16 DBA 18 DBA 20 DBA 22 DBA 24 DBA 2.6 2.8 3 3.2 3.4 Energy (GeV)
A Large Ring? Suggested by members of Board of trustee to have larger circumference, September 2004. Where will be this bigger ring located? Is it possible to be on the NSRRC site? How large?
TPS Site Plan
Design goals of the TPS December, 2004 Nominal energy: 3 GeV Maximum energy: 3.3 GeV Circumference: 518.4 m Target emittance < 2 nm-rad at 3 GeV Long straights > 10 m (quad to quad) Standard straights > 6 m Energy acceptance larger than 4% Beam current > 300 ma at 3 GeV Lifetime > 10 hr Top-up injection
Linear Lattice of the TPS Long Straight: 11.72 m (Q-t-Q) X 6 Standard Straight: 7 m (Q-t-Q) X 18 518.4 m, 24 cells, 6-fold High x in long straight for injection Low x,y in standard straight Reasonable x,y in the whole ring Horizontal tune between 26 and 27 Vertical tune between 12 and 13 Large betatron de-coupling in the arc for sextupole chromatic correction Large dispersion in the arc to reduce sextupole strength Reasonable distributed dispersion for reducing emittance Reasonable natural chromaticities
TPS Lattice Structure
TPS Lattice Functions OPTICAL FUNCTIONS TPS 24P18K1 OPTICAL FUNCTIONS TPS 2P18L1 β x β x 25 β y 25 β y Optical functions (m) 20 15 10 Optical function (m) 20 15 10 5 10*η x 10*η x 5 0 0 10 20 30 40 50 60 70 80 S(m) 0 0 10 20 30 40 50 60 70 80 S (m)
TPS parameters TPS Energy (GeV) Beam current (ma) Circumference (m) Nat. emittance ε x (nm-rad) Cell / symmetry / structure β x / β y / η x (m) LS middle RF frequency (MHz) RF voltage (MV) Harmonic number SR loss/turn, dipole (MeV) Straights Betatron tune ν x /ν y Non-achromatic 24p18K1 1.7 10.59 / 9.39 / 0.11 26.22 / 12.28 3.0 400 518.4 24 / 6 / DBA 499.654 5.0 864 0.98733 11.72m*6+7m*18 Achromatic 24p18L1 5.8 12.9 / 9.79 / 0.0 26.24 / 12.28
TPS parameters (contd.) Synchrotron tune ν s Bunch length (mm) Dipole B/L (Tesla)/(m) Number of dipoles Quad No. / Max. field(t/m) 240 / 17 Sext No. / Max. m*l (m -2) 168 / 6 Mom. comp. (α 1, α 2 ) 2.0 10-4, 2.3 10-3 2.5 10-4, 1.0 10-3 Nat. energy spread σ E 9.53 10-4 Damping partition (Jx /Jy / Js) 6.7 10-3 2.34 1.3789 / 0.95 0.997 / 1.0 / 2.003 Damping time (ms) ( τ x / τ y /τ s ) 10.5 / 10.5 / 5.25 Nat. chromaticity ξ x / ξ y -78.2 / -32.5-78.2 / -35.3 48 7.6 10-3 2.65
TPS Beam size and Divergence Source point σ x ( m) σ x ( rad) σ y ( m) σ y ( rad) 11.72 m Long straight 172.3 12.7 12.7 1.3 7 m Standard straights 126.5 17.7 4.5 3.7 Dipole centre 30.3 66.6 18.2 1.3 24P18K1, ε x = 1.72 nm-rad, ε y = 0.0172 nm-rad
Flux at 3.0 GeV of TPS 10 16 EPU70 EPU60 EPU46 IVXU28 SU15 Flux (Phot/s/0.1%bw) 10 15 10 14 U100 SW60 SEPU25 10 13 Bending 10 1 10 2 10 3 10 4 10 5 Photon Energy (ev)
Brilliance at 3.0 GeV of TPS Brilliance (Phot/s/0.1%bw/mm 2 /mr 2 ) 10 21 IVXU28 SU15 EPU46 10 20 10 19 10 18 10 17 10 16 10 15 10 14 10 13 10 12 EPU60 EPU70 U100 SW60 Bending SEPU25 10 1 10 2 10 3 10 4 10 5 Photon Energy (ev)
Nonlinear optimization Using OPA, BETA, Tracy-2, Patricia, etc., the sextupole configurations are optimized. 8 families of sextupoles are used. Chromaticities are corrected to zero. Weighting factors such as resonance strengths, de-tuning coefficients for amplitude-dependent tune shift, secondorder effects are given. And the sextupole families, positions are changed. However, still tune shifts with amplitude are large. Dynamic apertures are limited. Nonlinear momentum-dependent tune-shift are also investigated.
Sextupole scheme OPTICAL FUNCTIONS TPS 24P18K1 25 β x β y Half superpeiod 20 Optical functions (m) 15 10 5 10*η x S1 S2 SD SF SD S5 S6 S7 S8 SD SF SD S8 S7 0 0 5 10 15 20 25 30 35 40 S(m)
Tune shift vs. Amplitude &Energy Fractional tune 0.5 0.4 0.3 0.2 Tune shift with amplitude, TPS 24p18K1 Tune X Tune Y Fractional tune 0.5 0.4 0.3 0.2 Tune shift with amplitude 24p18L1 Tune X Tune Y 0.1-30 -20-10 0 10 20 30 x [mm] 0.1-30 -20-10 0 10 20 30 x [mm] Fractional tune tune vs. dp/p, TPS 24p18k1 0.5 X Y 0.45 0.4 0.35 0.3 0.25 0.2-4 -3-2 -1 0 1 2 3 4 dp/p [%} Fractional tune 0.8 0.7 0.6 0.5 0.4 0.3 tune shift vs. dp/p TPS 24p18L1 0.2-4 -3-2 -1 0 1 2 3 4 dp/p [%} X Y
Phase Space Tracking X'(mrad) Horizontal Phase Space Tracking TPS 24P18K1 4 Horizontal Phase Space 24P18K1 3 2 1 0-1 -2-3 -4-30 -20-10 0 10 20 30 X(mm) Y'(mrad) Vertical Phase Space Tracking TPS 24P18K1 2.5 Vertical Phase Space 24P18K1 2 1.5 1 0.5 0-0.5-1 -1.5-2 -2.5-20 -15-10 -5 0 5 10 15 20 Y(mm)
Beta beat vs. energy beta [m] beta vs. dp/p at straight middle 24p18K1 beta x 13 beta y 11 9 7-4 -3-2 -1 0 dp/p [%] 1 2 3 4 beta [m] beta vs. dp/p at straight middle 24p18L1 beta x beta y 13 11 9-4 -3-2 -1 0 dp/p [%] 1 2 3 4
Dynamic aperture w/o synchrotron oscillation 30 25 20 Dynamic aperture, 1000 turns, TPS 24p18k1 dp/p 0% dp/p 3% dp/p = -3% 30 25 20 Dynamic aperture, 1000 turns, no synchrotron oscillations TPS 24p18L1 DE=0 % DE= 3 % DE= -3 % y [mm] 15 10 5 y (mm) 15 10 5 0-30 -20-10 0 10 20 30 x [mm] 0-40 -30-20 -10 0 10 20 30 x(mm) 24P18K1 βx=10.59 m βy= 9.39 m 24P18L1 βx= 12.9 m βy= 9.79 m
Frequency Map Analysis v x 2v y 51 3v x 2v y 54 4v x 105
Frequency Map Analysis ID Chamber +/- 5 mm in vertical plane
Multipole Errors Effects Sextupole dipole -4.4 10-5 quadrupole sextupole 25 Dynamic aperture, 1000 turns, TPS 24p18k1 dp/p= 0 %, no errors multipole errors Octupole -1.6 10-6 20 Decapole -8.7 10-6 2.6 10-5 15 Dodecapole 14-pole -7.5 10-7 -1.5 10-6 3.3 10-5 y [mm] 10 18-pole -1.6 10-7 5 30-pole -8.6 10-10 0-30 -20-10 0 10 20 30 x [mm]
Insertion Devices Effects Dynamic aperture, 1000 turns, TPS 24p18k1 Insertion Device EPU5.6 U5 U9 25 dp/p= 0 %, no errors multipole errors Magnet Length (m) 3.9 3.9 4.5 20 Period Length (cm) Number of Periods 5.6 66 5 76 9 48 y [mm] 15 10 Max. By (Bx) Field (Tesla) 0.67 (0.45) 0.64 1.25 5 0-30 -20-10 0 10 20 30 x [mm]
Girder Support Precision ~ 15 µm
RMS Amplification factors Quad misalignment in x/y only Girder misalignment in x/y only A= 59/52 in x/y rms A= 33/9 in x/y rms Errors: rms Quad misalign w.r.t. girder: 0.03mm Girder misalign: 0.1mm Bend roll: 0.2 mrad Girder roll: 0.1 mrad Bend relative field error : 0.001 Results: rms COD X/Y= 3.07mm / 1.71mm
Amplification w.r.t Quad or Girder displacement Amplification factor 100 90 80 70 60 50 40 30 20 Quad amplification factor X Quad amplification factor Y 10 0 10 20 30 40 50 60 70 80 S(m) Amplication factor 60 50 40 30 20 10 Girder amplification factor X Girder amplification factor Y 0 0 10 20 30 40 50 60 70 80 S(m)
COD Correction Scheme
COD correction scheme (contd.) Correctors and BPMs Before & After correction
COD correction scheme (contd.) Horizontal Vertical Correctors Used Number of eigenvalues used Mean of < cor. Strength > (mrad) Max of < cor. Strength > (mrad) Max of < res. C.O. at BPM > (mm) (1,4,7) C1-C7 168 (2,6) (2,4,6) C1-C7 Correctors, eigenvalues in use. Corrector strengths
Injection scheme 2.8 2.8 2.8 K1 K2 K3 K4 Store beam 0.8 0.8 0.8 0.8 Kicker magnet Injected beam 1.8 Septum magnet In a long straight K-t-K: 9.2m Another option: Thick and Thin septa scheme x` A=13.86 mm Bumper height 6σ i 5 mm 4σ oi 20.11 mm Bumped beam acceptance Bumped store beam Injected beam Store beam Acceptance 22.6 mm Septum wall Beam stay clear TPS septum and kicker parameters x septum kicker Length (m) Field (T) Bend Angle (mrad) 1.8 0.97 174.5 0.80 0.0898 7.18
Physical Aperture Requirement Injection requirement 4% energy acceptance At least x: +/- 32 mm, y: +/- 6 mm BSC needed
Touschek & total lifetime Acceptance in one super-period Gap voltage=3.5 MV, Touschek lifetime=18.25 hrs. Acceptance (%) 4 3 2 1 0-1 -2-3 -4 Second order compaction factor limited Position (m) Acceptance in negative (%) Acceptance in positive (%) 0 20 40 60 80 15 10 5 0-5 -10-15 Touschek lifetime, bunch length and RF acceptance 45 40 35 30 25 20 15 10 5 0 2 2.5 3 3.5 4 RF gap voltage (MV) Touschek half life (hr) Bunch length (ps) RF acceptance (%) 0.6 ma/bunch Coupling = 1% Touschek lifetime calculation using BETA For 2.5mm haf gap ID chambers, 1 ntorr N2 equivalent gas lifetime is about 44 hours. >>>Total lifetime is around 22.5 hours for 3 MV RF, 0.6mA/bunch, and 1% coupling operation.
Instabilities No SRF generated coupled bunch long. & transverse instabilities With small gap undulators, transverse coupled bunch instabilities might occur No transverse single bunch MCI With 0.6 ma/bunch, longitudinal broadband impedance need < 0.05 ohm Beam-ion instabilities need to be addressed
Booster Ring Circumference [m] 499.2 499.2 162 Extraction energy [GeV] 3 3 3 Injection energy [GeV] 0.1 0.1 0.1 Revolution time [s/turn] 1.665*10-6 1.665*10-6 0.5404*10-6 Tune ν x /ν y 16.13/7.18 27.11/13.16 7.11/4.17 Nature chromaticity (ξ x /ξ y ) -14.12/-13.96-30.5/-22.8-8.02/-5.97 Emittance [nm-rad.] 36.6 5.30 126 Damping time (τ x /τ y /τ e ) [ms] 26.1/25.6/12.6 25.8/25.6/12.7 6.06/5.76/2.81 Damping partition (J x /J y /J e ) 0.98/1.0/2.02 0.993/1.0/2.01 0.95/1.0/2.05 Momentum compaction α 0.00492 1.68*10-3 0.025 Radiation loss [kev/turn] 390.8 390.8 562.78 Energy spread 5.97*10-4 5.99*10-4 7.11*10-4 Quantum lifetime [minutes] 13.6 (@0.7 MV) 2.02*10 20 (@0.8 MV) 2.29 (@1.2 MV)
TPS site
Summary DBA lattice structure with 24 cells, 6-fold symmetry could achieve natural emittance < 2nmrad with a constrained circumference 518.4m and required straight lengths. Booster options are studied. Optimization of the linear lattice and nonlinear effects is in progress. Other issues such as orbit correction scheme, coupling control scheme, lifetime calculations, injection scheme, instabilities, ground vibration effects are investigated.