1. PEP-X Ultra Low Emittance Storage Ring Design at SLAC Lattice Design and Optimization Min-Huey Wang SLAC National Accelerator Laboratory With contributions by Yuri Nosochkov, Y. Cai, K. Bane Mini-workshop on Dynamic Aperture Issues of USR IUCF, Bloomington, Nov. 11-12, 2010

2. Outline Introduction of PEP-X Lattice design Optimization of dynamic aperture IBS emittance and Touschek lifetime Future plan –Emittance optimization Emittance 30 pm-rad storage design –PEP X soft x-ray FEL –PEP X ERL

3. Existing PEP-II rings 2.2 km existing rings in PEP tunnel Six 243 m arcs and six 123 m long straights 60 or 90 deg FODO lattice Can reach ~5 nm-rad emittance at 4.5 GeV (w/o wiggler) – too high for a modern light source No dispersion free straights for IDS

4. Design a new low emittance ring in the PEP-II tunnel. –~0.1 nm-rad emittance at 4.5 GeV for high brightness –>24 dispersion free straights for insertion devices –Use existing PEP-II tunnel and utilities PEP-X low emittance ring Same ring layout as PEP-II in the exist tunnel using existing RF system New optics with: Two DBA arcs yielding 30 ID straights Four TME arcs for low emittance ~90 m wiggler to reach ~0.1 nmrad emittance at 4.5 GeV FODO optics in long straights PEP-II based injection system(Horizontal injection)

5. R. Hettel et al EPAC08 Conceptual Layout of PEP-X with photon beamlines at SLAC

6. PEPX Lattice DBA TME Straight Injection x =1.523 y =0.508 x =0.373 y =0.124

7. DBA Supercell low b IDhigh b ID 4 harmonic sextupoles, 2 families 6 chromatic sextupoles, 4 families Two standard cells are combined into one supercell with a low and high ID beta:  x,y = 3.00, 6.07 m and  x,y = 16.04, 6.27 m. 8 supercells per arc.Two standard cells are combined into one supercell with a low and high ID beta:  x,y = 3.00, 6.07 m and  x,y = 16.04, 6.27 m. 8 supercells per arc. Phase advance is optimized for compensation of both sextupole and octupole driving terms and maximum dynamic aperture:  x /2  = 1.5+3/128,  y =  x /3. Phase advance is optimized for compensation of both sextupole and octupole driving terms and maximum dynamic aperture:  x /2  = 1.5+3/128,  y =  x /3. Harmonic sextupoles are added for further reduction of the resonance effects and amplitude dependent tune spread.Harmonic sextupoles are added for further reduction of the resonance effects and amplitude dependent tune spread.

8. TME cell 7.6 m cell with ~0.1 nm-rad intrinsic emittance. 32 standard and 2 matching cells per arc. X and Y phase advance is set near 3  /4 and  /4 for compensation of sextupole and octupole effects and maximum dynamic aperture. X and Y phase advance is set near 3  /4 and  /4 for compensation of sextupole and octupole effects and maximum dynamic aperture. Optimized for maximum momentum compaction.

9. Injection straight section Existing PEP-II injection straight with 4 additional quads. PEP-II vertical injection optics is changed to horizontal to avoid vertical injection oscillations in the IDs. PEP-II vertical injection optics is changed to horizontal to avoid vertical injection oscillations in the IDs. Large horizontal  x = 200 m at septum for larger injection acceptance. Large horizontal  x = 200 m at septum for larger injection acceptance. Existing 4 DC bump magnets and 2 fast kickers. Phase space diagram at injection point

10. Wiggler straight Dispersion in ~5 m wiggler section  DBA and TME arcs without wiggler yield e = 0.38 nm-rad 89.3 m wiggler is inserted in one long straight section yielding  = 0.086 nm- rad. Wiggler is split in 18 identical sections to fit FODO cells.  Wiggler parameters optimized for strong damping effect: 10 cm period, 1.5 T field. The long wiggler can be split in half and placed in two separate straights for better handling of radiated power (4.7 MW at 1.5 A).

11. Optimization of wiggler parameters    vs L    vs B Based on analytic formulas: Most efficient damping for L < 100 m. More damping with a shorter period, higher field and lower  x, but the rate of reduction gradually decreases. High peak field requires a smaller gap which reduces vertical acceptance and increases resistive wall impedance. Selected parameters: 10 cm period, 1.5 T peak field, 89.3 m total length.

12. Complete ring lattice   Wiggler Symmetric locations of DBA and TME arcs and mirror symmetry with respect to injection point.

13. Main parameters of PEP-X ParameterDamping wiggler offDamping wiggler on Energy, E 0 [GeV]4.5 Beam current, I [A]1.5 Circumference, C [m]2199.31669 Emittance,  x [pm-rad, 0 current] 37985.7 Tunes, x / y / s 87.23/36.14/0.003787.23/36.14/0.0077 RF voltage/frequency, [MV]/ [MHz]2.0/4768.9/476 Harmonic number, h3492 Energy loss, U 0 [MeV/turn]0.523.12 Current/charge per bunch [mA/nC]0.43/3.15 Momentum compaction,  5.816x10 -5 5.812x10 -5 Energy spread,   0.55x10 -3 1.14x10 -3 Bunch length,  z [mm] 33 Damping times,  x /  y /  s [ms] 101/127/7320.3/21.2/10.8  x /  y at ID center, [m] (low  ) 3.00/6.07  x /  y at ID center, [m] (high  ) 16.04/6.27

14. Optimization of dynamic aperture Choose phase advance in a periodic cell which yields a unit (+I) linear transfer matrix in both planes for a section made of these cells (such as DBA or TME arc). In such a system the second-order geometrical (on momentum) aberrations will vanish. Fine tune the DBA and TME cell phase advance to minimize the higher order resonance driving terms. Optimize sextupole strengths in the DBA and TME cells while keeping the linear chromaticity canceled. Optimize the machine betatron tunes in order to minimize the effects of strong resonances and obtain the largest possible dynamic aperture. Add geometric (harmonic) sextupoles at non-dispersive locations in order to minimize amplitude dependent tune shifts and high order resonance effects.

15. Dynamic aperture tune scan 2 x +2 y =247  x +2 y =248 x +2 y =160 Nominal tune: x =86.23 and y =36.14

16. Chromatic correction  DBA and TME sextupole positions and strengths as well as cell and long straight phase advance are optimized for maximum energy dependent aperture. Optimization of non-linear chromatic terms using MAD HARMON and empiric optimization of momentum dynamic aperture in LEGO tracking simulations  W-functions2 nd order dispersion Tune vs Dp/p

17. Tune shift with amplitude 2 weak harmonic sextupoles near each ID straight reduce the amplitude dependent tune shift and resonance driving terms generated by chromatic sextupoles and increase dynamic aperture for horizontal injection. Minor adjustment will be needed to accommodate realistic length harmonic sextupoles.

18. Frequency map analysis Strong chromatic sextupoles generate high order resonance driving terms Dynamic apertureTune spread

19. Dynamic aperture (1) Without errors PEP-II multipole field errors only (10 seeds   Dp/p up to 3% Effect of multipole errors is small

20. Dynamic aperture (2) Multipole + field + quad misalignmentMultipole + field + all misalignment Quad misalignment is ok. Sextupole misalignment needs better orbit correction at sextupoles. Horizontal injection aperture is ok.

21. Momentum aperture Acceptance versus  p/p Obtained in LEGO dynamic aperture tracking w/o errors

22. IBS emittance and Touschek lifetime PEP-X parameters used for IBS calculations 1% current stability will require top-off injection every few seconds

23. PEP-X brightness

24. Emittance Optimization

25. MBA CELL (on going study) Seven bends per cell 8 cells per arc Total 6 arcs 336 dipoles(240,96) 2.2 km arc length 1.5 km 6 m ID straight Emittance 27.8 pm-rad Tune x =114.23, y =43.14 Energy spread 6.3e-4 Bunch length 3 mm Energy accep. 3.6% Natural chromaticity -141/-121 FODO x = 0.2635 y = 0.078975 MBA x = 2.125 y = 0.625

26. Chromatic correction  Pair of SD SF for chromaticity correction. Choose phase advance in a periodic cell which yields a unit (+I) linear transfer matrix in both planes for a section made of these. K2lSF = 24.68 m^-2, combined with QF K2lSD = -71.6 m^-2 combined with dipole W-functions2 nd order dispersion Tune vs Dp/p

27. Dynamic aperture bare lattice  x = 11.5 m,  x =1 8  m  y = 10.3 m  x =1.7  m 1% coupling

28. PEP X ERL Fit into PEPX ring. Superconducting RF 1.3 GHz, 20MV/m. 370.9 m long Linac accelerate, decelerate of energy range 150 MeV to 5 GeV. Try to accommodate both PEPX and ERL operation. e - 5 GeV e - 150 MeV

29. PEP X soft x-ray FEL PEP-X ultra-low emittance, high peak current, FEL exponential gain (without saturation) at soft xray wavelengths can occur on a turn-by-turn basis Equilibrium energy spread (red dashed curve) and FEL power at r  = 3.3 nm (blue solid curve) as a function of the undulator length Z. Huang et al., NIM A 593, 120 (2008)

30. Conclusion The baseline lattice for PEP-X is presented. It uses DBA and TME cell optics and ~90 m damping wiggler yielding 30 ID straights and an ultra-low emittance. Photon brightness of ~10 22 (ph/s/mm 2 /mrad 2 /0.1 % BW) can be reached at 1.5 A for 3.5 m IDs at 10 keV. Dynamic aperture is adequate to accommodate a conventional off-axis injection system. More challenge designs of PEP-X Horizontal emittance to reach diffraction limit of 10 KeV photon-showing good progress Storage ring FEL ERL option