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Trajectory Stability P. Emma and J. Wu SLAC / LCLS LCLS Week, SLAC October 26, 2005

Trajectory Stability P. Emma and J. Wu SLAC / LCLS LCLS Week, SLAC October 26, 2005. Control undulator trajectory stability to <10% of rms beam size? Use BPM-based feedback loops (120 Hz) Specify stability of upstream systems Steering coil current regulation

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Trajectory Stability P. Emma and J. Wu SLAC / LCLS LCLS Week, SLAC October 26, 2005

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  1. Trajectory StabilityP. Emma and J. WuSLAC / LCLSLCLS Week, SLAC October 26, 2005 • Control undulator trajectory stability to <10% of rms beam size? • Use BPM-based feedback loops (120 Hz) • Specify stability of upstream systems • Steering coil current regulation • Quadrupole (& solenoid) vibrations • Quad (& solenoid) current regulation in presence of typical 200-mm misalignments • Charge jitter couples to RF cavity transverse wakefield in presence of typical 200-mm misalignments • Bunch length jitter couples to CSR wakefield in Chicane • Drive laser pointing stability

  2. Motivation • Undulator trajectory oscillation of 35 mm (1s) is 30% FEL power loss (3.5 mm is 0.5%), but x-ray pointing may be issue • Feedback loop runs at 120 Hz with effective band at f< 1 Hz (<10 Hz ?) • Linac & injector stability tolerances must control jitter at frequencies: f> 1 Hz References: P. Emma, PRD 1.1-006, 1.1-007,1.1-008

  3. Source-1:Current Regulation Errors of Dipole Corrector Steering Magnets sI1/I1 sI2/I2 sI3/I3 sIN/IN y z q1 q2 q3 qN yi' = qimaxsIi/Iimax

  4. Source-2: Transverse Mechanical Vibrations of Quadrupole Magnets y sy1 sy2 sy3 syN z yi' = kilisyi

  5. Source-3:Misaligned Quadrupole Magnets and Current Regulation Errors sI3/I3 sI1/I1 sI2/I2 sIN/IN y z y1 y3 yN y2 yi' = kiliyisIi/Ii

  6. Source-4:Charge jitter couples to RF cavity transverse wakefield due to alignment error y z sNe/Ne y1 y3 yN y2 yi' = ByisNe/Ne

  7. Source-5:Bunch length jitter couples to CSR in Chicane y z

  8. Normalized invariant amplitude per item (n-sigma) Total amplitude2 for N uncorrelated kicks Total jitter goal: <10% of rms beam size (~4 mm peak undulator osc.) tolerance sensitivity Form budget with a few discreet tolerance levels, opening challenging tolerances but holding tight on more standard ones

  9. O Horizontal Vertical field-sensitivity/corrector  Ai = 10% for each

  10. Corrector Current Regulation Tolerances 241 x and y correctors (0.01% to 0.003%)

  11. I = 6 A I = 3 A 30-yr old SCOR6 supplies D. MacNair 2003 I = 1 A I = 0

  12. vibration sensitivity/quad  Ai = 10% for each  Horizontal  Vertical group on rigid girders?

  13. Quadrupole & Solenoid Magnet Vibration Tolerances 12 quads need rms vibration 500 nm 101 magnets need rms vibration 100 nm 35 quads need rms vibration 50 nm 148 magnets

  14. Measured Quad-Magnet Vertical Vibration in the SLAC Linac R. Stege, J. Turner, SLAC, 1994 before rubber boot on water pump new measurements are planned – J. Turner et al. after rubber boot on water pump

  15. Quadrupole Current Regulation Tolerances long-term short-term 146 quadrupole magnets misaligned ~200 mm

  16. Linac Power Supply Current Regulation Measurements Antonio de Lira, May 2005 rms < 0.02% ? Data rate too slow – new measurements are planned for  120 Hz

  17. Feedback Loop Trajectory Measurement Resolution (5-mm BPM res.) coils x/sx = 6.3%, 5.4%, 3.8%, 5.0% undulator start at z= 0 coils

  18. Charge jitter and RF Cavity transverse wakefield • RF Cavity Wakefield [K.L.F. Bane, et al., PAC1997, p.515] • Neglecting -tron motion, and assuming uniform longitudinal distribution, one has

  19. Charge jitter and RF Cavity transverse wakefield • For Solid (red), x-plane Dash (green),y-plane

  20. Charge jitter and RF Cavity transverse wakefield • Scaling

  21. Charge jitter and RF Cavity transverse wakefield • Tolerance along beam line Red dot, x-plane Green dot, y-plane

  22. Bunch length jitter and CSR • Energy loss rate due to CSR [J.B. Murphy, et al., PAC2001, p.465] • In a bend

  23. Bunch length jitter and CSR • Tolerance due to bunch length jitter – scaling

  24. Bunch length jitter and CSR • Steady-state CSR vs. Transition CSR • Double-horn vs. Gaussian • Elegant simulation • Gaussian, transition, entire chicane, entire bunch • Double-horn, transition, entire chicane, entire bunch • P. Emma’s CSR-Tracking code

  25. 1-nC nominal

  26. 1-nC nominal

  27. 10% bunch length change 1-nC 20 mm 22 mm 18 mm

  28. 8% bunch length change 0.2-nC 7.0 mm 7.6 mm 6.4 mm

  29. 1-nC 0.2-nC

  30. Summary • Other Jitter Sources Not Included Yet • Drive laser pointing stability (not an issue – Henrik, Sasha) Total jitter for all examined sources: Corrector regulation: <10% (6%) Quad regulation @ 200 mm: <10% (6%) Vibration of all quads: ~10% Wakefield @ 2% charge jitter: ~2% CSR @ 10% bunch length jitter: ~20% Drive Laser pointing jitter: ~1% (?) AT (62 + 62 + 102+22+202+12)1/2 24% (x- plane)  (62 + 62 + 102+22+12)1/2 13% (y- plane)

  31. Conclusions • Trajectory stability sets tight requirement on alignment for dipoles and quadrupoles • Transverse wakefields coupled with 2% charge jitter are not an issue (1.5% trajectory jitter) • CSR wakefield in BC2 coupled with 10% bunch length jitter is an issue (15-25% trajectory jitter at 1 nC and 6-12% trajectory jitter at 0.2 nC) – best solution is better RF stability?

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