1. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS BBA Related Issues Heinz-Dieter Nuhn, SLAC / LCLS June 28, 2004 TechniqueSimulations Earth Field Considerations TechniqueSimulations LCLS

2. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Basic Strategy Save BPM readings as a function of large, deliberate changes in e  energy (e.g., 14, 7, and 5 GeV) LCLS Calculate and correct quad & BPM misalignments and adjust ‘launch’ Repeat ~3 times with first application Re-apply one iteration per ~1 month (?) Courtesy of Paul Emma

3. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS The Method BPM readings, m i, written as sum of upstream kicks + offset, b i Kicks are sensitive to momentum, p k, while offsets, b i, are not Reference line defined by incoming x 0, x 0 launch conditions BPM readings, m i, written as sum of upstream kicks + offset, b i Kicks are sensitive to momentum, p k, while offsets, b i, are not Reference line defined by incoming x 0, x 0 launch conditions s b i > 0  E = 0  E < 0 quad offsets and/or pole errors i th BPM  j  j Courtesy of Paul Emma

4. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Extrapolation to infinite momentum give BPM offsets The Method 1/p mimimimi offset =  b i (15 GeV/c)  1 (10 GeV/c)  1 (5 GeV/c)  1 p  linear only if C ij independent of p Courtesy of Paul Emma

5. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS The Method Define… then solve the linear system… Define… BPM readings at p 1 BPM readings at p 2 BPM offsets quad offsets known optical functions at each p k Courtesy of Paul Emma

6. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Constraints Solve with ‘soft-constraints’* on resulting BPM and quad offsets * C. Adolphsen, 1989 PAC ~1 mm Without this ‘reasonability’ weighting, resulting BPM and quad offsets can stray out to large values at low frequencies Scanning beam energy gives sensitivity to (and ~correction of) all field errors, including undulator poles, Earth’s field, etc… Courtesy of Paul Emma

7. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Schematic layout ~300  m UNDULATOR (120 m) LTU best final trajectory steering elements x0x0x0x0 x0x0x0x0 original incoming launch error Undulator misaligned w.r.t. linac axis with uncorrelated and correlated* (‘random walk’) component permanent magnet quadrupoles and undulator poles * suggested by C. Adolphsen BPMsquads Courtesy of Paul Emma 130

8. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Beam-based alignment steps ×3 Courtesy of Paul Emma

9. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Input Errors Used for Simulation 0.04 4444 100 100 2 Courtesy of Paul Emma

10. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Initial BPM and quad misalignments (w.r.t. linac axis) + Quadrupole positions positions o BPM offsets quad positions BPM offsets Now launch beam through undulator  Courtesy of Paul Emma 130 130

11. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Initial trajectory before any correction applied + Quadrupole positions positions o BPM readback e  trajectory e  trajectory fit used to smooth launch Note, all trajectory plots are w.r.t. linac axis (except last two) ‘real’ trajectory quad positions BPM readings Courtesy of Paul Emma 130 130

12. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Trajectory after initial rough steering (14.3 GeV) + Quadrupole positions positions o BPM readback e  trajectory e  trajectory Save as 1 st set of BPM readings Courtesy of Paul Emma 130 130

13. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Energy now reduced to 10 GeV + Quadrupole positions positions o BPM readback e  trajectory e  trajectory Save as 2 nd set of BPM readings Courtesy of Paul Emma 130 130

14. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Energy reduced again to 5 GeV + Quadrupole positions positions o BPM readback e  trajectory e  trajectory Save as 3 rd set of BPM readings Now analyze BPM data… Courtesy of Paul Emma 130 130

15. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Fitted quadrupole offsets Fit results Fit results Actual offsets Actual offsets similar plot for BPM offsets (not shown) Now correct quad and BPM positions… results differ by straight line… ‘real’ offsets fitted offsets use linear component of fitted offsets to re-adjust launch Courtesy of Paul Emma 130 130

16. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Absolute trajectory after 1 st pass of BBA (14.3 GeV) + Quadrupole positions positions o BPM readback e  trajectory e  trajectory Courtesy of Paul Emma 130 130

17. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Possible Absolute Trajectory LTU Beam is launched straight down undulator, with possible inconsequential kink at boundary dispersion generated is insignificant Now look at trajectory w.r.t. undulator axis  Courtesy of Paul Emma

18. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS After 1 st pass of BBA (now w.r.t. undulator line) + Quadrupole positions positions o BPM readback e  trajectory e  trajectory Now repeat procedure of energy changes two more times…  x  48  m  y  24  m Courtesy of Paul Emma 130 130

19. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS After 3 rd pass of BBA (14.3 GeV) + Quadrupole positions positions o BPM readback e  trajectory e  trajectory RON (FEL-code) simulation shows L sat increased by <1 gain-length; R. Dejus, N.Vinokurov   100°  x  1.7  m  y  2.7  m rms beam size:  30  m Courtesy of Paul Emma 130 130 Was confirmed with GENESIS simulation

20. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Trajectory After BBA Convergence Trajectory through undulator at 14 GeV after 3 passes of BBA procedure. 2-  m BPM resolution 50-  m initial BPM & quad offsets  1-  m mover backlash 14-7-4.5 GeV   204° 2-  m BPM resolution 50-  m initial BPM & quad offsets  1-  m mover backlash 14-7-4.5 GeV   204° + Quadrupole positions positions o BPM readback e  trajectory e  trajectory Courtesy of Paul Emma

21. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS BPM read-backs through undulator at 14 GeV (top) and 4.5 GeV (bottom) after rough steering, but before the BBA procedure. The energy is changed and the launch is re-established. Trajectory changes are expected at the 500-  m level. 500  m Verify BBA Convergence by noting orbit change from 14 to 4.5 GeV Before BBA procedure 14.1 GeV 4.5 GeV drop energy, reset launch, note change Courtesy of Paul Emma

22. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS BPM read-backs through undulator (note scale change) at 14 GeV (top) and 4.5 GeV (bottom) after three rounds of the BBA procedure, where trajectory changes with energy are expected at the 20-  m level. 20  m Verifying BBA Convergence After BBA procedure drop energy, reset launch, note change 14.1 GeV 4.5 GeV Courtesy of Paul Emma

23. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS 0.1-Gauss Earth’s field in x- direction – perfect system, quads on, no steering Courtesy of Paul Emma

24. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS 0.1-Gauss Earth’s field in x-direction – perfect system, after BBA Courtesy of Paul Emma

25. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS 0.1-Gauss Earth’s field in x-direction – standard errors, after BBA no Earth’s field – standard errors, after BBA Courtesy of Paul Emma

26. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS 0.2-Gauss Earth’s field in x-direction – standard errors, after BBA Courtesy of Paul Emma

27. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Summary BPMs resolve trajectory to ~1  m rms BPM readings ‘drift’ <1  m over 1-2 hr (temperature) Magnet movers are settable to within  1  m (or use coils) BPM readings are not sensitive to variable beam size, etc. Trajectory is stable enough to <20% of beam size (already demonstrated in FFTB) Earth magnetic field needs to be compensated BPMs resolve trajectory to ~1  m rms BPM readings ‘drift’ <1  m over 1-2 hr (temperature) Magnet movers are settable to within  1  m (or use coils) BPM readings are not sensitive to variable beam size, etc. Trajectory is stable enough to <20% of beam size (already demonstrated in FFTB) Earth magnetic field needs to be compensated Alignment can be achieved at adequate level using beam-based technique, given that… LCLS 4

28. BBA Related Issues Nuhn@slac.stanford.edu Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLS End of Presentation