1. Synchronization System for LUX John Staples, LBNL 26 July 2004

2. Deflecting cavities 3.9 GHz Dipole mode Accelerating linacs 1.3 GHz TESLA-like Linearizer cavities 3.9 GHz Longitudinal mode Requirements ● Synchronization between pump lasers and probe X-rays to better than 50 fsec ● LUX pulse rate of 10 kHz ● 100-150 meter footprint of facility ● Many end-stations, always in flux ● 1.3 and 3.9 GHz supercon cavities, photoinjector

3. Pulse Compression ● Start with 20-30 psec from photoinjector, compress to 2-3 psec in arcs ● Final compression to 50 fsec optically – asymmetric crystal on spatially chirped beam – 3.9 GHz SC transverse deflecting cavity ● Electron beam timing less critical, deflecting cavity timing very critical ● The end-station lasers must be synchronized to X-ray pulse Undulator Radiation from head electrons Radiation from tail electrons RF deflecting cavity Electron trajectory in 2 ps bunch ∆l∆l Input x-ray pulse >> diffraction limited size and natural beamsize Synchronous bunch Timing jitter results in position/angle jitter of compressed x-ray pulse Early bunch Late bunch Asymmetricall y cut crystal

4. Fundamental Approach to Timing ● Distribute accurate clock to all accelerator elements and end-station pump lasers ● Measure residual jitter of accelerator components, sum them up, and transmit to end-station lasers ● All elements ride on top of common-mode clock jitter ● Differential jitter between X-ray pulse and end-station lasers is reduced to 50 femtosecond regime ● Long term mechanical drifts also very important – 10 fsec is equivalent to a 3 micron motion – 1 meter of aluminum or SS grows 3 microns for 0.1 degree C temperature change, invar about 0.1 microns – transport systems geometric changes must also be monitored

6. Why Should This Work? ● Spectral density of timing jitter dominated by low- frequency phenomena – flicker and random walk of frequency and phase ● The coherence time of the significant spectral components is long (audio to sub-audio) ● The jitter components above this frequency range are usually below the noise floor of the monitors ● The integral over frequency space, the time jitter, is dominated by the low-frequency part of the spectrum.

7. Available Technology ● Stabilized fiber laser links show promise for transporting timing signals with femtosecond jitter over short distances ● ML lasers have been synchronized to 1 fsec relative jitter using electrical techniques, at 10-14 GHz ● Commodity fiber components are widely available – but the fiber must be actively stabilized ● Don't need a super-stable clock – Crystal oscillators useable, a Poseidon not necessary – Common-mode jitter of a picosecond acceptable

8. NLC Approach: Frisch et al. Transmit 357 MHz timing signal over 15 km About 1 degree X-band over moderate time scales (240 fs)

9. Timing jitter 0.58 fs (160 Hz BW) Timing jitter 1.75 fs (2 MHz BW) Top of cross-correlation curve Total time (1 s) Cross-Correlation Amplitude 30 fs 0 1 (two pulses maximally overlapped) (two pulses offset by ~ 1/2 pulse width) Ma et al., Phys. Rev. A 64, 021802(R) (2001) Sheldon et. al. Opt. Lett 27 312 (2002). Synchronization electrically of two independent 100 MHz ML lasers, at 100 MHz and 14 GHz. Measured by correlating in non-linear crystal. femtosecond timing attainable electrically. --Reported by David Jones

10. Hardware Approach ● Start with a good (<1 psec jitter) clock ● Distribute clock very accurately (<25 fsec) to all elements in accelerator and endstations – Use 1550 nm fiber optics components – Stabilize each fiber distribution link – Will try to stabilize based on modulation, not optical carrier – Fiber has much better bandwidth than coax cable ● Local loops stabilize elements within gain/bandwidth limitations, provide residual error signal ● Weighted sum of low-frequency error signal distributed over low-bandwidth digital link to TBCs ● End-station lasers follow low-bandwidth correctors

11. Example: Crab Cavity ● 3.9 GHz deflector ● include clock, microphonics ● I-Q LLRF system ● simulate residual noise after control loop is closed ● 350 watts klystron output power ● 12 fsec residual

12. Timing Distribution ● Require timing distribution system that provides differential-mode jitter of a few femtoseconds to all clients over the entire facility. ● Demonstrate a stabilized fiber network that can satisfy this requirement – fiber has wide bandwidth capability – use RF techniques to achive jitter stabilization – if inadequate, revert to interferometric techniques

15. Proof-of-Principle Experiment ● The key is low-jitter distribution of a 1 GHz clock ● Demonstration is constrained by budget ● 1 GHz crystal clock (Wenzel 100 MHz + multipliers) ● 1.5 mW 1550 nm DFB single-mode laser – EDFA increases power up to about 40 mW – Mach-Zehnder modulator, no chirp ● 100 m single-mode fiber, APC/PC connectors ● Low-noise (75K, 1 db NF) RF amplifiers ● Low-noise op-amps in LLRF circuits ● Piezo stabilization of fiber

17. Contributions to Jitter in POP ● LLRF system operational bandwidth rolloff at 1 kHz ● 1 dB noise figure of ZRL-1150LN amplifiers following photodiodes operating at -8 dBm adds about 9 fsec noise at 1 GHz over a 10 kHz bandwidth ● LMH6624 Low-noise op amps following phase detectors will add noise in the fsec range. – Still characterizing ZFM-4 mixers (phase detectors), but contribution may be significant ● Wenzel clock is measured to have a 1.0 psec jitter

18. Example: Noise contribution of op-amp following mixer Integrate noise current and voltage, including Johnson noise over working bandwidth. With a 10 kHz 2-pole LPF, the noise integrates to 0.2 uV, for a sub-femtosecond phase jitter.

19. Characterizing the Piezo Fiber Optic Phase Modulator Strong 18 kHz mechanical resonance, Q=139, measured interferometrically Shape and stabilize feedback loop around modulator Open-loop Bode Plot Nyquist Stability Plot

20. Present Status ● Have all the optical components – have measured and verified their specifications ● LLRF system designed, not yet constructed – all items are at hand, including PC boards ● Signal generators, spectrum analyzers, etc. are all acquired

22. Future Developments ● Will establish capabilities of a fiber stabilization system at 1 GHz. ● Move on to 10 GHz region ● Improve laser itself, if budget permits – Mode-locked – A gas-stabilized reference would be nice ● Look at interferometric techniques if necessary