LCLS Longitudinal Feedback and Stability Requirements P Emma
LCLS Longitudinal Feedback and Stability Requirements P. Emma LLRF Review November 23, 2005 LCLS 23 Nov. 2005 LLRF Meeting 1 P. Emma@SLAC. Stanford. edu
Critical LCLS Accelerator Parameters Final energy 13. 6 Ge. V (stable to 0. 1%) Final peak current 3. 4 k. A (stable to 12%) Transverse emittance 1. 2 mm (stable to 5%) Final energy spread 10 -4 (stable to 10%) Bunch arrival time (stable to 150 fs) (stability specifications quoted as rms) 23 Nov. 2005 LLRF Meeting 2 P. Emma@SLAC. Stanford. edu
FEL Power Sensitivity to e- Beam 12% DIpk/Ipk 20% DP/P 0. 1% DE/E 0. 2% Dlr/lr 23 Nov. 2005 LLRF Meeting 3 P. Emma@SLAC. Stanford. edu
Electron Bunch Compression DE/E z i ‘chirp’ z z z i Dz = R 56 V = V 0 sin(kz) RF Accelerating Voltage 23 Nov. 2005 LLRF Meeting Path-Length Energy. Dependent Beamline 4 undercompressi on P. Emma@SLAC. Stanford. edu z
Compression Stability Df z RF phase jitter becomes bunch length jitter… Compression factor: 23 Nov. 2005 LLRF Meeting 5 P. Emma@SLAC. Stanford. edu
Phase and Bunch Length Stability Example (not LCLS) 23 Nov. 2005 LLRF Meeting 6 P. Emma@SLAC. Stanford. edu
Machine Schematic with Parameters 6 Me. V z 0. 83 mm 0. 05 % 250 Me. V 4. 30 Ge. V z 0. 19 mm z 0. 022 mm 1. 6 % 0. 71 % Linac-X L =0. 6 m rf= -160 Linac-1 Linac-2 Linac-3 L 9 m L 330 m L 550 m rf -25° rf -41° rf 0° 135 Me. V z 0. 83 mm 0. 10 % rf gun m 32 Linac-0 L =6 m 21 -1 b 21 -1 d . . . existing linac DL 1 L 12 m R 56 0 3 klystrons X BC 1 L 6 m R 56 -39 mm 21 -3 b 24 -6 d 1 X-klys. 1 klystron 26 klystrons SLAC linac tunnel 23 Nov. 2005 LLRF Meeting BC 2 L 22 m R 56 -25 mm 7 13. 6 Ge. V z 0. 022 mm 0. 01 % undulator L =130 m 25 -1 a 30 -8 c 45 klystrons LTU L =275 m R 56 0 research yard P. Emma@SLAC. Stanford. edu
Correlated or Uncorrelated Errors? Suppose the mean RF phase of all 26 Linac-2 klystrons changes by: 0. 21° | Ipk/Ipk| 12% This may arise statistically with 26 random uncorrelated phase errors with rms spread of: f 2 1/2 = 0. 21° 261/2 = 1. 07°, or with 26 identical phase errors. Since we don’t fully understand the correlations, we choose the conservative (smallest) tolerance of 0. 21° rms/klys. and then reduce this by ~ N, where N (=12) is the number of major error sources. 23 Nov. 2005 LLRF Meeting 8 P. Emma@SLAC. Stanford. edu
Phase, Amplitude, and Charge Sensitivities parameter | E/E 0| = 0. 1% Dti 1. 6 D Q/ Q 0 46 3. 5 Df 0 DV 0 /V 0 0. 32 Df 1 DV 1 /V 1 0. 29 5. 5 Df. X DVX/VX 2. 0 0. 54 Df 2 DV 2 /V 2 1. 1 0. 35 Df 3 DV 3 /V 3 0. 15 23 Nov. 2005 LLRF Meeting | I/I 0| = 12% 4. 4 5. 2 0. 65 0. 24 0. 17 0. 25 1. 4 1. 2 0. 21 1. 0 24. 8 5. 7 9 | tf| = 100 fs 1. 5 24 5. 9 0. 95 1. 0 0. 78 7. 6 6. 3 0. 084 0. 13 15 8. 6 unit psec % deg-S % deg-X % deg-S % P. Emma@SLAC. Stanford. edu
Longitudinal Fast-Jitter Tolerance Budget tolerances are rms values laser timing (w. r. t. RF) laser energy 0. 50 mean phase of 2 klys. 1 X-klys. mean phase of 26 klys. mean phase of 45 klys. mean amp. of 2 klys. 1 X-klys. mean amp. of 26 klys. mean amp. of 45 klys. 23 Nov. 2005 LLRF Meeting X- X-band 10 P. Emma@SLAC. Stanford. edu
Jitter Simulations (Particle Tracking) 0. 09% 0. 004% Lg 96 fs Pout 10% 23 Nov. 2005 LLRF Meeting 11 P. Emma@SLAC. Stanford. edu
LCLS Longitudinal Beam-Based Feedback (stabilizes beam for jitter frequencies < 10 Hz @ 120 -Hz rep-rate) V 0 gun z 1 0 L 0 1 1 V 1 L 1 DL 1 BPM 2 V 2 z 2 2 L 2 X BC 1 3 V 3 L 3 BC 2 DL 2 CSR detector J. Wu, et al. , PAC’ 05, May 16 -20, 2005, Knoxville, TN. 23 Nov. 2005 LLRF Meeting 12 P. Emma@SLAC. Stanford. edu
CSR Relative Bunch Length Monitor Red curve: Gaussian Black curve: Uniform Blue curve: ‘Real’ J. Wu, et al. , PAC’ 05, May 16 -20, 2005, Knoxville, TN. 23 Nov. 2005 LLRF Meeting 13 P. Emma@SLAC. Stanford. edu
LCLS Feedback Performance (use CSR P/P) feedback off DIpk/Ipk 0 (%) feedback on J. Wu (undulator entrance) 23 Nov. 2005 LLRF Meeting 14 P. Emma@SLAC. Stanford. edu
Feedback System Bode Plot at 120 Hz J. Wu Define fast-jitter as variations faster than 2 seconds Slow drift occurs on time-scales > 2 seconds (to 24+ hr) 23 Nov. 2005 LLRF Meeting 15 P. Emma@SLAC. Stanford. edu
Slow Drift Tolerance Limits (Top 4 rows for De/e < 5%, bottom 4 limited by feedback dynamic range) Gun-Laser Timing Bunch Charge Gun RF Phase Gun Relative Voltage L 0, 1, X, 2, 3 RF Phase (approx. ) L 0, 1, X, 2, 3 RF Voltage (approx. ) 2. 4* 3. 2 2. 3 0. 6 5 5 deg-S % (Tolerances are peak values, not rms) * for synchronization, this tolerance might be set to 1 ps (without arrival-time measurement) 23 Nov. 2005 LLRF Meeting 16 P. Emma@SLAC. Stanford. edu
x (deg) Compensate X-band Phase Step Error. . . x-band phase LX phase error = 5 o final energy final peak current L 1 adjustment: phase +2. 1 o, voltage -2. 1% final arrival time J. Wu 23 Nov. 2005 LLRF Meeting 17 P. Emma@SLAC. Stanford. edu
Gun Timing Jitter and Energy Feedback E E Dtf E > E 0 E = E 0 Dt 0 without energy feedback 23 Nov. 2005 LLRF Meeting t 18 Dt 0 E = E 0 Dtf = Dt 0 with energy feedback P. Emma@SLAC. Stanford. edu t
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