1. Bunch length measurements 2007-11-16 Alan Fisher, Weixing Cheng PEP-II MAC Review 2007

2. Bunch length measurement methods (mm to several tens of mm RMS bunch length) Direct sample by oscilloscope in time domain BPM button electrode function like HPF, but cable loss is a big problem Very high sampling rate / wideband oscilloscope (10ps 100 GHz), un-realistic for electron beam Streak Camera Optical measurement using synchrotron radiation Commercial available, widely used ~ 2ps resolution Hamamatsu C5680 Dual-sweep, horizontal sweep ~ 10Hz Measure the spectrum => getting the bunch length information Frequency domain Get the spectrum envelop, offline data analysis Spectrum components amp. difference => bunch length Takao Ieiri @ KEKB Frequency domain real-time measurement

3. Basic equations t VcVc U0U0 T RF T rev Synchrotron particle V c – RF voltage U 0 – energy loss per turn Φ s – synchronous phase f s – synchronous frequency α – momentum compact factor f rf – RF frequency E 0 – energy T 0 – revolution period σ E /E – energy dispersion σ z – bunch length

4. Interesting topics Besides synchronous radiation, there may have other effect to change the energy loss per turn: –As the beam current increase, energy loss must include the wakefield, synchrotron phase shift left, fs getting smaller, σ t getting longer. Single bunch wide band wakefield change the distribution. –Bunch feedback add another term to the energy loss per turn. –Effective cavity voltage difference along the bunch train. Measure σ t vs. I b, => impedance; Potential well bunch lengthening, microwave instability threshold etc. Measure σ t vs. V c, Phase shift along the bunch train. Compare the bunch length difference for HER 90/60 deg lattice, etc. VcVc U0U0 ФsФs ΔE => ΔФ s => Δf s => Δσ t

5. Bunch lengthening example -- Zotter’s potential well distortion model for |Z/n| = 0.2, 0.25, 0.3, 0.35, 0.4 Ohm; (sigma_t0=20.4ps) o Measured bunch length for SPEAR3 LE lattice |Z/n| eff,// ~ 0.3 Ohm Microwave instability threshold ~ 15mA ? 0.2 Ohm 0.25 Ohm 0.3 Ohm 0.35 Ohm 0.4 Ohm

6. Streak camera locations e-e- e+e+ LER: Building 620 2 nd floor, Synchrotron light dark room HER: Building 675 BPM signal and SA, Building 641

7. Streak camera setup slit C5680-21S Main unit M5675 Synchroscan sweep unit M5679 Dual timebase extender unit C4742-95-12ER digital camera C4547 Streak trigger unit ORCA-ER camera controller Power supply unit DG535 Digital delay/pulse generator C5680/M5675/M5679 CCD Camera controller ORCA-ER PC Monitor out Ext Trig Camera head Serial cable Video cable GPIB Power supply DG535 C4547 f rev ~ 10Hz ÷4÷4 f RF TrigIn SyncIn BPF 450nm 30nm BW ATT Vertical sweep: f RF /4 = 119MHz Horizontal sweep: ~10Hz, lock to the revolution frequency

8. Calibration Focus mode: 450nm, 30nm BW, slit=10um, MCP gain= 34, we get focus point with FWHM = 4.76 pixels  3.3ps in Time Range 2 Operate mode: Calibrate using 15mm Etalon, n=1.46, delta_t=2 ΔL*n/c=146ps; measure the echo distance for different time range, 119MHz synchroscan delay changed to shift the streak in full range. Δt = 146ps fixed 119MHz delay 15mm Etalon We can believe the factory calibration result; For time range 2 and 3, it’s almost linear in full range; Near the central part has good linearity.

9. Calibration-cont. Time range 2: 0.6844 ps/px; Time range 3: 1.1882 ps/px; Time range 4: 1.6650 ps/px;

10. Space charge and MCP noise e-e- Too much photons into the cathode produce high intensity e -, which may have space charge effect to blow up => increase the measured bunch length Too much MCP gain increase the noise Add more attenuators (filters) to reduce the photons, reasonable MCP gain to get a clear spot on the screen. ATT Bunch length stays constant around 22ps while the MCP gain changing Filter 12-bit AD 120ms exposure time

11. Test measurement @ LER 2007-07-31 LER, I = 2600mA Time range 2 Slit 10 um MCP gain 14 Delay 76 Fit gauss RMS ~ 40.29 ps ~ 12 mm (V RF = 4.5MV) Single sweep Sweeping all 1722 bunches up and down for many turns: Frf = 476 MHz; HarNum = 3492; Sweeping frequency = 119 MHz; Frev = 136.3 KHz; Trev = 7.336 us; CCD exposure time = 120ms; About 16358 turns sweeping for one frame of picture Measurement @HER during the beam-beam machine study: I = 1290mA, 1530mA, 1730mA 1722 bunches, Vrf = 16.45MV RMS ~ 36ps ~ 10.8 mm No significant bunch lengthening for these currents

12. Test measurement @ LER 2007-07-31 LER, I = 2600mA Time range 2 Slit 30 um MCP gain 45 Delay 78 Horizontal scale 10us Dual sweep head tail head tail From the dual sweep, there has synchronous phase shift along the bunch train, at the beginning of bunch train, the synchrotron phase is larger due to higher effective cavity voltage. Fitting gauss bunch length in single sweep is not accurate since there has such kind of synchrotron phase shift. Better to measure the bunch length at single bunch with various bunch current and RF voltage.

13. 200ns horizontal scale Near the bunch train gap, 1722 bunches with 24 bunches gap 4.2ns ~ 50ps  8.6 deg

14. Effect of phase shift along the bunch train 50ps 1722 bunches (max. 1746) ΔФ| head-tail = 8.6deg (50ps) Linear phase change along the bunch train Same bunch length and current for these 1722 bunches Sum effect of all the bunches is near to gauss distribution Head of the 1722 trainTail of the 1722 train

15. BPM Spectrum => Bunch length One set of HER/LER BPM buttons signal feeds to Building 641, spectrum analyzer available from: 9 KHz – 13.6 GHz 6 feet (~1.83m) FSJ1-50A jumper cable from BPM detector to 1dB attenuator, SMA-N 1 dB Att from Weinschel Aeroflex, fixed coaxial attenuators Model 1, N-N HER 186 feet (~56.69m) LDF2-50 cable, N-N with N to SMA connectors in the panel at 641 LER 113 feet (~ 34.44m) LDF2-50 cable, N-N with N to SMA connectors in the panel at 641 Beam spectrum (single bunch, multi-bunch); => FFT -1 bunch length Button-type BPM frequency response, HPF; Cable loss and other components attenuations; SA measurement setting (SNR, noise floor, resolution etc.) Real measured spectrum

16. Beam spectrum – single bunch 1 … f(t) T rev t f 0 … f rev C 0 is DC beam current Negative and positive components has same amplitude

17. Beam spectrum – single bunch 2 Spectrum analyzer can measure positive frequency power f rev 2f rev 3f rev 4f rev f S b (f) 0 m = 0 m > 0 Very short bunch, delta function  constant in frequency domain Coast beam, constant in time domain  delta function in freq. domain, only DC components Gaussian distribution bunch  gauss envelop in freq. domain, shorter bunch -> wider spectrum Ration of different revolution line in frequency domain tells the bunch distribution f(t)

18. Beam spectrum - Multi-bunch (equal space M bunches) f(t) T rev 0 … f rev F(ω) t f f(t) T rev 0 … Mf rev F(ω) t f T rev /M If every bucket is filled (same bunch current), only spectrum lines at n*f rf appears

19. Beam spectrum - Multi-bunch (burst of M bunches) f(t) T rev t T RF =T rev /h Every bucket filled * rectangle function M bunches f f rev f RF PEP-II now: 3492 harmonic number; (1746 bunches max.) 1722 bunches, every two bucket fill; 24 bunches gap, about 1.4% gap; BIC controls even fill.

20. Bunch length measurement from two frequency signal Detecting two frequency spectrum components (ω 2 > ω 1 ), below cutoff freq. ω σ t < 1 (giga-Hz range) ω 1 ~ 2f RF, ω 2 ~ 5f RF Much narrow frequency range (1GHz ~ 3GHz), cable loss and BPM button frequency response can be treat as constant. Frequency components selected to be lower than beam pipe cutoff frequency, avoid wakefield. Spectrum amp. difference vs. bunch length: (ω1 ~ 1GHz, ω2 ~ 2.5GHz) Log(ω2 / ω1 )Bunch length 0.1dB 47ps 0.2dB66ps 0.3dB82ps Specific electronics needed T. Ieiri, KEKB

21. Equations- fitting from beam spectrum Gaussian distribution q – particle charges in the bunch σ t – RMS bunch length Shorter bunch -> wider spectrum From measured power spectrum -> fitting coefficient a, c -> bunch length σ t and bunch charge q Suitable for Gauss bunch only; BPM wide-band spectrum, neglect low freq. (>1GHz); Wide-band spectrum analyzer (~ 10GHz) Cable loss included; Other components loss such as attenuator, connectors etc. not included; Fitting try to neglect the spectrum spikes/DIPs above cutoff frequency.

22. Beam spectrum => measured spectrum 3. Above vacuum chamber cutoff frequency, spikes and DIPs from HOM => fitting can minimize the influence to the bunch length measurement How accurate for the fitted bunch length? Check with streak camera result 1. BPM button frequency response (HPF); 2. Cable and connector loss, especially the connector loss is hard to estimate, but should be small compared to long cable loss; (LPF) C ~ 5pF, R = 50 Ohm, f c = 1/(2πRC) = 1/(2πτ) ~ 0.64 GHz Consider the frequency > 1GHz, flat response for BPM button

23. Fitting spectrum example – multi-bunch Filename: 020 1722 bunches I=615mA 10kHz-13GHz RBW 30 kHz VBW 100 kHz SWT 14.5 sec Ref 0 dBm Att 30dB Data for HER 90 deg lattice machine study, 2007-08-23 238MHz bunch frequency

24. Fitting spectrum example – single bunch Filename: 014 SingleBunch I=2.2mA 10kHz – 9GHz RBW 3 MHz VBW 10 MHz SWT 100 ms Ref -20 dBm Att 10dB Many 136.3 KHz revolution frequency harmonic lines inside

25. Fit result Multi-bunch, 90 deg lattice has about 5ps shorter bunches; ~ 15% shorter Spectrum analyzer settings influence the fitting result, for the same setting, 90 deg lattice has shorter bunch length in single bunch mode;

26. Compare 60 and 90 deg lattice - 1 HER 1722 bunches V_rf = 16.5MV * http://pepii-wienands1.slac.stanford.edu:8080/HER_Online_Docs/html/HERManual.htmlhttp://pepii-wienands1.slac.stanford.edu:8080/HER_Online_Docs/html/HERManual.html Calculation for 0-current bunch length* : HER 90 deg, sigma_z ~ 9.2mm, sigma_t ~ 30.7 ps at low beam current; HER 60 deg, sigma_z ~ 10.5mm, sigma_t ~ 35 ps at low beam current Measurements agrees with the theoretic calculation well.

27. Compare 60 and 90 deg lattice - 2 HER single bunch V_rf = 16.5MV, I ~ 1.2 mA 016.txt 90 deg lattice 1.2 mA single bunch Sigma_t = 31.3ps 027.txt 60 deg lattice 1.2 mA single bunch Sigma_t = 35.9ps

28. Compare 60 and 90 deg lattice - 3 HER single bunch V_rf = 16.5MV, I ~ 2.2mA 014.txt 90 deg lattice 2.2 mA single bunch Sigma_t = 32.8ps 028.txt 60 deg lattice 2.2 mA single bunch Sigma_t = 38.0ps

29. Summary Streak camera has been well configured, ready for more bunch length measurement. –Setup at LER/HER and tested in multi-bunch operation; –Calibrated using Etalon; –Know well the behavior of streak camera; –σ t vs. I b, σ t vs. V c, phase shift; –HER 90/60 deg bunch length; –Frequently measurement of bunch length since the machine is always improving. –Others Bunch length fitting from the BPM button spectrum (S. Novokhatski) –Data for the HER 90 deg lattice MD shows reasonable result; ~ 15% shorter –The method suit for Gauss bunch only; –Single bunch signal is small, need to program the SA to get every revolution harmonic spectrum (high resolution); –Might be necessary to consider other components attenuation; –Easy to switch between LER/HER. Difficult to get rid the synchronous phase difference in the bunch train (in multi-bunch mode), that means measured value in multi-bunch mode is not correct. => Gate, bunch-by-bunch synchronous phase monitor –Simple calculation for 1722 bunches phase shift effect, 8% increase for 36ps bunch length

30. Backup

31. Principle of streak camera ~ 10Hz Vertical sweep: f RF /4 = 119MHz Horizontal sweep: ~10Hz, lock to the revolution frequency C4547 123456789 1 – slit; 2 – focus lens; 3 – photo cathode; 4 – accel. Mesh; 5 – vertical sweep; 6 – horizontal sweep; 7 – MCP; 8 – phosphor screen; 9 – CCD camera

32. Calibration-idea. 119MHz C4547 DG535 f rev 10Hz C5680/M5675/M5679 ΔLΔL Make sure the 119MHz has small jitter compare to the RF frequency. ΔL=1.5mm/step => Δt = 10ps/step 800ps/120mm adjustable range Delta_t (ps) Position (px)

33. Determine the head and tail 119MHz vertical sweep~10Hz horizontal sweep t 476MHz RF 119MHz Ver. Sweep head tail head tail While V rf , φ s , two spot getting closer to the center; 119MHz delay , spots getting away from center 119MHz Ver. Sweep head tail head While V rf , φ s , two spot getting away from the center; 119MHz delay , spots getting closer to the center

34. Program the Spectrum Analyzer Improve the SNR with narrow SPAN; (1MHz for 1722 bunches, 100KHz for single bunch) Set the Fcenter = n * Frev, increase the center frequency by m*Frev SA variablesMulti-bunchesSingle bunch Center frequencyn* Frf/2n* Frf/4 SPAN1 MHz100 KHz Fc stepFrf/2 = 238MHzFrf/4 = 119MHz Measurement range1GHz – 10GHz Total point for fitting~ 40 point~ 80 point Many other information with the narrow SPAN trace data Fcenter = 2 Frf SPAN = 50 kHz 90 deg lattice 1722 bunches I ~ 203 mA Fs ~ 5.7 kHz