Bunch length measurements 2007 11 16 Alan Fisher

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

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 (10 ps <-> 100 GHz), un-realistic for electron beam • Streak Camera Optical measurement using synchrotron radiation Commercial available, widely used ~ 2 ps resolution Hamamatsu C 5680 Dual-sweep, horizontal sweep ~ 10 Hz • 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

Basic equations Vc Synchrotron particle U 0 t TRF Trev Vc– RF voltage U 0 – energy loss per turn Φs – synchronous phase fs – synchronous frequency α – momentum compact factor frf – RF frequency E 0 – energy T 0 – revolution period σE/E – energy dispersion σz – bunch length

Interesting topics Vc U 0 Фs ΔE => ΔФs =>Δfs=> Δσt 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, σt 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 σt vs. Ib, => impedance; Potential well bunch lengthening, microwave instability threshold etc. Measure σt vs. Vc, Phase shift along the bunch train. Compare the bunch length difference for HER 90/60 deg lattice, etc.

Bunch lengthening example -- Zotter’s potential well distortion model for |Z/n| = 0. 2, 0. 25, 0. 35, 0. 4 Ohm; (sigma_t 0=20. 4 ps) o Measured bunch length for SPEAR 3 LE lattice 0. 4 Ohm 0. 35 Ohm 0. 3 Ohm 0. 25 Ohm 0. 2 Ohm |Z/n|eff, // ~ 0. 3 Ohm Microwave instability threshold ~ 15 m. A ?

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

Streak camera setup Power supply slit C 5680/M 5675/M 5679 ATT CCD BPF 450 nm Sync. In 30 nm BW Monitor out Trig. In Camera head GPIB DG 535 ÷ 4 f. RF C 5680 -21 S Main unit M 5675 Synchroscan sweep unit M 5679 Dual timebase extender unit C 4742 -95 -12 ER digital camera C 4547 Streak trigger unit ORCA-ER camera controller Power supply unit DG 535 Digital delay/pulse generator ~ 10 Hz C 4547 PC Ext Trig Camera controller ORCA-ER Serial cable Video cable frev Vertical sweep: f. RF/4 = 119 MHz Horizontal sweep: ~10 Hz, lock to the revolution frequency

Calibration Focus mode: 450 nm, 30 nm BW, slit=10 um, MCP gain= 34, we get focus point with FWHM = 4. 76 pixels 3. 3 ps in Time Range 2 Operate mode: Calibrate using 15 mm Etalon, n=1. 46, delta_t=2ΔL*n/c=146 ps; measure the echo distance for different time range, 119 MHz synchroscan delay changed to shift the streak in full range. 119 MHz delay Δt = 146 ps fixed 15 mm 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.

Calibration-cont. Time range 2: 0. 6844 ps/px; Time range 3: 1. 1882 ps/px; Time range 4: 1. 6650 ps/px;

Space charge and MCP noise ATT Filter 12 -bit AD 120 ms exposure time 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. Bunch length stays constant around 22 ps while the MCP gain changing

Test measurement @ LER Single sweep 2007 -07 -31 LER, I = 2600 m. A Time range 2 Slit 10 um MCP gain 14 Delay 76 Fit gauss RMS ~ 40. 29 ps ~ 12 mm (VRF = 4. 5 MV) Sweeping all 1722 bunches up and down for many turns: Frf = 476 MHz; Har. Num = 3492; Sweeping frequency = 119 MHz; Frev = 136. 3 KHz; Trev = 7. 336 us; CCD exposure time = 120 ms; About 16358 turns sweeping for one frame of picture Measurement @HER during the beam-beam machine study: I = 1290 m. A, 1530 m. A, 1730 m. A 1722 bunches, Vrf = 16. 45 MV RMS ~ 36 ps <-> ~ 10. 8 mm No significant bunch lengthening for these currents

Test measurement @ LER Dual sweep 2007 -07 -31 LER, I = 2600 m. A tail Time range 2 Slit 30 um MCP gain 45 head Delay 78 Horizontal scale 10 us 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. head tail Better to measure the bunch length at single bunch with various bunch current and RF voltage.

200 ns horizontal scale Near the bunch train gap, 1722 bunches with 24 bunches gap ~ 50 ps 8. 6 deg 4. 2 ns

Effect of phase shift along the bunch train 1722 bunches (max. 1746) ΔФ|head-tail = 8. 6 deg (50 ps) Head of the 1722 train Tail of the 1722 train 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 50 ps

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. 83 m) FSJ 1 -50 A jumper cable from BPM detector to 1 d. B attenuator, SMA-N • 1 d. B Att from Weinschel Aeroflex, fixed coaxial attenuators Model 1, N-N • HER 186 feet (~56. 69 m) LDF 2 -50 cable, N-N with N to SMA connectors in the panel at 641 • LER 113 feet (~ 34. 44 m) LDF 2 -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

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

Beam spectrum – single bunch 2 Spectrum analyzer can measure positive frequency power m=0 m>0 Ration of different revolution line in frequency domain tells the bunch distribution f(t) Sb(f) 0 frev 2 frev 3 frev 4 frev f 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

Beam spectrum - Multi-bunch (equal space M bunches) F(ω) Trev f(t) frev … t 0 Trev f F(ω) Trev/M Mfrev f(t) … t 0 f If every bucket is filled (same bunch current), only spectrum lines at n*frf appears

Beam spectrum - Multi-bunch (burst of M bunches) Trev TRF=Trev/h f(t) M bunches t Every bucket filled * rectangle function frev f. RF f 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.

Bunch length measurement from two frequency signal Detecting two frequency spectrum components (ω2 > ω1) , below cutoff freq. ω σt < 1 (giga-Hz range) ω1 ~ 2 f. RF, ω2 ~ 5 f. RF Much narrow frequency range (1 GHz ~ 3 GHz), 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 ~ 1 GHz, ω2 ~ 2. 5 GHz) Log(ω2 / ω1 ) Bunch length 0. 1 d. B 47 ps 0. 2 d. B 66 ps 0. 3 d. B 82 ps Specific electronics needed T. Ieiri, KEKB

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

Beam spectrum => measured spectrum 1. BPM button frequency response (HPF); C ~ 5 p. F, R = 50 Ohm, fc = 1/(2πRC) = 1/(2πτ) ~ 0. 64 GHz Consider the frequency > 1 GHz, flat response for BPM button 2. Cable and connector loss, especially the connector loss is hard to estimate, but should be small compared to long cable loss; (LPF) 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

Fitting spectrum example – multi-bunch Data for HER 90 deg lattice machine study, 2007 -08 -23 Filename: 020 1722 bunches I=615 m. A 10 k. Hz-13 GHz RBW 30 k. Hz VBW 100 k. Hz SWT 14. 5 sec Ref 0 d. Bm Att 30 d. B 238 MHz bunch frequency

Fitting spectrum example – single bunch Filename: 014 Single. Bunch I=2. 2 m. A 10 k. Hz – 9 GHz RBW 3 MHz VBW 10 MHz Many 136. 3 KHz revolution frequency harmonic lines inside SWT 100 ms Ref -20 d. Bm Att 10 d. B

Fit result Multi-bunch, 90 deg lattice has about 5 ps 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;

Compare 60 and 90 deg lattice - 1 HER 1722 bunches V_rf = 16. 5 MV Calculation for 0 -current bunch length* : HER 90 deg, sigma_z ~ 9. 2 mm, sigma_t ~ 30. 7 ps at low beam current; HER 60 deg, sigma_z ~ 10. 5 mm, sigma_t ~ 35 ps at low beam current Measurements agrees with theoretic calculation well. * http: //pepii-wienands 1. slac. stanford. edu: 8080/HER_Online_Docs/html/HERManual. html

Compare 60 and 90 deg lattice - 2 HER single bunch V_rf = 16. 5 MV, I ~ 1. 2 m. A 016. txt 90 deg lattice 027. txt 60 deg lattice 1. 2 m. A single bunch Sigma_t = 31. 3 ps Sigma_t = 35. 9 ps

Compare 60 and 90 deg lattice - 3 HER single bunch V_rf = 16. 5 MV, I ~ 2. 2 m. A 014. txt 90 deg lattice 028. txt 60 deg lattice 2. 2 m. A single bunch Sigma_t = 32. 8 ps Sigma_t = 38. 0 ps

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; σt vs. Ib, σt vs. Vc , 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 36 ps bunch length