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 domainBPM 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 CameraOptical measurement using synchrotron radiation

Commercial available, widely used

~ 2ps resolution Hamamatsu C5680

Dual-sweep, horizontal sweep ~ 10Hz

• Measure the spectrum => getting the bunch length informationFrequency domain

Get the spectrum envelop, offline data analysis

• Spectrum components amp. difference => bunch lengthTakao Ieiri @ KEKB

Frequency domain

real-time measurement

Basic equations

t

Vc

U0

TRF

Trev

Synchrotron particle

Vc– RF voltage

U0 – energy loss per turn

Φs – synchronous phase

fs – synchronous frequency

α – momentum compact factor

frf – RF frequency

E0 – energy

T0 – revolution period

σE/E – energy dispersion

σz – bunch length

srfc

s feV

U

2sin 01

scrfss TE

Vef cos2

00

Ef

c E

sz

2

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, 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.

srfc

fbwkID

thighcurrens feV

eVeVEU

2sin 01

Vc

U0

Фs

ΔE => ΔФs =>Δfs=> Δσt

c

cc

tV

VU

V

1

sincos

1

01

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

36

38

40

Bunch current (mA)

Bun

ch le

ngth

RM

S (

ps)

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

/3

0200

3

0

zs

b

z

z

z

z R

E

nZeI

0.2 Ohm

0.25 Ohm

0.3 Ohm

0.35 Ohm0.4 Ohm

Streak camera locations

e-

e+

LER:

Building 620

2nd floor, Synchrotron light dark room

HER:

Building 675

BPM signal and SA, Building 641

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

frev

~ 10Hz

÷4

fRF

TrigInSyncIn

BPF

450nm

30nm BW

ATT

Vertical sweep: fRF/4 = 119MHz

Horizontal sweep: ~10Hz, lock to the revolution frequency

Calibration

222focusrealmea

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=2ΔL*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.n

c

Lt

2

Calibration-cont.

Time range 4 calib

y = -0.0001x3 + 0.0024x2 - 0.0678x + 89.103

82

84

86

88

90

92

0 5 10 15 20 25 30 35

steps

Eta

lon

ec

ho

(p

x)

Calibration in time range 2

212

213

214

215

216

0 2 4 6 8 10

Frf/4 signal delay (steps)

Eta

lon

echo

(px

)

Calibration in time range 3

121

122

123

124

125

0 5 10 15 20

Frf/4 signal delay (steps)

Eta

lon

ech

o (

px)

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

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

Chi2-MCPGain(SPEAR3, 280bunches, I~95mA, OD=4, Fc=550nm,BW=10nm)

0

5

10

15

20

25

0 5 10 15 20 25 30

MCPGain

Ch

i^2

Bunch length stays constant around 22ps while the MCP gain changing

Filter12-bit AD

120ms exposure time

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 (VRF = 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

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.

200ns horizontal scale

Near the bunch train gap, 1722 bunches with 24 bunches gap

4.2ns

~ 50ps 8.6 deg

Effect of phase shift along the bunch train

Sigma_1722 vs. Sigma_bunch(50ps linear phase shift from head to tail of

1722 bunch train)

37.0038.0039.0040.0041.0042.0043.00

34 35 36 37 38 39 40 41

Sigma_bunch (ps)

Sig

ma

_1

72

2 (

ps)

-2 -1 0 1 2

x 10-10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

time (ps)

amp

(au.

), b

unch

Tot

al/1

000

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 train Tail of the 1722 train

3548.22ln22FWHM

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

Beam spectrum – single bunch 1

n

revbb nTtfqNti

m

tjmmb

reveCti

2/revT

2/revT

revjm

rev

bm def

T

qNC

…

f(t)Trev

t f0

…

frev

rev

b0 T

qNC C0 is DC beam current

Negative and positive components has same amplitude

Beam spectrum – single bunch 2

1mrev

2m

2

rev

bb mffCR20R

T

qNfS

Spectrum analyzer can measure positive frequency power

2

0CR

21CR2 2

2CR2 23CR2 2

4CR2

frev 2frev 3frev 4frev f

Sb(f)

0

2

2

0

2 mm

rev

b

CRP

T

qNRP

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)

Beam spectrum - Multi-bunch (equal space M bunches)

f(t)

Trev

0

…

frevF(ω)

t f

f(t)

Trev

0

…

Mfrev

F(ω)

t f

Trev/M

If every bucket is filled (same bunch current), only spectrum lines at n*frf appears

Beam spectrum - Multi-bunch (burst of M bunches)

m

tMjmm

reveCtA )(

f(t)

Trev

t

TRF=Trev/h

tBtAtib

2/

2/

rev

rev

rev

T

T

jmh

rev

bm def

T

qNhC

Every bucket filled * rectangle function

trevjn

n

eh

nMSa

h

MtB

m

tnmhrevj

nmb e

h

nMSaC

h

Mti

M bunches

0 5 10 15 20 25 30 35 40 45 50

Revolution Harmonicf

frev

fRF

x

xxSa

sin

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

2

121

22

ln2

F

Ft

Detecting two frequency spectrum components (ω2 > ω1) , below cutoff freq.

ω σt < 1 (giga-Hz range)

ω1 ~ 2fRF, ω2 ~ 5fRF

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

0.2dB 66ps

0.3dB 82ps

Specific electronics needed

T. Ieiri, KEKB

Equations- fitting from beam spectrum

2

2

2exp

2 tt

tqti

Gaussian distribution

q – particle charges in the bunch

σt – RMS bunch length

2exp

22exp

2

22

2

2tqq

I

2lg20

4lg10

2lg204lg10

lg20

22

2

222

qc

ea

cfa

qfe

IP

t

t

Shorter bunch -> wider spectrum

From measured power spectrum

-> fitting coefficient a, c

-> bunch length σt 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.

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

LDF2-50 Att vs. Freq (100 ft)

0

5

10

15

20

0 2000 4000 6000 8000 10000 12000 14000

Freq (MHz)

Att

(d

B)

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, fc = 1/(2πRC) = 1/(2πτ) ~ 0.64 GHz

Consider the frequency > 1GHz, flat response for BPM button

Fitting spectrum example – multi-bunch

0 2 4 6 8 10 12 14

x 109

-70

-60

-50

-40

-30

-20

-10

0

freq (Hz)

dB

m

SpectrumFit,HER 90deg,Multi-Bunch 615mA

RawData

CorrectedDataFittedCurveFilename: 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

Fitting spectrum example – single bunch

0 1 2 3 4 5 6 7 8 9

x 109

-70

-65

-60

-55

-50

-45

-40

-35

-30

freq (Hz)

dB

m

SpectrumFit,HER 90deg,SingleBunch 2.2mA

RawData

CorrectedDataFittedCurve 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

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;

Compare 60 and 90 deg lattice - 1

90 deg HER bunch length vs. current

30.5

31

31.5

32

32.5

33

0.00 0.10 0.20 0.30 0.40 0.50

mA

ps

60 deg HER bunch length vs. current

37.237.337.437.537.637.737.837.9

0 0.1 0.2 0.3 0.4 0.5

mA

ps

HER 1722 bunches

V_rf = 16.5MV

* http://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.

Compare 60 and 90 deg lattice - 2

HER single bunch V_rf = 16.5MV, I ~ 1.2 mA

0 1 2 3 4 5 6 7 8 9

x 109

-70

-65

-60

-55

-50

-45

-40

-35

-30

freq (Hz)

dB

m

SpectrumFit,HER 90deg,SingleBunch 1.2mA

RawData

CorrectedDataFittedCurve

0 1 2 3 4 5 6 7 8 9

x 109

-70

-65

-60

-55

-50

-45

-40

-35

-30

freq (Hz)

dB

m

SpectrumFit,HER 60deg,SingleBunch 1.2mA

RawData

CorrectedDataFittedCurve

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

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

0 1 2 3 4 5 6 7 8 9

x 109

-70

-65

-60

-55

-50

-45

-40

-35

-30

freq (Hz)

dB

m

SpectrumFit,HER 90deg,SingleBunch 2.2mA

RawData

CorrectedDataFittedCurve

0 1 2 3 4 5 6 7 8 9

x 109

-70

-65

-60

-55

-50

-45

-40

-35

-30

freq (Hz)

dB

m

SpectrumFit,HER 60deg,SingleBunch 2.2mA

RawData

CorrectedDataFittedCurve

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 36ps bunch length