Bunch length measurements
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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
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