Online Bunch Length Monitoring for Storage Ring
using a Fast Photodiode12th International Beam Instrumentation Conference
Sep. 13, 2023
Garam Hahn, Woojin Song, Changbum Kim, Dotae Kim (PAL,Pohang), Ji-Gwang Hwang (Gangneung-Wonju Natl. Univ.)

Contents• Introduction• Experimental Setup• Analysis Method• Result• SummaryPLS-II @ Pohang Accelerator Laboratory

PLS-IIPAL-XFEL

PLS-II Parameter
Beam Energy

3 GeV

Beam Current
Circumference

400 mA
281.82 m

RF Frequency

499.97RMS Bunch Length
Sep. 13, 2023

Value UnitMHz

21.3 ps•

PLS-II operates a hybrid filling pattern
to support pump-probe experiments.

•Online information of bunch lengths and fillpattern could be worth for users

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

3/21

PLS-II @ Pohang Accelerator Laboratory
470 buckets

PLS-II

2 ns
Camshaft
Bunch

PAL-XFEL

Bunch Train,
330 bunches total

PLS-II Parameter
Beam Energy

3 GeV

Beam Current
Circumference

400 mA
281.82 m

RF Frequency

499.97RMS Bunch Length
Sep. 13, 2023

Value UnitMHz

21.3 ps•

PLS-II operates a hybrid filling patternto support pump-probe experiments.

•Online information of bunch lengths and fillpattern could be worth for users

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

3/21

Longitudinal Beam Diagnostics
Bunch Length

Streak Camera• High temporal resolution(< RMS 1 ps)• Slow acquisition rate
• Incompatible for turn-by-turn me
asurements

Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

4/21

Longitudinal Beam Diagnostics
Bunch LengthFill-Pattern

Streak Camera• High temporal resolution(< RMS 1 ps)• Slow acquisition rate
• Incompatible for turn-by-turn measurements

Sep. 13, 2023

BPM pick-up / FCT• Fill-pattern monitoring• Limited bandwidth• Moderate accuracy• Non-linear behavior causes
an intolerable error
Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

4/21

Longitudinal Beam Diagnostics
Bunch Length
Bunch Length + Fill-PatternFill-Pattern

Fast Photodiode• Intermediate resolution (~2 ps)• Bunch length and fill-patternreal-time measurement

Streak Camera• High temporal resolution(< RMS 1 ps)• Slow acquisition rate
• Incompatible for turn-by-turn measurements

Sep. 13, 2023

BPM pick-up / FCT• Fill-pattern monitoring• Limited bandwidth• Moderate accuracy• Non-linear behavior causes
an intolerable error
Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

4/21

Previous studies• Australian Synchrotron [1]• Successful online fill-pattern (FP) measurement• We could not find analog input bandwidth informationof bias tee, digitizer or cables.
 We use similar experimental set-up
BUT chose all devices’ ABW near 15 GHz for bunch length detection.

[1] D. J. Peake et al., “Measurement of the real time fill-pattern at the Australian Synchrotron”, NIM. A. (2008)

Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

5/21

Previous studies• Australian Synchrotron [1]• Successful online fill-pattern (FP) measurement• We could not find analog input bandwidth informationof bias tee, digitizer or cables.
 We use similar experimental set-up
BUT chose all devices’ ABW near 15 GHz for bunch length detection.

• Bessy-II, HZB [2]• Successful online bunch length, fill-pattern, and phase measurement.
• Bunch length data fit result seemed valid locally.
We developed a new analysis method
to handle nonlinear frequency response of the system.
[1] D. J. Peake et al., “Measurement of the real time fill-pattern at the Australian Synchrotron”, NIM. A. (2008)[2] J. Hwang, Bunch length measurement by using a fast photodiode, Private Discussion, (2019)
Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

5/21

MSM Photodiode
Incident Light• Metal-Semiconductor-Metal Photodiode
SchottkyBarrier ΦB• Metal-semiconductor Junction
 Schottky diode’s potential barrier is ruled byEC- --Metal

the metal and silicon work functions.

MSM photodiode with wedge-comb
structure has fast and strong response.

Sep. 13, 2023

-e-h pairHole + +P. R. Berger, 1996

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

ElectronSi

EV Metal

6/21

MSM PhotodiodeIncident Light• Metal-Semiconductor-Metal Photodiode
SchottkyBarrier ΦB• Metal-semiconductor Junction
 Schottky diode’s potential barrier is ruled by-EC- --Metal

the metal and silicon work functions.

MSM photodiode with wedge-comb
structure has fast and strong response.

e-h pairHole + +P. R. Berger, 1996

ElectronSi

EV Metal• Hamamatsu G4176-03(GaAs MSM photodiode)• Rise time ~ 35 ps @ 7 V bias
• Active area : 200 µm2• Dark current : 100 pA @ Ta = 25 °C
Rise time vs. Applied Voltage
Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

Spectral Response

6/21Experimental Setup (1/2)
Visible part (600~900 nm 𝝀𝝀) of synchrotron radiation –Visible Light Beam Diagnostic Hutch (BL1B)
lens + B.P. filter + Polar. filter

lens + slits

Photodiode – Bias Tee – Amp – Cable – Digitizer – PC
Interferometer

StreakCameraorPhotodiode𝝀𝝀 < 600 nm
𝝀𝝀 > 600 nm

Capacitor

attenuator + iris + lensDC 8 VAmp

1 MHz Revolution Trigger

LightMSM Photodiode+ Bias Tee

CableAnalysis Machine

32 coreAnalysis Machine

opticaltablecontrol network• To maximize gain and efficiency, dichroic mirror was used.
• higher than 600 nm for photodiode• lower for interferometer• Beam splitter was used for simultaneous measurement withphotodiode and streak camera.
• Multi-channel DC P/S 8 - 12V was installed to feed the voltage to thephotodiode (connected at the bias tee) and the amplifier.

Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

7/21

Experimental Setup (2/2)

Component

Model

Analog Bandwidth (-3 dB)

Etc.

PhotodiodeG4176-03, Hamamatsu~ 10.4 GHz *No Freq. Response Info.

Bias Tee5541A, Picosecond(Tektronix)

26 GHzAmplifier

ZX60-14012L-1+, Mini-Circuits

14 GHzCable

Lab-made26.5 GHz

Digitizer

Picoscope9404-16, Pico Technology
DPO71304SX, Tektronix

16 GHz13 GHzSep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

2 TS/s sequential, 0.5 GS/s real time sample
50 GS/s real time sample

8/21

Experimental Setup (2/2)

20 ps (rms)Component

Model

Analog Bandwidth (-3 dB)

Etc.

PhotodiodeG4176-03, Hamamatsu~ 10.4 GHz *No Freq. Response Info.

Bias Tee5541A, Picosecond(Tektronix)

26 GHzAmplifier

ZX60-14012L-1+, Mini-Circuits

14 GHzCable

Lab-made26.5 GHz

Digitizer

Picoscope9404-16, Pico Technology
DPO71304SX, Tektronix

16 GHz13 GHzSep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

2 TS/s sequential, 0.5 GS/s real time sample
50 GS/s real time sample

8/21

Analytic Gaussian Deconvolution (AGD)
Input signal
Output signal𝑥𝑥(𝑡𝑡) Impulse response y(𝑡𝑡)Vℎ(𝑡𝑡)

time

Sep. 13, 2023

𝜎𝜎𝑦𝑦2 = 𝜎𝜎𝑥𝑥2 + 𝜎𝜎ℎ2deconvolving the output signal with a Gaussian kernel.
• The system’s impulse response is used
as a deconvolution kernel.

𝑦𝑦 𝑡𝑡 = 𝑥𝑥 𝑡𝑡 ∗ ℎ 𝑡𝑡 = � 𝑥𝑥 𝜏𝜏 ℎ 𝑡𝑡 − 𝜏𝜏 𝑑𝑑𝑑𝑑
System response function: ℎ𝑠𝑠𝑠𝑠𝑠𝑠 = ℎ𝑃𝑃𝑃𝑃 ∗ ℎ𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑇𝑇 ∗ ℎ𝑎𝑎𝑎𝑎𝑎𝑎 ∗ ⋯• The input signal is reconstructed by analyticallyAnalytic Gaussian Deconvolution
Pros• Practical• FastCons• Inaccuracy(Error with Gaussian assumption)

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

9/21

AGD Measurement Results
Bunch Length Measurement

𝜎𝜎𝑃𝑃𝑃𝑃 = 32.38ps

6 mA, central bunch• The noise level (without beam, room temperature, hutch-doorclosed) was equivalent to a bunch current of 3 μA.

𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆= 25.20 ps

𝜎𝜎ℎ = 20.43 ± 0.81 ps• The wideband system enables the bunch-resolved current
measurement.
• Applying the fit form of typical Gaussian deconvolution, weobtained a calibration curve for photodiode measurement.
• Is the Point Spread Function 𝜎𝜎ℎ,𝐴𝐴𝐴𝐴𝐴𝐴 true?

Sep. 13, 2023

Fit form : 𝜎𝜎𝑃𝑃𝑃𝑃 =2𝜎𝜎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠+ 𝐴𝐴2Fit result : 𝐴𝐴 ⇒ 𝜎𝜎ℎ,𝐴𝐴𝐴𝐴𝐴𝐴 = 20.43 ± 0.81 𝑝𝑝𝑝𝑝

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

10/21

AGD Processed PD Bunch Length
Cross-check, Using Femtosecond Laser?

• The PSF was measured with a laser pulse widthof ~ 200 fs, as a delta function.
• RMS PSF(Gaussian Fit) was obtained
about 25.68 ± 2.56 ps which is way out of 1-sigma
confidence interval.
Sep. 13, 2023

• AGD PSF is inconsistent with the measured response
function !

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

11/21

Numerical Compensation (NC)
(0)

(1)

Radiation(2)(3)
OutputSignal

DiodeTech. Document(4)

Bias Tee Pre-amp Cable, Scope

Tech. Document

Measured using VNA, Signal
Generator, and Power meter The measured signal is distorted strongly by
the frequency response of analog components.
Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

12/21

Transmission Ratios• Ultra-fast Photodiode• Bias Tee• Gain• rise time(t) = ~35 ps @ 7 V (bias)• Eq. bandwidth = 0.35/t ~ 10 GHz• Eq. point spread function = 20.7 psCapacitor

Diode

Sep. 13, 2023

Bias Tee

Pre-amp Cable

Scope• Pre-amp• GainDC 10 V

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

13/21

Transmission Ratio Measurement• Cable ABW Measurement• Tr. Ratio (S21, VNA)
• Spec. was 26.5 GHz but obtained 19.5 GHz as -3 dB level

Sep. 13, 2023

• Scope ABW Measurement (16 GHz-ABW, 2 TS/s EQ)• Tr. Ratio -> Gain (By well calibrated signal generator, we scanned frequency,
and we measured voltage level at the digitizer)

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

14/21

Numerical Compensation
(0)

(1)

Radiation

(2)

(3)

Bias Tee Pre-amp Cable, Scope
Diode

1. Calculate the overall frequency response map R
by convolution of all real frequency response maps

(4)
OutputSignal𝑅𝑅 𝜔𝜔 = 𝑅𝑅1 𝜔𝜔 ⋅ 𝑅𝑅2 (𝜔𝜔) ⋅ 𝑅𝑅3 (𝜔𝜔) ⋅ 𝑅𝑅4 (𝜔𝜔)

2. Measurement data was Fourier-transformed,
And recovered by Rℎ′ 𝑡𝑡 = 𝑭𝑭−𝟏𝟏𝑭𝑭 ℎ 𝑡𝑡
𝑅𝑅 𝜔𝜔

𝑭𝑭 ∶ 𝐹𝐹𝐹𝐹𝐹𝐹𝑭𝑭−𝟏𝟏 ∶ 𝑖𝑖𝐹𝐹𝐹𝐹𝐹𝐹

Loop over

3. To find the bunch length, calculate Gaussian fit,
FWHM or whatever
Numerical Compensation

Sep. 13, 2023

Pros

• Still fast
• Accurate

Cons• Frequency response can be changed according
to circumstance. (ex. Temp, Connection …)

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

15/21

Numerical Compensation (in detail)1. Calculate the overall frequency response map R
by convolution of all real frequency response maps
𝑅𝑅 𝜔𝜔 = 𝑅𝑅1 𝜔𝜔 ⋅ 𝑅𝑅2 (𝜔𝜔) ⋅ 𝑅𝑅3 (𝜔𝜔) ⋅ 𝑅𝑅4 (𝜔𝜔)

1.1 Accumulate data to reduce error caused by revolution trigger
jitter (Typically 30-120 seconds using the Picoscope9400.
We are currently using Tektronix DPO71304SX which isindependent from the Rev. trigger jitter)
Rev. Trigger Jitter Measurement

1.5. Apply low pass filter G (Butterworth, -3 dB at 16 GHz),
to remove HF noise
2. Measurement data was Fourier-transformed,
And recovered by Rℎ′ 𝑡𝑡= 𝑭𝑭−𝟏𝟏𝑮𝑮(𝜔𝜔)𝑭𝑭 ℎ 𝑡𝑡
𝑅𝑅 𝜔𝜔𝑭𝑭 ∶ 𝐹𝐹𝐹𝐹𝐹𝐹
𝑭𝑭−𝟏𝟏 : 𝑖𝑖𝐹𝐹𝐹𝐹𝐹𝐹

2.5 Partitioning data-points into every RF bucket andconverting time to phase3. To find the bunch length, perform Gaussian fit
Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

16/21

Bunch Lengthening Experiment𝜎𝜎𝑁𝑁𝑁𝑁 =2𝜎𝜎𝑆𝑆𝑆𝑆+ 𝐴𝐴2 + 𝐵𝐵

Bias Tee Pre-amp Cable, Scope
Diode

What we
don’t know
24.74 ± 0.47 ps

Sep. 13, 2023

Freq. Response Map- The numerical compensation method lacks completenesssince we don’t know a Freq. response of the photodiode.
- However, in contrast to AGD, slope of quadratic curve waswell matched.
- The extrapolated quadratic curve (Y interception point) isconsistent with the laser experiment.
- Not perfect, but it is still a good method to provide
longitudinal information in the operation range.
Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

17/21

Statically Estimated Resolution, by Monte Carlo Study
1. Artificially generate time domain signals hMC(t, σ0)ℎ𝑀𝑀𝑀𝑀 𝑡𝑡, 𝜎𝜎0 = ℎ𝑃𝑃𝑃𝑃𝑃𝑃,𝑃𝑃𝑃𝑃 𝑡𝑡 𝜎𝜎0 =0 ∗ ℎ𝐼𝐼𝐼𝐼𝐼𝐼 𝑡𝑡, 𝜎𝜎0 ∗ ℎ𝐵𝐵𝐵𝐵 (𝑡𝑡) + ℎ𝑀𝑀𝑀𝑀 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑡𝑡, 𝜎𝜎0ℎ𝑃𝑃𝑃𝑃𝑃𝑃,𝑃𝑃𝑃𝑃 |𝜎𝜎=0 𝑡𝑡ℎ𝐼𝐼𝐼𝐼𝐼𝐼 (𝑡𝑡, 𝜎𝜎0 )ℎ𝐵𝐵𝐵𝐵 (𝑡𝑡)ℎ𝑀𝑀𝑀𝑀 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑡𝑡, 𝜎𝜎0: Point spread function (Gaussian profile 𝜎𝜎 = 25.68 ps): Ideal bunch-train profile: Overall frequency response (PD, Amp, cable & digitizer): Digitizer noise (random error based on technical note)

2. Calculate bunch lengthusing both methods
𝜎𝜎𝐴𝐴𝐴𝐴𝐴𝐴 ± 𝜎𝜎𝐴𝐴𝐴𝐴𝐴𝐴 𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

3. Definition of systematic error
𝜎𝜎𝑠𝑠𝑠𝑠𝑠𝑠 𝑒𝑒𝑒𝑒𝑒𝑒 =Sep. 13, 2023

𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗
𝑁𝑁# 𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

𝜎𝜎𝑁𝑁𝑁𝑁 ± 𝜎𝜎𝑁𝑁𝑁𝑁 𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
22+ 𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 = 30 𝑝𝑝𝑝𝑝, 𝑁𝑁# 𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 500, 𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = 𝜎𝜎𝐴𝐴𝐴𝐴𝐴𝐴 𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 || 𝜎𝜎𝑁𝑁𝑁𝑁 𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

18/21

Discussion- The NC results are closest to the ideal curve, despite the absence of the photo-diode’s frequency response- BUT still we could not understand why the fit form looks like below

Sep. 13, 2023

𝜎𝜎𝑁𝑁𝑁𝑁 =2𝜎𝜎𝑆𝑆𝑆𝑆+ 𝐴𝐴2 + 𝐵𝐵

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

19/21

Current Status
We are monitoring bunch length online

Old system (with Picoscope-9404-16, Pico Technology):- Data acquisition time : 30 ~ 120 seconds for statistically mitigating the error
mainly due to the revolution trigger jitter of 30 ps and vertical noise of the scope.
New system (with DPO71304SX, Tektronix):- Real time data acquisition : PV updating rate is about 0.1 ~ 1.0 Hz(mostly data transferring time)- Trigger jitter free (non-averaged)
Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr> International Beam
Instrumentation Conference 2023

20/21

Summary• We have experimentally demonstrated a compact monitor that enables filling pattern (~ 3 µA resolution) andbunch length (~ 1 ps resolution) monitoring with visible light at the PLS-II storage ring
• Both analytical Gaussian deconvolution and numerical compensation methods were investigated to improvemeasurement accuracy
 We achieved better resolution with numerical compensation method• Recently we installed a new digitizer for online Turn-by-turn and Bunch-by-bunch measurements are undercontemplation as a future upgrade project.

Sep. 13, 2023

Garam HAHN <garam@postech.ac.kr>
International Beam Instrumentation Conference 2023

21/21

Thank you for your attention