1. Progress Report on the Data Analysis of
Bunched Electron Cooling Experiment
Haipeng Wang (JLab lead)
Lijun Mao (Exp. Spokesperson), He Zhao (PhD Student)
Institute of Modern Physics, CAS, Lanzhou, Gansu, China
Yuhong Zhang, (LDRD 2014 PI) He Zhang, Tom Powers, Mike Spata, Shaoheng Wang
Thomas Jefferson Lab, Newport News, VA USA

2. Cooling of both coasting and bunched ion are observed
First Bunched Electron Cooling of Ion Experiment at IMP, China, May 17-22, 2016
7MeV/u 12C6+ ion bunches stored and captured by 450kHz, h=2 RF in CSRm ring
Modulated 3.78keV DC electron bunches in ms long at 225kHz at E-cooler
Cooling of both coasting and bunched ion are observed
Data analysis both at IMP and JLab are in good progress
Initial 1D modeling with RF capture and electron bunch trapping shows the ion cooling and synchrotron sideband effects, agree with experimental observation
Experiment data observation on BPMs
1D beam dynamic modeling
cooled ion bunches
uncooled ion bunches
Electron bunches 1.5ms
Simulated trapped ions and bunch peak current in longitudinal phase space with RF voltage on and electron bunch cooling

3. Current Effort and Status of Data Analysis
8GB of raw data, most of them from electron/ion BPM signals (pulsed signals only, no transverse position information). Also data from DCCT (ion average current) and Schottky diodes (RF harmonic signal with 1D FFT)
Strategy:
Understand experiment setup, diagnostic hardware/software and their limitation
Survey data, look for consistent physical evident (majorly from the BPMs)
Develop simulation model to explore the key physics and relevant critical beam parameters
Process “good” experiment data for the parameter fitting of cooling model
Using common data/tool/report work area on “srfnode3” server
Labview tool development for data view/scan/batch processing (Tom and Haipeng)
Python (He Zhang) and Mathematica (He Zhao) tool development for initial data analysis
Understand experimental configuration setup, delay, triggering and synchronization, control software and hardware issues (all)
1D beam dynamic with RF and e-cooling potential wells modeling (Shaoheng)
Experimental condition, logbook and data consistency check with possible physical explanation (all)
Effort: Weekly (3-hour internal team) work meeting and WebEx (1-hour) meeting with IMP. (30~50% 5 FTE)

4. IMP Pulsed E-Cooling Triggering Setup – Tom Powers, May 21, 2016
225kHz (for max. HV pulser rep rate)
450kHz from RF (for min. h=2)
B=T0+A+PWe
FOR E-GUN PULSER
TRIGGER
Digital delay generator
10Hz gating (for scope sync only not for cooling exp. data which is DC +5V ) A B
0-5V TTL T0
FOR BPM SCOPE
MONITORING
RF ON + wait (1sec) +T0 (scope delay) on the traces of Labview data
A= ns is from T0 to AB OUT front edge

5. IMP Pulsed E-Cooling Triggering Setup, May 22, 2016
225kHz (for max. HV pulser rep rate)
450kHz (for min. h=2)
10Hz gating (for scope sync)
On-time 2us off time >790ns
B=T0+A+PWe T0
Digital delay generator
FOR E-GUN PULSER
TRIGGER
FOR BPM SCOPE
MONITORING

6. BPM Measurement Delay and Triggering and Display on LabView DAS
scope ion BPM signal
2.219ms Ai Di t
(ti - te)-332.8ns=(Ai - Ae) + (De - Di) = 1sec +T0sec+A + Dfol (N+1/2)4.438 ms
ion bunches in the ring
ti=T0+Ai-Di
uncooled
uncooled
cooled
cooled t
Ai is from t=T0 to center of narrow ion BPM bunch signal measurable in LV screen
Ae is from t=T0 to start edge of electron BPM bunch signal measurable in LV screen
T0 is read by LV DAS, cooling time reference #
A= ns set by DG535
PWe = 0.15 – 2.2ms is electron bunch width set by DG535. Pwe=B-A
Di=? is delay from ion bunch to ion BPM signal
De=? is delay from electron bunch to electron BPM signal
Dfol=100ns is a hardware delay from AB OUT to HV pulser to launch pulse which is mostly fiber optic link and electronic delay of hardware
t=T0
2.219ms ( kHz)
Ai-Ae
4.438ms
scope electron BPM signal De Ae
PWe t
te=T0+Ae-De
A+1280ns
electron bunches in the cooler
4.438ms ( kHz) t
PWe
PWe

7. BPM Measurement Delay and Triggering and Display on LabView DAS
(ti - te)-332.8ns=(Ai - Ae) + (De - Di) = 1sec +T0sec+A + Dfol (N+1/2)4.438 ms
Ai is from t=T0 to center of narrow ion BPM bunch signal measurable in LV screen
Ae is from t=T0 to start edge of electron BPM bunch signal measurable in LV screen
T0 is read by LV DAS, cooling time reference #
A= ns set by DG535
PWe = 0.15 – 2.2ms is electron bunch width set by DG535. Pwe=B-A
Di=? is delay from ion bunch to ion BPM signal
De=? is delay from electron bunch to electron BPM signal
Dfol=? is a hardware delay from AB OUT to HV pulser to launch pulse which is mostly fiber optic link and electronic delay of hardware
(ti - te)= 𝑷𝑾 𝒆 𝟐 or
Ai – Ae= 𝑷𝑾 𝒆 𝟐 −𝟑𝟑𝟐.𝟖𝒏𝒔− De − Di
when electron bunch center aligns with ion bunch center
A is the delay ( ) ns set up by DG535 from AB OUT (front edge) to the HV pulser to fire the electron bunch front edge
0.121clight332.8ns=12.072m
electron-BPM at gun position
ion-BPM after the cooler position T0 A
AB OUT

8. The Evolvement of the Cooled Ion Bunch with RF On and Off (Shaoheng 1)
12C+6 ion revolution frequency 225kHz
FWHM=~80ns << 1us of electron pulse length
T0 = 0.2 sec sec sec sec
Electron profile, 1us PW, 225kHz rap rate
RF (h=2) captured bunch length ~2.2us
RF ON
RF OFF
Ions profile with both cooled and uncooled bunches
4.2 sec (RF is turned off at time = 4 sec)

9. Data Information Confirmation with IMP (He Zhao 1)
Bunched beam cooling with pulse electron beam (cooling process)
Data: record_book1.pdf page 1-3 ( )
We measured the cooling process for different e-beam pulse width and different e-beam current
RF ON
RF OFF
E-pulser on
Saving data
Next injection 1s 5s
Time
Vrf=600 V
E-pulser on 1s
Saving data 5s
2. Coasting beam cooling with pulse e-beam (sidebands in schottky spectrum)
Data: record_book1.pdf page 3-5 ( )
We measured Schottky spectrum with different e-beam pulse width and different e-beam current. There was always no RF. Schottky was also used to measure the synchrotron sideband and energy spread signal
Other recorded data are for other experiments or experimental testing, which we don’t use.

10. Data Information Confirmation with IMP (He Zhao 2)
Bunched E-cooling process measurement
RF ON
RF OFF
E-pulser on
Saving BPM fast data with different delay time 1s 5s
Time
Vrf=600 V A B C A B C
peak di/dt envelop signal of ion BPM

11. Compare with Different Electron Pulse Lengths (Shaoheng 2)
D:\LABVIEW DATA-05-20\Diag_120520_ txt
D:\LABVIEW DATA-05-20\Diag_120520_ txt
2 us
1 us
D:\LABVIEW DATA-05-20\Diag_120520_ txt
D:\LABVIEW DATA-05-20\Diag_120520_ txt T0
LABVIEW DATA-05-20\Diag_120520_ txt
D:\LABVIEW DATA-05-20\Diag_120520_ txt

12. Compare with Different Electron Pulse Lengths (Shaoheng 3)
D:\LabView Data_05_21_16\Diag_120521_ txt
D:\LabView Data_05_21_16\Diag_120521_ txt
0.8 us
0.6 us
D:\LabView Data_05_21_16\Diag_120521_ txt
D:\LabView Data_05_21_16\Diag_120521_ txt T0
D:\LabView Data_05_21_16\Diag_120521_ txt
D:\LabView Data_05_21_16\Diag_120521_ txt

13. RF Off with Coasting Ion Beam (Shaoheng 4)
D:\LABVIEW DATA-05-20\Diag_120520_ txt
2 us
0.3 us
D:\LABVIEW DATA-05-20\Diag_120520_ txt
Ion bunch profile follows e bunch profile, the only potential well ions can see
This potential has a flat bottom, so no ion bunch shortening effect appears.
1 us

14. RF Off with Coasting Ion Beam (Shaoheng 5)
Beam synchronization between electron pulse and ion bunch is critical
Both electron and cooled ion have the same bunch length ~150ns
Without fine tune the electron pulser’s frequency with the ion revolution frequency, the cooling effect can be lost
150 ns
Zoom in:

15. Data Analysis Independently from IMP (He Zhao 1)
Without e-beam
Ion beam
Energy:6.88 MeV/u
f: 224 kHz
T: 4.4us
Current: 50 uA
V-RF: 600 V
h=2
E-beam
Energy: 3.77 kev
f: 224 kHz
Pulse width: 2us
Current(max): 17mA
(Data file: pulse=2us_anode=800)
Cooling end
Cooling begin
~2us
~2us
~2us
E-beam
E-beam

16. Method 1: Fit by Bi-Gaussian distribution
Data Analysis Independently from IMP (He Zhao 2)
Method 1: Fit by Bi-Gaussian distribution
𝑚𝑜𝑑𝑒𝑙=𝑚1∗ 𝑒 − (𝑥−𝑢) 2 2𝜎 𝑚2∗ 𝑒 − (𝑥−𝑢) 2 2𝜎 2 2
May 21’s data with RF ON

17. X= (Signal strength) * time
Data Analysis Independently from IMP (He Zhao 3)
Method 2: Calculate the RMS value
Time distribution:
X= (Signal strength) * time
Numbers:
N=∑(signal strength)
Signal strength
May 21’s data with RF ON
Time/s
𝑅𝑀𝑆= 1 𝑁 i=1 𝑛 ( 𝑋 𝑖 − 𝑋 ) 2
RMS bunch length definition is questionable?

18. Evolution of the RMS Bunch Length (He Zhang 1)
Algorithm:
Use the first integral of the BPM signal as the beam density function.
Make the start and the end point of the first integral to be zero to remove DC slope.
If any value is less than zero after the slope adjustment, make it zero.
The rms bunch length is calculated using the following formula:
dz (s)
May 21’s data with RF ON
Blue: uncooled ion bunch
Red: cooled ion bunch
Cooling reach equilibrium at about 1.5 s.
RMS bunch length needs to be standardized
t (s)

19. Evolution of the RMS Bunch Length (He Zhang 2)
First integral of the BPM signal ∝ charge density function
Second integral of the BPM signal ∝ total charge
Algorithm:
Integrate the BPM signal and find the peak of the cooled beam.
Select the range of half period, centered at the peak, as the whole cooled beam.
Make the start and the end point of the first integral to be zero to remove DC slope, and calculate the second integral.
Select the following half period as the uncooled beam, and calculate the second integral in the same way.
Calculate the rate between two second integrals of the cooled and the uncooled beam.
1st Integral
1st Integral
1st Integral
Rate
t=0.025 s
t = 0.45 s
t = 1.7 s
t (s)
t (s)
t (s)
time (s)
1st Integral of ion BPM signal
Rate of the two 2nd integrals

20. Data Information Confirmation with IMP (He Zhao 4)
Data\ CoolingExperimentData\frequency domain data\001.bmp
~0.6 kHz
RF OFF
New: The sideband signal appeared when pulsed e-beam is used on the coasting ion beam
Old: The width of center peak 26th harmonics of revolution frequency is also used for the ion energy spread measurement
dp/p~4E-4

21. Data Information Confirmation with IMP (He Zhao 5)
Compare with the sideband signals induced on the RF Schottky pickup
It is coincidence that the sideband of coasting beam caused by pulse e-beam is same as the sideband caused by the synchrotron motion with RF on Vrf=600V
There are also other sidebands in the coasting beam case
Sideband frequency of with different RF voltages was consistent to the synchrotron tune ftune 𝑉 𝑟𝑓
Quest: What cause the sideband frequency of coasting beam, electron potential barrier?
Coasting beam
Bunched beam
~0.6 kHz
~0.6 kHz

22. Data Information Confirmation with IMP (He Zhao 6)
Actually, the sampling rate and the sampling time set on LabView program are not agree with the saved DCCT data. So we use the time between two injection to calibration the timeline.
We will try to fix the bug in LabView program with our colleagues for the next experiment. And the program will send to JLab side.
DATA: record_book1.pdf page 5-7 [The time between two injection is 50 s]
There is no so much correlated DCCT data can be used with BPM data
No timestamp on all raw data
We are still looking for the cause of shorter life issue with pulsed e-cooling
Beam current (uA)
Max
Average
Min
Injection

23. Two Mechanisms of Bunched E- Cooling (Shaoheng 6)
Mechanism I: coasting beam + bunched e-cooling
cooled low energy spread ions are trapped in the flat bottomed potential well produced by the e bunch, so the ion bunch profile follows the e bunch density profile.
low efficiency
Mechanism II: RF on + bunch e-cooling
RF produces a potential well will shorten cooled ions longitudinal distribution
The length of final cooled ion bunch is limited by IBS equilibrium energy spread.
It operates just like transverse cooling, where betatron motion + e cooling produce similar sharp cooled ion core. Longitudinal cooling is enhanced by the synchrotron motion which is sharp in the bunch center
for every 10 mA e beam with 25 ns rising time: Ve.kick = 94 V. It’s potential well is shallower compare to Vrf=600V. The synchrotron motion due to the electron barrier is also slower compare to the RF potential well
So, if not synchronized, all ions are kicked away in a short time period.

24. Summary
Preliminary data has been surveyed and sorted. They are a large amount of BPM data are valuable for understanding pulsed electron cooling to both RF captured ions in bunched and coasting beam condition
1D beam longitudinal dynamic modeling with/without RF and the pulsed electron cooling has been developed with promised result which could explain observed experiment data (next talk by Shaoheng)
Further data analysis, fitting to the simulation model is in continues and enhanced effort
Publication and next experiment plan at IMP is under the discussion

25. Backup Slides

26. HIREL-CSR Layout and Performance Specification
EC-35 cooler
Sector Focusing Cyclotron
separated-sector cyclotron

27. First Bunched Electron Cooling Experiment Parameters on May 17-22, 2016
150
h=2 0.

28. EC-35 DC Cooler and Commissioned Performance
1—electron gun, 2—electrostatic bending plates, 3—toroid, 4—solenoid of cooling section, 5—magnet platform, 6—collector for electron beam, 7—dipole corrector, 8—vacuum flange for CSRm. Two BPMs placed in the cooling station, one is at upstream of electron beam at gun side in position 9, another one is at downstream collector side in the mirror symmetric position relative to 9.
Single plate of this BPM has been used for the bunched e-beam measurement
Recommissioned in March 2016
vacuum 21011 mbar,
high voltage 20 kV,
electron beam current 1.5 A,
collector efficiency >99.99%,
angle of magnetic field line in cooling section <210-5

29. Terminal Circuit Diagram and Average Current Measurement
electrons
ions
Collector efficiency
= 𝐼 𝑐𝑎𝑡ℎ𝑜𝑑𝑒 − 𝐼 𝑏𝑒𝑎𝑚 𝐼 𝑐𝑎𝑡ℎ𝑜𝑑𝑒 100%
𝐼 𝑏𝑒𝑎𝑚 = 𝐼 𝑐𝑜𝑙𝑙𝑒𝑐𝑡 − 𝐼 𝑏𝑎𝑐𝑘
𝐼 𝑐ℎ𝑎𝑟𝑔𝑒 = 𝐼 𝑙𝑒𝑎𝑘 + 𝐼 𝑐𝑎𝑡ℎ𝑜𝑑𝑒 − 𝐼 𝑏𝑒𝑎𝑚

30. EC-35 Pulse Modulation + DC Bias Scheme for Bunched Electron Beam Formation
Option 1 (JLab, using HV pulser)

31. FEL Ampare-Class Cryomodule Conceptual Design Review
Beam Diagnostic Devices for Bunched Electron Cooling Demo Experiment
existing
modification
new installation (not used in this exp.
Measurement
EC35-electron
CSRm-ions
Data-acquisition
average beam current
dc readings on PSs, sampling resistors
DCC(current)T(transformer)s
existing calibra. and DAS
peak beam current
and pulse length
mod. freq. fm
Pearson coil on E-collector
rf or harmonic freqs n*f0
fiber optical link readout
Beam position
capacitive BPMs
Re-calibra. and DAS put new attenuator
Beam trans.-profile
(off-line screen)
residual gas BPMs
DAS
Beam long.-profile
BPMs
on BPMs
on BPMs or DCCTs
Stochastic cooling pickup
fast scope and on-line DAS
Cooling rates
n.a.
Schorttky resonator and pickups
Off-line side-band signal analysis

32. Existing BPM Devices at ECC-35 and CSRm for Electron/Ion BPMs
𝑉 𝑡 = 𝑅 1+𝑗𝜔𝑅𝐶 𝐼 𝑡 = 1 𝛽𝑐 𝐴 𝜋𝑎 𝑗𝜔 𝑅 𝑒𝑞 1+𝑗𝜔 𝑅 𝑒𝑞 𝐶 𝐼 𝑏 𝑡
𝑥=2𝑎 𝑉 𝑥 𝑉  =2𝑎 𝑉 𝑅𝑖𝑔ℎ𝑡 − 𝑉 𝐿𝑒𝑓𝑡 𝑉 𝑅𝑖𝑔ℎ𝑡 + 𝑉 𝐿𝑒𝑓𝑡 + 𝑉 𝑈𝑝 + 𝑉 𝐷𝑜𝑤𝑛
𝑦=2𝑎 𝑉 𝑦 𝑉  =2𝑎 𝑉 𝑈𝑝 − 𝑉 𝐷𝑜𝑤𝑛 𝑉 𝑅𝑖𝑔ℎ𝑡 + 𝑉 𝐿𝑒𝑓𝑡 + 𝑉 𝑈𝑝 + 𝑉 𝐷𝑜𝑤𝑛

33. 1D Signal Calculation for Gaussian Bunch and Ring-shape Pickup
Gaussian bunch shape distribution (black) in 7ns (rms) bunch length current picked up by 50 W shunt impedance’s voltage (red, calculation) and comparison to the experimental data (blue) for one of 12C+6 bunches accelerated in the CSRm ring at the 0.5 velocity. The blue data is measured by a fast oscilloscope on a Ls=15cm pickup cylinder. The voltage gain of such signal is ~350. The ion current is ~3mA. Signal ringing on the back is due to the pickup circuit.

34. 1D Signal Calculation for Square Bunch and Ring-shape Pickup
Electron (red solid line) and ion (green solid line) bunch signals picked up by modified capacitive type BCM plates and their bunch shapes (dashed red line for electron, dashed green line for ion) calculated by MathCAD program for =0.121, average beam currents of 70mA for electron and 3mA for 12C+6. The voltage signal is picked up on the total shunt resistor of R=150. The voltage signal gain on the ion current is 40dB (80dB in power) for this display. In this calculation example, there are 7 electron bunches with in one ion bunch.

35. 1D Signal Calculation for Gaussian Bunch and Ring-shape Pickup
Gaussian bunch shape distribution (black) in 7ns (rms) bunch length current picked up by 50 W shunt impedance’s voltage (red, calculation) and comparison to the experimental data (blue) for one of 12C+6 bunches accelerated in the CSRm ring at the 0.5 velocity. The blue data is measured by a fast oscilloscope on a Ls=15cm pickup cylinder. The voltage gain of such signal is ~350. The ion current is ~3mA. Signal ringing on the back is due to the pickup circuit.

38. BPM Signal Raw Data Integrator for Bunch Shapes Display in LabView
Integrator to recover beam bunch pulse shape from BPM signal (di/dt) and remove the DC offset slope
Integrated data with offset =Calibration×deltaT − i=index of integration start end of live index Raw Data i −offset tweak −auto offset tweak i=index of integration start end of live index 𝑖
auto offset tweak= − i=index of integration start end of live index Raw Data i −offset tweak index of T Final for offset−index T 0 for integration start
index of T0 for integration start= T0 for integration start deltaT

39. Reference: Cavity Schottky Pickup RF harmonic signal