1. Beam Diagnostic System Analysis in HIRFL-CSRm at IMP, China for the Bunched Electron Cooling Demo Experiment
Haipeng Wang
Also thanks to Lijun Mao (Exp. Host) at IMP and Yuhong Zhang, (LDRD 2014 PI) and He Zhang (Cooling Simulation) at JLab

2. HIREL-CSR Layout and Performance Specification
EC-35 cooler

3. Proposed Bunched Electron Cooling Experiment Parameters

4. 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.
Commissioned in March 2003
vacuum 21011 mbar,
high voltage 20 kV,
electron beam current 1.6 A,
collector efficiency >99.99%,
angle of magnetic field line in cooling section <210-5

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

6. EC-35 RF Modulation + DC Bias Scheme for Bunched Electron Beam Formation
bunch length
∆ 𝑡 𝑒 = 𝐴𝑟𝑐𝑐𝑜𝑠 𝑉 𝑐𝑢𝑡𝑜𝑓𝑓 + 𝑉 𝑏𝑖𝑎𝑠 𝑉 𝑟𝑓 2𝜋 𝑓 𝑚
fm3 MHz
𝐼 𝑐𝑎𝑡ℎ𝑜𝑑𝑒 𝑡 𝑒 ≈
𝑃 𝑔𝑢𝑛 𝑉 𝑟𝑓 1−𝑐𝑜𝑠 2𝜋 𝑓 𝑚 ∆𝑡 𝑒 𝑉 𝑎𝑛𝑜𝑑𝑒 𝑓𝑖𝑡 𝑉 𝑎𝑛𝑜𝑑𝑒 1.5

7. RF Amplifier Resonant Circuit Design, Prototype and test Result
Courtesy of Dr. L.J. Mao, IMP
Input（mV p-p）
Output（V p-p）
100
4.63
200
300
400
500
600
700
800
900
1000
25.4
73.8
145
222
305
398
476
547
606

8. Electron Gun Simulation by CST EM-Static and PS Tracking Solvers
E-potential
E-field-am
Solid beam
Hollow beam

9. Hollow Beam Formation in Simulation and Experiments
Reduction of transversal instability of cooled ion beam. It may be achieved by using the electron beam with the density increasing radially but low at the center.
Problems arisen due to space charge effect may be partially solved by using the hollow electron beam with low transversal electric field near its center.
Reduction of the effect of recombination between the accumulated ions and the electron beam.
Suppress the electron heating effect in the center

10. Existing BPM Devices at EC-35 Cooler and CSRm Ring
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

11. Capacitive Beam Pickup Principles and Sensitivity to Beam Current
Our bunched beam electron cooling experiment is at the  range of 0.121~ So either type of the pickup is OK for the BCM
𝑖 𝑡 𝑅 𝑢 𝑡 = 𝑢 𝑐𝑎𝑝 𝑢 𝑖𝑛𝑑 ≈ 𝑐 𝜀 0 𝑅 𝛽 ≈ 𝛽
𝑢 𝑡 = 1 𝐶 0 𝑡 𝑖 𝑢 𝑒 − 𝑡−𝑢 𝑅𝐶 𝑑𝑢
𝑢 𝑠 =𝑖 𝑠 𝑅 1+𝑅𝐶𝑠
For RCs <<1, fm<<fc, R is preferred in low resistance for high roll-off frequency fc.
𝑢 𝑠 ≈𝑅𝑖 𝑠 or 𝑢 𝑡 =𝑅𝑖 𝑡 ∝𝑅 𝑑 𝑑𝑡 𝑖 𝐵 𝑡
Too weak!
We need to modify the external circuit of BPM to be a resonant circuit in order to improve the bunch edge sensitivity
𝑖 𝑟𝑖𝑛𝑔 = 160 𝛿𝑡 𝑝𝐴 𝑛𝑠 𝑘 𝐿 𝑠 𝛽𝑐∆𝑡 𝑎 𝐿 𝑠
~0.046 𝑝𝐴 𝑒

12. Modification Suggestion to Existing BPM External Circuits to BCM
Can tune harmonic of the ion accelerating frequency f0 and electron modulation frequency fm separately on different BPMs if not synchronized
Detune due to the resistive loss is small and the inductance can be compensated by a tunable inductor element.
Bunch beam charging time t >> the resonance RLC circuit (or cavity) filling time Q/r. Say 2 times at least. So the induced voltage V(t) will not drop between the bunches 1/f0-t.
Data sampling rate fs has to be fast enough to resolve the bunch rise time scale of ~10ns.

13. 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.

14. Resonant Signal Processing and Sampling Rate to Improve S/N
Res. BCMs
E-cooler
Ion-ring
voltage gain
0 dB
40 dB
sensitivity
7.8V/70mA
6.2mV/3.2uA
S/N
n.a.
1938
sampling rate
2131.2 MHz
frequency
103MHz
10frf tunable

15. BCM Resonant Circuit Design Parameters

16. Using Longitudinal Schottky Diodes to Measure the Cooling Rates
Courtesy of Dr. L.J. Mao, IMP

17. Summary
Bunched electron Beam Cooling at IMP has been proposed in 2014 at JLab and carried out by the collaboration team at 2015
HV power supplies and RF amplifier hardware are under commissioning for the electron beam modulation scheme
Demo experiment is scheduled in 2016
Modification of IMP CSRm BPM system into a BCM measurement device to measure the beam bunch length and peak current is possible for our demo bunched electron cooling experiment
Using existing EC-35 BPM system, a minor circuit modification (with parallel connection to the pickup cylinder pairs) using a resonant circuit is possible for the electron current measurement
For the BPM devices in the CSRm ring, using them for the ion beam bunch length and current measurement, the modification to a resonant circuit can greatly increase the S/N ratio. The new BCM circuit design parameters have specified
EC-35 and CSRm can do all of these schemes: DC to coasting, bunch to coasting and bunch to bunch, synchronization and unon-sychronization

18. References
[1] Yuhong Zhang, He Zhang, et al JLab LDRD 2014 proposal, funded in FY2015.
[2] CSR Design Group, “CSR Storage Ring Parameters List”, HIRFL-CSR/General/02-1, January 25, 2002, Submitted by J.W. Xia.
[3] Li Guo-Hong, etc. “A Beam Position Monitor System for Electron Cooler in HIRFL 2 CSR (in Chinese)”, Nuclear Physics Review, Issue 1, Vol. 27, March, 2010, Article No (2010) – 05.
[4] V. Bocharov et al. “HIRFL-CSR electron cooler commissioning”, Nuclear Instruments and Methods in Physics Research A 532 (2004) 144–149.
[5] E. Bekhtene, L.J. Mao, H. Wang and Y. Zhang, the discussion of bunched beam formation by the RF modulation scheme in the MEIC collaboration meeting in March, 2014.
[6] L.J.Mao et al, “Longitudinal electron cooling experiments at HIRFL-CSRe”, to be published in 2015.
[7] A.V. Bubley et al. “Measuring a hollow electron beam profile”, Nuclear Instruments and Methods in Physics Research A 532 (2004) 413–417.
[8] A.V. Bubley et al, “The Electron Gun with Variable Beam Profile for Optimization of Electron Cooling”, Proceedings of EPAC 2002, Paris, France, WEPRI049.
[9] G. R. Lambertson, Dynamic Devices – Pickups and Kickers, LBL-22085, BECON-63, LBL, UC Berkeley, August, 1986.
[10] D. A. Goldberg and G. R. Lambertson, Dynamic Devices, A Primer on Pickups and Kickers LBL-31664, November, 1991.
[11] Strehl P. Beam Instrumentation and Diagnostics. Berlin Heidelberg : Springer , 2006 ,
[12] Phone meeting conversation between Haipeng Wang, He Zhang and Yuhong Zhang at JLab with Lijun Mao at IMP on August 5, 2015.
[13] Strehl, P., Klabunde, J., Schaa, V., Vilhjalmsson, H., Wilms, D., Das Phasen-sondensystem am Unilac : Sondendimensionierung und Signalauswertung, GSI-Report 79–13, (1979), translated for the Los Alamos Scientific Laboratory by Leo Kanner Associates, Redwood City, (1980), LA-TR-80–43.
[14] A MathCAD program by Haipeng Wang, last updated on September 15, 2015.