1. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 1 Associated colleagues: Michel CHANEL Alan FINDLAY Wolfgang HOFLE Reinier LOUVERSE Increasing the beam intensity in LEIR Possible challenges for the transverse feedback Present situation: multi(70)-turn injection with 22μA-Pb54+ up to 7 times every 200 ms under electron cooling. 6E10 charges ejected on h2 with a 200 ns bunch length (4 sigma). Foreseen: multi(70)-turn injection with 22μA-Pb54+ up to 13 times every 100 ms under electron cooling. 8.6E10 charges ejected on h2 with a 200 ns bunch length (4 sigma).

2. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 2 Executive summary: In case of an increase of the beam intensity in LEIR, the present bandwidth (100 MHz) of the transverse feedback system might be insufficient to preserve the beam stability. The other parameters are compatible.

3. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 3

4. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 4 2 stripline PUs UDHV 41 and 42 almost 90 Betatron deg apart (whatever the tune) Signal processing in 3 racks in the middle of the ring 1 stripline kicker KDHV21 receives the processed Betatron transverse error, synchronous with the beam and with the apropriate 90 deg Betratron phase shift.

5. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 5

6. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 6 PU bandwidth = 280 MHz PU length = 0.47 m

7. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 7 ModelPU de-skew Buffer PS/AAC 0020/2 Bandwidth (+/5 o phase error) [1 kHz ; 100 MHz] Bandwidth of the setup with pick-up (31.4 pF pick-up, 50 pF coaxial interconnect) [19.5 kHz ; 100 MHz] Input impedance100 kΩ Gain (50 Ω load)0 dB Drive3 V P-P into 50 Ω (3V P-P on the input) Noise Factor≤ 30 dB (50 Ohm source impedance) Noise level740 nV/√Hz with OPA 656 (op-amp) Gain28 dB PU head amplifier

8. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 8 Estimation of the possible saturation of the PU head amplifiers with the increased beam intensity: Voltage developed on the PU head amplifier input for a 200 ns long bunch with sinusoidal shape and 4.3E10 charges? In the worst case (beam really off-center close to a single PU-plate) V PU = -1.31 V to +2.31 V The PU head amplifier can accept +/- 3 V => No saturation expected on the PU amplifier

9. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 9 Power amplifiers Output Power100 W In/Out impedance50 Ohm Gain50 dB Frequency range100 kHz – 100 MHz Phase ripple+/- 5 deg Power is required: To improve the damping time with injection trajectory errors (no estimation yet of the requirements with the multi-turn injection and cooling) To compensate the imperfect rejection of the PU closed orbit related signal within the BOSS (not measured yet) To absorb the beam signal as picked-up by the kicker (< 0.2 W = negligible)

10. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 10 Required Bandwidth

11. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 11 References concerning bandwidth requirements http://cds.cern.ch/record/316202/files/ps-96-009.pdf http://cds.cern.ch/record/280706/files/p177.pdf

12. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 12 coasting Bunched h = 2 injection Bunched h = 2 extraction hvhvhv T[MeV/n)4,2 72 beta0,09464190,094642 0,371954 gamma1,004508861,004509 1,077295 Qh,v1,822,721,822,721,822,72 Half chamber[m]0,060,030,060,030,060,03 N Z5,00E+10 Bf110,38  Q coherent 0,00210,00560,00550,01460,00030,0008 eh,norm0,5 0,8 ev,norm0,3 0,5  Q incoh(0,0) 0,03720,04800,06060,07660,01340,0170 eta0,87 0,74  p/p(2  ) 4,00E-04 3,00E-03 1,00E-03 n threshold for Instability31838567755669 Frev(Hz)3,62E+05 1,42E+06 Lower stability limit [MHz]11513924277998 Table created by Michel Chanel for 4.8 E10 charges. The tune shifts, and thus the frequency limits, should scale linearly with the intensity. ( => multiply by 1.8 for 8.6E10 charges)

13. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 13 Conclusion: With the increased intensity in LEIR, the transverse Landau damping is theoretically only obtained above 207 MHz in the worst case (value to be confirmed) Below this limit an active damping is required. Open questions: Do we need to need to “actively” cover this entire range to remain stable? Would the available 100 MHz be sufficient? … else can we relax some beam parameters? Δp/p?, transverse emittances?

14. LEIR Transverse Dampers Alfred Blas LIU-ION LEIR Internal Review 20.08.2014 14 Some references: http://betacool.jinr.ru/COOL/COOL%2703/137.pdf http://cas.web.cern.ch/cas/BRUNNEN/Presentations/PDF/Albert-II.pdf