Limits on damping times LHC Transverse Damper Limits on damping times Wolfgang Hofle CERN AB/RF/FB Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Effects limiting the achievable damping times 1. Stability of FB loop with kickers in one location 2. Saturation limit due to available kick strength and size of injection error 3. Saturation limit imposed by necessity to damp kicks from tune kicker 4. Constraints from noise properties of damper system Conclusions Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

1. Stability of FB loop If tunes are close to integer or half-integer, two kickers are required with phase advance in between them to guarantee stability (see SPS vertical damper, fixed target beam Qv=26.58, one kicker moved in 2001/2002 shutdown to cure intermittent feedback instability when tune is too low at very high gain) Damping times faster than 10 turns difficult to achieve and require generally also two kickers with phase advance in between them or even a larger number of kickers distributed around rind (“fast damper system” as was planned for UNK, Russia) In LHC, kickers are installed in one location, hence ~10 turns damping will be an absolute limit in practice for this configuration Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

2. Saturation at injection Design specification: 3.3 s can be damped in 38 turns at injection in absence of instability Instability rise-times of 208 turns as quoted in the LHC design report or 190 turns (E. Métral 8/2/2008) can be easily handled at 450 GeV, provided these fast instabilities are limited to ~ 1MHz At 20 MHz capabilities are a factor 10 lower in power, however if instabilities are intercepted early enough and do not start from large “seeds” the gain at high frequency can be boosted Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Damper Signal Processing high gain at low frequency for injection damping adapt gain vs. frequency to instability rise-time after injection damping and during the cycle G. Kotzian / V. Rossi Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

3. Saturation at during ramp & at 7 TeV Tune kicker can kick by 2 s at 450 GeV and 0.5 s at 7 TeV Damper must be able to cope with these oscillations, i.e. not saturate Limits the damping to 23 turns (using same reasoning as for injection damping) Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

4. Constraints from noise in the damper system Normal operating range of feedback is with high gain such that tD << tF i.e. coherent oscillations are damped faster than they convert into an increase of emittance must distinguish “monitor noise” : noise entered at level of ADC, due to ADC and analog front-end “kicker noise” : noise added after DAC and gain adjustment Emittance blow-up effect on beam of kicker noise is reduced by an increase in FB gain monitor noise is increased by an increase in FB gain Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

kicker noise monitor noise Kicker + fixed gain amplification Signal gain g adjustable Signal processing t signal t beam monitor noise D Pick-up 1 Pick-up 2 kicker and monitor noise entering FB loop Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

BPMC - Coupler type pick-ups 8 Dedicated Pick-ups BPMC @ Q7L, Q7R, Q9L, Q9R 50 W couplers of 150 mm length on one end short circuited Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

BPMC - Coupler type pick-ups Frequency Domain t = 2 L/c ~ 1 ns |ZT (w)| ^ ZT = 6.46 W Beam L=150 mm … w 500 MHz ^ ZT (w) = ZT j sin(wt/2) e -jwt/2 Length of electrodes 150 mm ^ Frequency domain: maximum of transfer impedance ZT = 6.46 W @ 500 MHz Peak voltage (beam centered) for ultimate beam @ collision: ~140 V -> very large Peak sensitivity: 0.264 W / mm => 8.1 V/mm peak in time domain after ideal hybrid Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Signal levels from pick-up LHC Beam Parameters Injection Collision Beam Energy 450 GeV 7000 GeV g 479.6 7461 RMS bunch length in cm 11.24 7.55 FREV in kHz 11.245 FRF in MHz (h=35640) 400.789 400.790 ^ Range of intensities for LHC beam and expected pick-up signal levels (ZT = 3.23 W; ZT (w) = 6.46 W) Pilot Nominal beam Ultimate beam Particles per bunch 5x109 1.15x1011 1.7x1011 Number of bunches 1 2808 Circulating current (DC) in A 9 x 10-6 0.582 0.860 Bunch peak current @ injection in A 0.9 19.6 29.0 Bunch peak current @ collision in A 1.3 29.2 43.1 Peak Voltage from PU @ inj. in V 2.8 63.4 93.6 Peak Voltage from PU @ coll. in V 4.1 94.3 139.4 Intensity range to be covered: factor 50 Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Realistic simulation model is being developed to include actual characteristics of hardware Cable (650 m for Q9) BPM BP IQ demod RF=400.8 MHz Bunch synchronous sampling @ 40 MHz and digitization with 16 bit normalization (D/S) after calculation of sqrt(I*I+Q*Q) in digital part G. Kotzian Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Simulations using simulink/matlab Simulation results, bunch to bunch oscillations Simulation model enables us to study imperfections of hardware and also propagate noise or interferences through system and evaluate their impact bunch synchronous sampling with a 40 MHz clock rate ongoing study G. Kotzian Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Simulations using simulink/matlab Some simulation results, single bunch Signal from pick-up Base band signal S after LP Response of BP filter to D signal from pick-up Base band D signal after LP G. Kotzian Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Numerical simulations (Ohmi) on blow-up by damper noise Ohmi calculated that (numerical simulations, LHC Project Report 1048): 10 turns damping with a monitor resolution of 0.6 % of s (i.e. at 7 TeV 1.8 mm at our pick-ups) gives a luminosity life time of 1 day with a transverse synchrotron radiation damping time for the emittance of 26 hours -> no blow-up at all Hence, we can use damper if we have a mm resolution Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Available signal from pick-ups compared to thermal noise Assume bunches oscillate with 1 mm rms (bunch-to-bunch) Power available from pick-up @400 MHz (+/- 20 MHz): 433 pW (nominal beam) to be checked with final measurements of all cables etc. Thermal noise at 290 K: kBT = 4x10-21 W/Hz; in 40 MHz BW: 0.16 pW Digitization with effective 14 bit: 16384 discrete levels, assume 1 mm -> 4 steps then 14 bit are sufficient to cover +/- 2 mm Large margin with respect to thermal noise: To use this margin we should limit orbit variations at the pick-ups to less than +/- 2 mm (Q7 and Q9 left and right of IP4) Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008

Conclusions If oscillations can be intercepted at the 1 mm level noise is not expected to limit the achievable damping times Limit on damping time will come from the available kick strength at 7 TeV and the size of the largest oscillation that one wants to damp, take tune kicker, with 0.5 s kicks -> 23 turns limit on damping time Normal operating range of FB at 7 TeV should be at gains corresponding to 20-40 turns damping times Good control of orbit in damper pick-ups essential for high gain and low noise operation of damper systems Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008