1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. BPMC - Coupler type pick-ups
8 Dedicated Pick-ups 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

10. 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 = MHz
Peak voltage (beam centered) for ultimate collision: ~140 V -> very large
Peak sensitivity: W / mm => 8.1 V/mm peak in time domain after ideal hybrid
Wolfgang Hofle AB/RF
LHC Coll WG - April 18, 2008

11. 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) ^
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 injection in A
0.9
19.6
29.0
Bunch peak collision in A
1.3
29.2
43.1
Peak Voltage from inj. in V
2.8
63.4
93.6
Peak Voltage from 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

12. 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 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

13. 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

14. 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

15. 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

16. Available signal from pick-ups compared to thermal noise
Assume bunches oscillate with 1 mm rms (bunch-to-bunch)
Power available from 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: 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

17. 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 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